Essays in Financial Economics
Lira Rocha da Mota Mertens
Submitted in partial fulfillment of therequirements for the degree of
Doctor of Philosophyunder the Executive Committee
of the Graduate School of Arts and Sciences
COLUMBIA UNIVERSITY
2021
© 2021
Lira Rocha da Mota Mertens
All Rights Reserved
Abstract
Essays in Financial Economics
Lira Rocha da Mota Mertens
This dissertation studies topics in financial economics. In the first chapter, The Corporate
Supply of (Quasi) Safe Assets, I examine whether the demand for safe assets affects nonfinancial
corporations in the US. Investors value safety services in financial assets, such as the ability to serve
as a store of value, to serve as collateral, or to meet mandatory capital and liquidity requirements.
I present a model in which investors value safety services not only in traditional safe assets such
as US Treasuries, but also in corporate debt. Shareholders thus maximize the value of the firm
by complementing standard business operations with safe asset creation. Based on this theoretical
framework, I use the CDS-bond basis to derive a measurement of the safety premium of corporate
bonds. I document substantial cross sectional variation in the safety premium of corporate bonds,
which allows me to test the model’s predictions. I show that a high safety premium leads to
a marked increase in debt issuance by relatively safer firms. These debt proceeds have a small
impact on real investment and are largely used instead for equity payouts. This mechanism can
explain why, in the aftermath of the financial crisis, non-financial investment grade companies
significantly increased their debt issuance and equity payout while investment remained weak.
The second chapter, The Cross-Section of Risk and Return, focuses on a common practice
in the finance literature which is to create characteristic portfolios by sorting on characteristics
associated with average returns. We show that the resultant portfolios are likely to capture not only
the priced risk associated with the characteristic but also unpriced risk. We develop a procedure
to remove this unpriced risk using covariance information estimated from past returns. We apply
our methodology to the five Fama-French characteristic portfolios. The squared Sharpe ratio of the
optimal combination of the resultant characteristic efficient portfolios is 2.13, compared with 1.17
for the original characteristic portfolios.
In the third chapter, Should Information be Sold Separately? Evidence from MiFID II, we ex-
amine whether selling information separately improves its production. We use a recent regulation
in Europe (MiFID II) that unbundles research from transactions to investigate this question. We
show that unbundling causes fewer research analysts to cover a firm. This decrease does not come
from small- or mid-cap firms but is concentrated in large firms. Contrary to conventional wis-
dom, the reduction in the coverage quantity is accompanied by an increase in the coverage quality.
Further analyses suggest that the enhancement of analyst competition could drive the results: inac-
curate analysts drop out (extensive margin) and analysts who stay produce better-quality research
(intensive margin). Our findings suggest that selling information separately improves information
quality at the cost of reducing information quantity.
Table of Contents
List of Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vii
List of Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . x
Acknowledgments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xii
Chapter 1: The Corporate Supply of (Quasi) Safe Assets . . . . . . . . . . . . . . . . . . . 1
1.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 Related Literature . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
1.3 Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
1.3.1 Setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
1.3.2 Model Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
1.3.3 Comparative Statics and Empirical Predictions . . . . . . . . . . . . . . . 15
1.3.4 Bringing the Model to the Data . . . . . . . . . . . . . . . . . . . . . . . . 18
1.4 Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
1.5 Measuring the Corporate Safety Premium . . . . . . . . . . . . . . . . . . . . . . 21
1.5.1 Empirical construction of the CDS-bond basis . . . . . . . . . . . . . . . . 23
1.5.2 The Validity of Cross-Basis as the Relative Safety Premium Measure . . . . 25
1.6 Firms’ Response to Safety Premium . . . . . . . . . . . . . . . . . . . . . . . . . 27
1.6.1 Impact of Safety Premium on Net Debt Issuance . . . . . . . . . . . . . . 27
i
1.6.2 Impact of Safety Premium on Firms’ Real Decisions . . . . . . . . . . . . 32
1.6.3 Heterogeneity across Firms’ Characteristics . . . . . . . . . . . . . . . . . 34
1.6.4 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
1.7 Robustness and Additional Tests . . . . . . . . . . . . . . . . . . . . . . . . . . . 36
1.7.1 Is the Cross-basis Really Capturing Variation in the Safety Premium? . . . 36
1.7.2 Delayed Reactions: Effect of Safety Premium in Different Time Horizons . 39
1.7.3 Limits to Arbitrage and the Demand for Safety . . . . . . . . . . . . . . . 40
1.8 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41
1.9 Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51
Chapter 2: The Cross-Section of Risk and Return . . . . . . . . . . . . . . . . . . . . . . . 63
2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63
2.2 Theory and examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69
2.2.1 A simple example . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70
2.2.2 The general case . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78
2.3 Empirical results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84
2.3.1 Hedge portfolio construction . . . . . . . . . . . . . . . . . . . . . . . . . 84
2.3.2 Description of the sorted portfolios . . . . . . . . . . . . . . . . . . . . . . 88
2.3.3 Pricing results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91
2.3.4 Industry-neutral characteristic portfolios . . . . . . . . . . . . . . . . . . . 95
2.4 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97
Chapter 3: Should Information be Sold Separately? Evidence from MiFID II . . . . . . . . 116
3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 116
ii
3.2 Regulation background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 122
3.3 Hypotheses development . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125
3.4 Empirical design and data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 128
3.4.1 Empirical design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 128
3.4.2 Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 129
3.5 Investigating the impact of unbundling: firm level analyses . . . . . . . . . . . . . 132
3.5.1 The impact of unbundling on analyst coverage . . . . . . . . . . . . . . . . 134
3.5.2 The impact of unbundling on analysts forecast quality . . . . . . . . . . . . 135
3.6 Investigating the channel: analyst level analyses . . . . . . . . . . . . . . . . . . . 137
3.6.1 Intensive margin . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 137
3.6.2 Extensive margin . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 140
3.7 Robustness check and extensions . . . . . . . . . . . . . . . . . . . . . . . . . . . 145
3.7.1 Firm’s brokerage house coverage . . . . . . . . . . . . . . . . . . . . . . . 145
3.7.2 Other quality measures . . . . . . . . . . . . . . . . . . . . . . . . . . . . 146
3.7.3 Alternatives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 150
3.7.4 Brokerage house level employment . . . . . . . . . . . . . . . . . . . . . . 152
3.7.5 Capital market effects . . . . . . . . . . . . . . . . . . . . . . . . . . . . 154
3.8 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 156
3.9 Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 157
3.10 Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 162
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 187
Appendix A: Chapter 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 188
iii
A.1 Data Appendix . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 188
A.1.1 Variable definitions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 188
A.1.2 Measuring SG&A . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 188
A.1.3 FISD Cleaning . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 189
A.1.4 Merge FISD to Compustat . . . . . . . . . . . . . . . . . . . . . . . . . . 190
A.2 Measures of Aggregate Safety Premium . . . . . . . . . . . . . . . . . . . . . . . 191
A.3 Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 192
A.3.1 Price of the Bond . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 192
A.3.2 Optimization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 195
A.4 Infinite Horizon Dynamic Model . . . . . . . . . . . . . . . . . . . . . . . . . . . 195
A.4.1 Simulation Strategy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 195
A.4.2 State Space Discretization . . . . . . . . . . . . . . . . . . . . . . . . . . 196
A.4.3 Main Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 197
A.5 Additional Empirical Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 198
A.5.1 Cash Flow Identity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 199
A.6 CDS-bond Basis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 201
A.7 Alternative Model with Limits to Arbitrage . . . . . . . . . . . . . . . . . . . . . 203
A.7.1 Explicit Model of Arbitrageurs . . . . . . . . . . . . . . . . . . . . . . . . 203
A.7.2 An Example of a Negative CDS-bond Trade . . . . . . . . . . . . . . . . . 205
Appendix B: Chapter 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 209
B.1 Notation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 209
B.2 Proofs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 210
iv
B.2.1 The characteristic efficient portfolios . . . . . . . . . . . . . . . . . . . . . 210
B.2.2 Proof of Proposition 2.1 . . . . . . . . . . . . . . . . . . . . . . . . . . . 212
B.2.3 Proof of Proposition 2.2 . . . . . . . . . . . . . . . . . . . . . . . . . . . 212
B.2.4 The optimal hedge ratio . . . . . . . . . . . . . . . . . . . . . . . . . . . . 214
B.3 Empirical details . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 215
B.3.1 Empirical definition of main variables . . . . . . . . . . . . . . . . . . . . 215
B.3.2 Loading estimation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 217
B.3.3 Dealing with missing prices . . . . . . . . . . . . . . . . . . . . . . . . . 217
B.4 Supplemental results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 218
B.4.1 Portfolio bin population . . . . . . . . . . . . . . . . . . . . . . . . . . . . 218
B.4.2 High power vs. low power . . . . . . . . . . . . . . . . . . . . . . . . . . 219
Appendix C: Chapter 3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 224
C.1 Data construction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 224
C.1.1 Firm level observations . . . . . . . . . . . . . . . . . . . . . . . . . . . . 224
C.1.2 Choice of data frequency . . . . . . . . . . . . . . . . . . . . . . . . . . . 225
C.1.3 Variable definitions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 226
C.2 Additional figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 228
C.3 Other summary statistics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 232
C.4 Additional regression results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 237
C.4.1 Dynamic coefficients point estimates . . . . . . . . . . . . . . . . . . . . . 237
C.4.2 Additional results for firm level coverage . . . . . . . . . . . . . . . . . . 239
C.4.3 Additional results for analyst informativeness . . . . . . . . . . . . . . . . 242
v
C.5 Propensity score matching . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 243
vi
List of Tables
1.1 Calibration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51
1.2 Number of Bonds and Firms with Valid CDS-Bond Basis . . . . . . . . . . . . . . 52
1.3 Firm-Level Summary Statistics . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53
1.4 CDS-bond Basis Summary Statistics . . . . . . . . . . . . . . . . . . . . . . . . . 54
1.5 CDS-Bond cross section Analyses . . . . . . . . . . . . . . . . . . . . . . . . . . 55
1.6 Treasury Safety Premium Proxies . . . . . . . . . . . . . . . . . . . . . . . . . . . 56
1.7 CDS-Bond Time Series Analyses . . . . . . . . . . . . . . . . . . . . . . . . . . . 57
1.8 Impact of Safety Premium on Net Debt Issuance . . . . . . . . . . . . . . . . . . . 58
1.9 Impact of Safety Premium on Firms’ Decisions . . . . . . . . . . . . . . . . . . . 59
1.10 Heterogeneous Impact of Cross-Basis on Firms’ Decisions . . . . . . . . . . . . . 60
2.1 Low book-to-market stocks in the Money industry as of June 2008 . . . . . . . . . 105
2.2 Average monthly excess returns for the sorted portfolios . . . . . . . . . . . . . . . 106
2.3 Alphas and loadings . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107
2.4 Results of time-series regressions of hedge-portfolios . . . . . . . . . . . . . . . . 112
2.5 Sharpe Ratio improvement. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113
2.6 Ex-post optimal Markowitz weights . . . . . . . . . . . . . . . . . . . . . . . . . 114
2.7 Spanning tests for HML . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 114
vii
2.8 Correlations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115
3.1 Firm Level Summary Statistics (Sample for Coverage Quantity) . . . . . . . . . . 162
3.2 Firm Level Summary Statistics (Sample for Coverage Quality) . . . . . . . . . . . 163
3.3 Analyst Level Summary Statistics (Sample for Intensive Margin) . . . . . . . . . . 164
3.4 Analyst Level Summary Statistics (Sample for Extensive Margin) . . . . . . . . . . 165
3.5 One Difference (Pre and Post) . . . . . . . . . . . . . . . . . . . . . . . . . . . . 166
3.6 Firm Level Outcomes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 167
3.7 Analyst Level Outcomes (Intensive Margin) . . . . . . . . . . . . . . . . . . . . . 168
3.8 Analyst Level Outcomes (Extensive Margin). Probability of Stop or Dropping Outafter Unbundling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 169
3.9 Analyst Level Outcomes (Extensive Margin). Probability of Stop or Dropping OutBefore and After Unbundling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 170
3.10 Placebo Test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 171
3.11 Firms’ Brokerage House Coverage . . . . . . . . . . . . . . . . . . . . . . . . . . 172
3.12 Other Measures of Quality . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 173
3.13 Abnormal Return and Analyst Informativeness . . . . . . . . . . . . . . . . . . . . 174
3.14 Learning Effect (Lagged Forecast Error as Control) . . . . . . . . . . . . . . . . . 175
3.15 Brokerage House Employment . . . . . . . . . . . . . . . . . . . . . . . . . . . . 176
3.16 Capital Market Effects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 177
A.1 Impact of Cross-basis on Firm’s Decisions Conditional on Positive Debt IssuanceIncluding Ratings FE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 198
A.2 Impact of Cross-basis on Firm’s Decisions Conditional on Positive Debt IssuanceIncluding Ratings FE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 199
A.3 Negative CDS-bond Basis Cash Flow Diagram . . . . . . . . . . . . . . . . . . . . 205
viii
A.4 A Negative CDS-bond Basis Example . . . . . . . . . . . . . . . . . . . . . . . . 207
A.5 Implicit Funding Cost . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 208
B.1 Number of firms in each portfolio . . . . . . . . . . . . . . . . . . . . . . . . . . . 218
B.2 Results of time-series regressions on characteristic-balanced hedge-portfolios . . . 223
C.1 Summary Statistics (Country Information) . . . . . . . . . . . . . . . . . . . . . . 232
C.2 Summary Statistics (Small vs. Large in Sample for Quantity) . . . . . . . . . . . . 233
C.3 Summary Statistics (Small vs. Large in Sample for Quality) . . . . . . . . . . . . . 235
C.4 Firm Level Outcomes (Dynamic Coefficients) . . . . . . . . . . . . . . . . . . . . 237
C.5 Intensive Margin (Dynamic Coefficients) . . . . . . . . . . . . . . . . . . . . . . . 238
C.6 Firm Level Coverage (Sample for Coverage Quality). . . . . . . . . . . . . . . . . 239
C.7 Firm Level Coverage (Results in logs). . . . . . . . . . . . . . . . . . . . . . . . . 240
C.8 Firm Level Coverage (EU Small vs. US Small and EU Large vs. US Large) . . . . 241
C.9 Analyst Informativeness (Small vs. Large). . . . . . . . . . . . . . . . . . . . . . . 242
C.10 Covariates Balance Table. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 246
C.11 Firm Level Outcomes (Propensity Score Matching). . . . . . . . . . . . . . . . . . 247
ix
List of Figures
1.1 Corporate Safety Premium and Bond Price . . . . . . . . . . . . . . . . . . . . . . 44
1.2 Firm’s Total Value as a Function of Debt Issuance . . . . . . . . . . . . . . . . . . 45
1.3 Response to Perceived Safety . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46
1.4 Response to Aggregate Safety Premium . . . . . . . . . . . . . . . . . . . . . . . 47
1.5 Interaction Effects of Bond Issuance Response to Safety Premium . . . . . . . . . 48
1.6 Heterogeneous Effects on Bond Issuance Due to Initial Net Worth . . . . . . . . . 48
1.7 The CDS-bond Basis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49
1.8 US Treasury Safety Premium. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49
1.9 Effect of Cross-Basis on Firms’ Decisions for Different Time Horizons. . . . . . . 50
2.1 Six assets in the space of loadings on priced and unpriced factors. . . . . . . . . . . 72
2.2 Rolling regression R2s – HML returns on industry returns . . . . . . . . . . . . . . 99
2.3 HML loadings on industry-portfolios . . . . . . . . . . . . . . . . . . . . . . . . . 100
2.4 Volatility of the money industry-portfolios . . . . . . . . . . . . . . . . . . . . . . 101
2.5 Rolling regression R2s – HML returns on Money industry returns . . . . . . . . . . 101
2.6 Ex-post HML/RMW/CMA loadings vs. characteristics . . . . . . . . . . . . . . . 102
2.7 Ex-post MktRF loadings vs. characteristics . . . . . . . . . . . . . . . . . . . . . 103
2.8 Ex-post SMB loadings vs. characteristics. . . . . . . . . . . . . . . . . . . . . . . 104
x
3.1 Illustration of Bundling and Unbundling . . . . . . . . . . . . . . . . . . . . . . . 157
3.2 Average Analyst Coverage Over Time (EU vs. US) . . . . . . . . . . . . . . . . . 158
3.3 Average Analyst Coverage Over Time between Small Firms and Large Firms inthe EU . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 158
3.4 Empirical Cumulative Distribution of Forecast Error at the Firm Level . . . . . . . 159
3.5 Firm Level Outcomes (Dynamic Coefficients) . . . . . . . . . . . . . . . . . . . . 160
3.6 Analyst Level Forecast Error (Dynamic Coefficients) . . . . . . . . . . . . . . . . 161
A.1 Successful Mergers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 190
A.2 Firm’s Total Value as Function of Capital and Debt Issuance . . . . . . . . . . . . 195
A.3 Issuance Response to Perceived Safety . . . . . . . . . . . . . . . . . . . . . . . . 197
B.1 Ex-post loading vs. characteristic . . . . . . . . . . . . . . . . . . . . . . . . . . . 222
C.1 Geographic Composition of Stocks in Analyst Portfolio. . . . . . . . . . . . . . . . 228
C.2 Average Analyst Coverage (EU vs. US) . . . . . . . . . . . . . . . . . . . . . . . 229
C.3 Firm Level Forecast Error Distribution . . . . . . . . . . . . . . . . . . . . . . . . 230
C.4 Average Number of Analysts per Brokerage House Over Time in the EU, Small vs.Large . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 231
C.5 Distributions of Propensity Scores after Matching. . . . . . . . . . . . . . . . . . . 245
xi
Acknowledgements
I am grateful to my advisers Kent Daniel, Olivier Darmouni, Tano Santos, and Jesse Schreger.
They provided me with safe ground to discuss ideas, guided me through the process of shaping
raw ideas into developed papers, and always offered me support when needed. Kent and Tano
made me believe in my potential as a researcher. They were my mentors and source of inspiration
throughout the PhD. Tano always encouraged me to be ambitious in my research endeavors and
gave me the support to do so. He followed my steps from the idea generation to the writing of
this dissertation, always with wit and wisdom, making me laugh even in the darkest hour. Kent,
always nice and sharp, pushed my research to new heights. Olivier was always present, giving
timely and detailed feedback. I would never have survived the Job Market had he not listened to
my presentation countless times and encouraged me to do better. Jesse always reinvigorated my
energies by being optimistic about my progress, while also provided precise and wise comments
that helped me write a better dissertation.
I want to thank my coauthors, Yifeng Guo and Simon Rottke. Cooperating with them taught
me not only about finance but also about friendship and partnership. Simon had endless patience
with my ups and downs with research, and no matter how many times he could have been mad, he
always found a way to say something to cheer us up. Yifeng was my companion from homeworks
in the first year to dissertation in the later years. I thank Yifeng for making the journey easier and
more joyful.
I am also thankful to other faculty members in Columbia for their advice and help. I am
xii
particularly grateful to Jose Scheinkman, who opened the Columbia doors when I came as a visitor
from Brazil. This was the first step of the journey that changed the course of my life. I am
also thankful to my friends, especially Amanda dos Santos, Polina Dovman, Kerry Siani, Melina
Papoutsi, Cristina Tessari, and Tuomas Tomunen. I was lucky to have them by my side to share
coffees, gossips, runs, and finance ideas.
I am deeply thankful to my husband, Luca Mertens. He was the first to support my decision
to start the PhD at Columbia. Luca was my best company, holding my hand and working with me
when the moment was difficult and celebrating when the victories arrived. I am also indebted to my
family. To my parents, Luzanira Mota and Jesus Mota, for being my inspiration of perseverance
and always making clear they were proud of my achievements. To my brother, Tomaz Mota, for
always having a positive word to say. And to my parents-in-law, Bertilla Diquigiovanni and Daniel
Mertens, for moving mountains to help in whatever was needed.
xiii
To Luca, per aspera ad astra.
xiv
Chapter 1
The Corporate Supply of (Quasi) Safe Assets 1
1.1 Introduction
There is a particular class of financial assets that can serve as a store of value, be used as
collateral, and be used to meet mandatory capital and liquidity requirements. The stability and
safety of their cash flows are what makes these assets ideal vehicles for the provision of these
safety services, and as a result, some refer to these securities as safe assets. When these assets are
in limited supply, they might command a safety premium, i.e., a value investors are willing to pay
above the discounted cash flows because of the aforementioned services they provide. Some have
argued that, since the global financial crisis, the demand for safety services has increased above
the supply of assets that can meet this demand, leading to an increase in the safety premium.2 The
literature has traditionally relied on a pragmatic and narrow definition of safe assets, which include
1This chapter is based on Mota (2021). I am grateful to my advisors Kent Daniel, Olivier Darmouni, Tano San-tos, and Jesse Schreger for their invaluable guidance and continuous support, and to Simona Abis, Patrick Bolton,Douglas Diamond, Jason Donaldson, Amanda Dos Santos, Polina Dovman, Philip Dybvig, Yifeng Guo, HarrisonHong, Jeremias Huber, Philip Kalikman, Yiming Ma, Harry Mamaysky, Daniel Mertens, Luca Mertens, Vrinda Mittal,Melina Papoutsi, Giorgia Piacentino, Simon Rottke, Jose Scheinkman, Kerry Siani, Suresh Sundaresan, Cristina Tes-sari, Tuomas Tomunen, Stijn Van Nieuwerburgh, Neng Wang, seminar participants at Macro and Finance at ColumbiaBusiness School and the Finance Colloquium at Columbia University Economics Department, and conference partic-ipants at the Diamond-Dybvig 36th Anniversary Conference, the 2020 AFA PhD Poster Session, and the Macro Fi-nance Research Program of the Becker Friedman Institute Summer Session for their helpful discussions and sugges-tions. I acknowledge the support of the Chazen Institute for Global Business at Columbia Business School. I welcomecomments, including references to related papers that I have inadvertently overlooked. All errors are my own.
2See inter alia Krishnamurthy and Vissing-Jørgensen (2012a), Gorton et al. (2012), Caballero et al. (2017),Caballero and Farhi (2018).
1
liabilities issued by developed countries or by the financial sector.3 In this paper, I argue that
non-financial corporations can act as a class of safety service suppliers, and I study their supply
responses to changes in the safety premium.
The starting point of this paper is the observation that safety is not a binary characteristic
of an asset. Different assets can provide different amounts of safety services, depending on the
underlying characteristics of their cash flows. I first show that US corporate bonds have earned a
safety premium in recent years, with safer firms earning a higher premium. Corporate bonds are
not entirely insulated from credit risk, but they can still function as a store of value, as collateral,
or as regulatory capital, thereby providing an imperfect substitute for traditional safe securities.
Thus, in the presence of a positive safety premium, corporate managers may create shareholder
value by issuing debt. I show that firms do indeed respond to an increase in their relative safety
premia by issuing more debt. In my sample, rather than using the new funds to invest, they pay out
the borrowed money to shareholders. The demand for safe assets therefore has direct implications
for corporate borrowing behavior and capital structure.
I begin by presenting a model that fleshes out the safety-creation mechanism in non-financial
firms. The model fulfills two purposes. First, it defines the safety premium component in corpo-
rate debt prices. The safety premium varies across both time and firms, and maps to an empirically
observable measure that I call the cross-basis. Second, it generates predictions about firms’ re-
sponses to shocks in the safety premium. I then use data on US non-financial corporations to test
the model’s predictions.
Following Krishnamurthy and Vissing-Jørgensen (2012a), I take a reduced-form approach and
model the demand for safety services as a primitive. The model innovates in assuming that all debt
securities can potentially provide some safety services.4 In equilibrium, two securities with the
same cash flows can have different prices simply because they provide different safety services.
3See inter alia Caballero et al. (2016), Gorton (2017), Caballero et al. (2017), Caballero and Farhi (2018), Farhiand Maggiori (2018), or more broadly, works that study the non-pecuniary value of US Treasuries or money-likesecurities such as Sunderam (2015), Nagel (2016), Du et al. (2018), Binsbergen et al. (2019), He et al. (2019), Jianget al. (2020), Diamond (2020).
4For the micro-foundations for investor’s demand for securities with stable cash-flows, such as debt, the readershould refer to Gorton and Pennacchi (1990), Dang et al. (2015), Dang et al. (2019).
2
The difference in prices between two such assets measures the relative safety premium between
them. This conceptual innovation allows me to use cross sectional data to bypass the traditional
difficulty faced by the literature of estimating the aggregate safety premium, the market price of
one unit of safety services. As a result, I can use the cross section of bond prices to identify the
effect of fluctuations of the relative safety premium on corporate debt issuance, as well as on other
firm policies such as capital and intangible investment and payout policy.
In my model, the firm-specific safety premium depends on both the aggregate safety premium,
which I assume to be exogenous, and on firms’ decisions, which are endogenous. In particular,
as firms issue more debt, the firm-specific safety premium goes down. Three main empirical
predictions emerge from the model. First, firms respond to an increase in the safety premium
by issuing more debt. Second, for financially constrained firms, an increase in the relative safety
premium relaxes this constraint and leads to more investment. Third, for financially unconstrained
firms, variation in debt issuance due to fluctuations in the safety premium mostly results in equity
payout.
To test the model predictions, the first empirical challenge is to measure the safety premium
of corporate bonds. The safety premium of a particular bond is the difference in the prices of the
bond and of a benchmark asset with the same cash flows but no safety services. This benchmark
is not readily available. I overcome this issue by constructing, for each bond in the sample, a
synthetic asset, which is a portfolio that combines the corporate bond and the maturity-matched
credit default swap (CDS). I call this synthetic asset the hedged bond. Under the assumption that
the CDS perfectly hedges the credit risk, for all bonds the hedged bond’s cash flows are the same.
Then, by comparing the yields of the hedged bonds, I am able to quantify the relative safety premia
among those assets.
Specifically, I introduce the cross-basis as a measure of relative safety premium in corporate
bonds. Theoretically, the cross-basis measures the safety premium of a specific firm relative to
the average firm. Empirically, I construct the cross-basis by first calculating the CDS-bond ba-
sis for each bond, which is the difference in yields between the hedged bond and the maturity-
3
and coupon-matched US Treasury, and then define the cross-basis as the firm-specific CDS-bond
basis minus the basis index, which is the face-value weighted average CDS-bond basis in the sam-
ple. There is a direct connection between the investors’ Euler equation from the model and the
cross-basis, which yields three predictions. First, in the cross section, cross-basis is monotonic
in perceived safety, i.e., the amount of safety services an asset provides. Second, one factor, the
aggregate safety premium (normalized to be the US Treasury safety premium), fully explains the
time series variation of cross-basis. Third, loadings on the aggregate safety premium are mono-
tonic in perceived safety. I find strong support for all three predictions in the data, which validates
the connection between the cross-basis and firm-specific safety premium.
Equipped with an empirical measurement of the safety premium in corporate bonds, I test how
firms react to variations in the safety premium. I find that in the cross section, firms with higher
cross-basis in a given quarter issue more debt in the following quarter. A one percentage point
increase in the cross-basis forecasts an increase of net debt issuance of 10 basis points as a share of
total assets, which translates to an increase of $27.4 million in debt issuance for the average firm or
a 31% increase relative to their quarterly average debt issuance. On the other hand, the cross-basis
has a small impact on real investment, measured by capital investment, intangible investment, or
acquisitions. Instead, the safety premium strongly forecasts equity payouts in the form of dividends
and equity repurchases. A one percentage point increase in the cross-basis forecasts a 8 basis points
increase in firms’ net payout as a share of total assets, or in dollars, $23.2 million, a number very
close to the effect of the cross-basis on net debt issuance. In light of the corporate bond supply
model I introduced, this is evidence that companies with relatively high safety premium are not
financially constrained, consequently almost all debt issued in response to the safety premium is
converted into equity payouts.
I conduct a battery of additional tests to confirm these findings. A possible worry with the
cross-basis as a measure of the relative safety premium is that it may be capturing frictions not
related to safety, such as counterparty risk, mis-measurement due to bond illiquidity, restructuring
uncertainty, or mismatch in the payoff structure of bonds. However, one important feature of the
4
cross-basis is that any friction that affects all bonds or CDS equally does not affect the cross-
basis. Moreover, only frictions that are systematically correlated with firms’ fundamentals are of
concern when assessing the impact of the cross-basis on firms’ choices, such as debt issuance. I
show that none of these confounders are large enough to explain the cross sectional variation of
the cross-basis5 or to be of concern regarding the interpretation of the results.
The results presented here give a new perspective on the impact of the demand for safety on
the overall economy. By using a narrow definition of safe assets, Caballero et al. (2017) predicted
that the high demand for safety would decrease risk-free interest rates, but would have the opposite
effect on risk premia. This is at odds with the observed historical low credit-spreads in corporate
bonds in recent years, since corporate bonds are intrinsically not risk-free. The fact that the safety
premium can affect yields of imperfect substitutes to traditional safe assets is one likely explanation
for the recent low yields, and it opens the possibility for a broader impact of the demand for safety,
one that affects firms’ cost of capital, capital structure, and business operation.
Most importantly, my paper sheds light on the determinants of the supply of safety services.
Historically, the government and the financial sector have been the main producers of safe assets.
The common feature of the public sector is that their debt issuance does not seem to respond
to demand pressures, even if this could be associated with economic gains (Jiang et al. (2020)).
Furthermore, given the high public indebtedness and the sluggish growth of most developed coun-
tries, many have argued that the public sector has exhausted its ability to expand the production of
safe assets (Caballero et al. (2017)). Likewise, in the aftermath of the financial crisis, the finan-
cial sector’s ability to engineer safe substitutes for Treasuries has been diminished by regulation
and constrained capital. In a landscape of limited alternative safe assets, non-financial firms with
ratings comparable to a sovereign are viable alternatives.
The findings in this paper also shed light on recent macroeconomic trends. In the aftermath of
the financial crisis, the aggregate amount outstanding of non-financial corporate bonds almost dou-
5For instance Arora et al. (2012) show that counterparty risk in CDS contracts is “vanishingly small," and Baiand Collin-Dufresne (2019) show that only bonds’ collateral value is persistently important in explaining the crosssectional variation of the CDS-bond basis.
5
bled, while aggregate investment remained weak (Gutiérrez and Philippon (2017) and Crouzet and
Eberly (2019)). Although investment grade (IG)6 firms are the largest bond issuers, their average
investment in capex and R&D together represents only 60% of their total net profits, suggesting
that all investment in the last ten years could have been financed with retained earnings alone. An-
other important empirical observation is that payouts have been largely financed by debt issuance
(Farre-Mensa et al. (2018)). In the last ten years, 90% of IG firms that issued debt in a given quarter
also engaged in positive distribution to shareholders in that same quarter. For every dollar issued in
IG bonds, 0.80 cents were paid back to shareholders within the same quarter by the median firm.7
In summary, evidence suggests that IG firms are changing their capital structure by issuing debt to
repurchase their own equity and pay dividends, but not necessarily to invest more. The theory of
corporate safety creation presented in this paper provides a coherent explanation for these facts.
1.2 Related Literature
This paper relates to and draws from several strands of literature. I build on the safe-assets
literature that shows that investors value safe assets with stable cash-flows and that there is a
shortage in supply of asset with this characteristic.8 The contribution of my paper is to study a
new class of safe-asset supplier, non-financial corporations, and to show that the response to the
safety premium is not concentrated on the safest firms in the US, as discussed in Krishnamurthy
and Vissing-Jørgensen (2012b), but rather is pervasive across the corporate sector.
Much like banks, I show that non-financial corporations respond to the discount in their lia-
bilities by issuing debt, even if this tends to be a purely financial operation unrelated to the firms’
business operations. The elasticity of the supply of corporate bonds to changes in safety premium
is akin to the creation of money-like short-term claims by the financial sector in response to shocks
in the safety and liquidity premia (see, e.g., Sunderam (2015), Nagel (2016), Krishnamurthy and
6Bonds rated BBB or more.7All summary statistics were calculated using the sample of Compustat firms described in Section 1.4.8A non-exhaustive list of related paper is Gorton et al. (2012), Krishnamurthy and Vissing-Jørgensen (2012a),
Caballero et al. (2016), Caballero et al. (2017), Caballero and Farhi (2018), Lenel (2020), Diamond (2020).
6
Vissing-Jorgensen (2015) and Kacperczyk et al. (2020)). The difference is that, instead of pro-
viding substitutes to money claims, highly rated corporate bonds can be good substitutes for the
safety properties of long-term Treasuries. Hence, my paper shows evidence that the private sector
elasticity of supply of safe assets is not concentrated in highly liquid short-term liabilities.
This paper relates to the literature that investigates the interconnection between Treasury bond
issuance and corporate decisions. I show that corporate bonds are imperfect substitutes to Treasury
bonds not only with respect to maturity, like in Greenwood et al. (2010) and Badoer and James
(2016), but also in providing safety services. Furthermore, an innovation with respect to this
literature is to measure the firm-level safety premium, which allows me to find variation in firms’
behavior that is not captured by the variation in the supply of US Treasury bonds, as is explored
in the aforementioned papers and in Graham et al. (2014), Liu et al. (2020) and Giambona et al.
(2020). This also allows for leveraging the cross section of firms to alleviate endogeneity concerns
related to the time series of the supply of Treasury bonds.
Kacperczyk et al. (2020) also look at the cross section to identify how fluctuations in the safety
premium affect issuance. Their focus is on short-term liabilities, certificate of deposits issued
by commercial banks and commercial paper issued by non-financial firms. They find that the
financial sector issues certificate of deposits in response to an increase in the safety premium, but
that non-financial corporations do not issue more commercial paper in response to this increase.
By focusing on longer maturity debt,9 I find that non-financial corporations actively respond to
an increase in the own safety premium by issuing more debt. I interpret these results as evidence
that while banks and other intermediaries are probably the marginal producers of short-term safe
assets, non-financial corporates have a role in producing safe assets in longer maturities.
Also related to this paper are the works by Lenel (2020) and Diamond (2020) who consider the
collateral value of corporate bonds for financial intermediaries and its interaction with the demand
for safe assets. Lenel (2020) studies how the variation in the supply of US Treasury bonds affects
asset prices and lending volumes in the financial sector, and Diamond (2020) presents a theory
9The empirical part of this paper looks at non-financial corporate debt with 1-year or more time to maturity.
7
on how the financial sector is organized to engineer safe assets backed by bonds, and how this
mechanism affects firms’ capital structure. I contribute to these works by using market prices to
construct a firm-level measure of the corporate safety premium, and provide empirical evidence
that variation in the safety premium, which include compensation to the collateral value corporate
debt, has a direct impact on firms’ cost of borrowing and therefore leverage decisions.
Finally, this paper also connects to the literature on the market timing of firms’ capital structure.
One explanation for the existence of market timing is information asymmetry, i.e., managers have
better information than the market about firm fundamentals (Baker and Wurgler (2002), Baker
et al. (2003), Warusawitharana and Whited (2016) and Ma (2019)). Another reason for corporate
market timing is precautionary savings, firms raise external finance when it is cheap, guaranteeing
liquidity for periods when external finance is expensive (Bolton et al. (2013) and Eisfeldt and Muir
(2016)). My model does not rely on information asymmetry, as the safety premium is observable to
all agents. Furthermore, I do not find that fluctuations in the relative safety premium are associated
with corporate savings, but instead, they are associated with equity payouts. Thus, my paper
presents a new channel explaining why we might observe corporate debt issuance when corporate
debt yields are depressed. That is, if the safety premium is positive, some firms are able to create
value to shareholders by issuing debt because in doing so, they increase the amount of safety
services in the economy.
1.3 Model
In this section, I present a model of safety creation by non-financial corporations. Section
1.3.1 presents the model, and the results are found in Section 1.3.2. Section 1.3.3 summarizes the
testable predictions derived from the model, and section 1.3.4 discusses how to empirically test
them. The empirical tests are performed in Section 1.6.
8
1.3.1 Setup
There are three sets of agents in the model: representative investors, a set of heterogeneous
firms, and an exogenous supplier of safe assets, like US Treasury bonds.
Investors
The key innovation of this paper is to allow for the possibility that different assets provide
different degrees of safety services. More formally, I normalize to one the amount of safety services
provided by one dollar of face value of US Treasuries (henceforth UST). Let αi,t+1 be the safety
services by unit of face value provided by any other bond i. Thus, if qT,t+1 and qi,t+1 are the total
face value of UST and bond i respectively, the total supply of safety services in the economy, St,
is given by
St = qT,t+1 +N∑i=1
αi,t+1qi,t+1. (1.1)
I refer to αi,t+1 as perceived safety throughout.
I follow Krishnamurthy and Vissing-Jørgensen (2012a) and take the demand for safety services
as a primitive. I assume investors derive utility from safety services in a way that is separable from
standard utility from consumption. Specifically, the problem of the representative investor is
max{ct,Qt+1}∞t=0
Et
[∑t
βtu (ct) + Θtv(St)
]
s.t ct + Qt+1Pt ≤ ωt + QtXt,
(1.2)
where Pt is a column vector of asset prices, Xt are realizations of the corresponding payoffs at time
t, Qt is a row vector of portfolio positions, ct is consumption, ωt is an exogenous wealth flow, and
β is the standard discount rate. The assumptions on the functions u and ν are standard: u′ > 0,
u′′ < 0, v′ > 0 and v′′ < 0. Finally, given the normalization of the safety services provided by
UST, Θt is a demand shifter that allows us to identify the impact of an aggregate shock in the
demand for safety services supplied by UST.
9
From the consumers’ Euler equation, the price for each asset i is
Pi,t = Et [Mt+1Xi,t+1] + αi,t+1ϕt, (1.3)
where Mt+1 := β u′(ct+1)u′(ct)
, θt := Θtβu′(ct)
and ϕt := θtv′(St).
Prices consist of the standard discounted cash flows component and the safety premium com-
ponent, measured by αi,t+1ϕt. I refer to ϕt as the aggregate safety premium; it is the market price
of one unit of safety services. Given that I have normalized to one the safety services associated
with one dollar of face value of UST, ϕt is also the safety premium of UST. In what follows, I refer
to ϕt as the aggregate safety premium or the UST safety premium interchangeably.
In this model, the law of one price does not hold: two assets can have the same cash flows X ,
but have different prices precisely because they provide different safety services. The difference
is measured by the perceived safety, αi,t+1. Perceived safety can be correlated with Xi, to allow
for the possibility that the amount of safety services an asset provides relates to its cash flow
characteristics, but in a way that is not fully captured by the correlation between M and Xi.
Environment
Firms’ production is subject to aggregate productivity shocks xt and idiosyncratic productivity
shocks zi,t. The two stochastic processes are described by
xt+1 = ρXxt + σXηxt+1, (1.4)
zi,t+1 = ρZzi,t + σZηzi,t+1. (1.5)
where ηxt and ηzi,t are IID standard normal random variables. The parameters ρX and ρZ repre-
sent the persistence of the aggregate and the idiosyncratic shocks, and σX and σZ the respective
volatilities.
The aggregate safety premium, ϕt, depends on preference shock θt, and the exogenous supply
of UST bonds and of other assets that provide safety services. I assume that the total amount of
10
safety services provided by the non-financial corporate sector is small, therefore ϕt is exogenous
in my model. The stochastic process that drives ϕt is described by
logϕt+1 = logϕ+ ρϕ logϕt + σϕηϕt+1, (1.6)
where ηϕ is an IID standard normal random variable; ϕ, σϕ, and ρϕ represent respectively the
median, volatility, and persistence of the aggregate safety premium.
I assume that the stochastic discount factor is given by
logMt,t+1 = log β − γ(xt+1 − xt), (1.7)
where β is the rate time of preference, γ is the relative risk aversion, and xt is the economy’s
aggregate productivity shock. Equation (1.7) follows from the reduced-form assumption that the
aggregate consumption ct is an affine function of the aggregate productivity ct = a + bxt with
b > 0. Notice then that this model is not a general equilibrium one, because there are sources of
consumption other than the dividends paid by the non-financial corporations.
Firms
There is a set of heterogeneous firms, indexed by i ∈ I. The operating profits of a firm are
determined by
Πi,t(ki,t;xt, zi,t) = exp(xt + zi,t)kζi,t, (1.8)
where xt and zi,t are the aggregate and idiosyncratic productivity shocks defined in (1.4) and (1.5),
ki,t is the capital of the firm, and 0 < ζ < 1 is the capital share of production. ζ < 1 implies firms’
technology exhibits decreasing return-to-scale.
Firms may need external funds to finance dividends or investment. To allow for a firm to be
financially constrained, equity issuance must be costly. Thus, for simplicity, I assume all external
finance is in the form of one-period debt. Let bi,t+1 ≥ 0 be the face value of debt issued at time
11
t, which is due at time t + 1. Pi,t is the market price for one dollar of face value of debt. At time
t, a solvent firm pays bi,t and receives bi,t+1Pi,t from bondholders. Shareholders are protected by
limited liability, and distributions to shareholders are denoted by di,t. Investment, equity payout,
and financing decisions must satisfy the budget constraint
di,t = Πi,t + (1− δ)ki,t − bi,t − ki,t+1 + Pi,tbi,t+1 ≥ 0 (1.9)
where δ > 0 is the depreciation rate of capital.
Let time t net worth be wi,t := Πi,t+ lv(1− δ)ki,t− bi,t and lv ∈ (0, 1) be the liquidation value
of capital. I assume that debt is protected by a positive net worth covenant, as in Brennan and
Schwartz (1984). Thus, default occurs whenever wi,t first becomes negative,10,11 and the default
region can be written as
∆{xt, zi,t} = {xt + zi,t < ln(wi,t)} where wi,t =bi,t − lv(1− δ)ki,t
kζi,t.
In a default scenario, the bondholders receive a default payoff equal to
L(bi,t, ki,t;xt, zi,t) = (1− ξ)Πi,t + lv(1− δ)ki,tbi,t
,
where ξ ∈ (0, 1) is the bankruptcy cost.
Let I∆i,t+1be an indicator variable for the default region of firm i, at time t + 1. The market
price of debt Pi,t is given by12
Pi,t = Et[Mt+1
((1− I∆i,t+1
)+ I∆i,t+1
L(bi,t+1, ki,t+1;xt+1, zi,t+1))]
+ αi,t+1ϕt. (1.10)
10For examples of other work that uses a solvency default definition see Crouzet (2018) Elenev et al. (2020).11The advantage of this approach, compared to the traditional strategic default, is that it allows, for each action and
state, a closed form solution for debt prices, as shown in A.3.1. This avoids the computational cost of solving jointlythe value of the firm and the default threshold. As discussed in Strebulaev and Whited (2012), the “loop-within-a-loop” algorithms to solve dynamic models with strategic defaults can be very computationally costly, in particularwhen we have many state variables, as my model does.
12I calculate the debt price in closed form for each (kt+1, bt+1; ∫t). This calculation can be found in A.3.1.
12
A key ingredient of the model is that, while the aggregate safety premium ϕt is exogenous,
firm’s decisions regarding debt issuance, payout, and investment affect the firm’s perceived safety,
αi,t+1. For most of the empirical results of the paper, the specific functional form and even the
determinants of αi,t+1 do not need to be specified. The reason is that, as shown later, my approach
allows for an estimate of αi,t+1 (up to a scalar) directly. However, the theoretical characterization
of this problem requires a functional form of αi,t+1. For this reason, I assume that
αi,t+1 = αµi,t exp(−ψ bi,t+1
EtΠi,t+1
), (1.11)
where the parameter µ represents the memory of investors and ψ is a positive scalar.
Expression (1.11) links the perceived safety to the inverse of the interest coverage ratio ( bi,t+1
EtΠi,t+1),
one of the key determinants of bond ratings.13 In addition, perceived safety is persistent, as mea-
sured by the parameter µ. These choices are made to match the empirical observations discussed
in Section 1.5, that perceived safety is monotonic in ratings and ratings are persistent in time.
Furthermore, equation (1.11) captures in a tractable way an important feature about safe assets:
“When it comes to forming beliefs about which assets are safe, reputation and history matter"
(Caballero et al. (2017)). Moreover, there is an additional benefit of specifying the functional
αi,t+1, which is that it allows for the structural estimation of the UST safety premium, ϕt, as
discussed in Section 1.5.2.
Finally, a firm’s value is defined as the discounted value of all future distributions to sharehold-
ers and can be written recursively as:
V (∫i,t) = maxki,t+1,bi,t+1
d(ki,t+1, bi,t+1; ∫i,t) + Et [Mt,t+1Vi,t+1(∫i,t+1)] (1.12)
where Mt,t+1 is the one-period stochastic discount factor in (1.7), the dividends dt satisfy the
budget constraint (1.9) and ∫i,t = {wi,t, αi,t, xt, zi,t, ϕt} are the state variables. The expectation
13A common practice is to measure the interest coverage ratio is the ratio between company’s earnings beforeinterest and taxes (EBIT) during a given period divided and the company’s interest payments due within the sameperiod. To see its importance for ratings, see Moody’s credit rating methodology here.
13
is taken over the joint conditional distribution of aggregate, idiosyncratic, and aggregate safety
premium shocks. Note that the limited liability assumption is naturally met by the positive dividend
constraint.
The firm’s model deviates from the Modigliani-Miller benchmark in two dimensions: (1) there
are financial constraints related to the solvency default and bankruptcy cost ξ, and (2) bonds carry
a safety premium αi,t+1ϕt. The underlying assumption is that firm managers can create value to
shareholders by changing their firm’s capital structure to produce safety services that are valuable
to investors.
1.3.2 Model Results
To allow for a sharp characterization of the results of the model, I restrict myself to a two-period
version of the model, and leave a complete treatment of the fully dynamic model for the appendix.
Qualitatively, both versions of the model deliver similar results; though obviously, quantitative
statements rely on the fully dynamic model.
Bond Prices
A firm’s safety premium depends on the aggregate safety premium, ϕt, and the firm-specific
perceived safety, αi,t+1. A positive safety premium acts as a discount in a firm’s cost of borrowing
by increasing the price of their debt. Furthermore, since perceived safety depends on the debt
coverage ratio, as bi,t+1 increases, the safety premium converges to zero.
Figure 1.1 illustrates how a firm’s safety premium and debt prices depend on the level of debt
issued for different levels of the aggregate safety premium for a fixed set of state variables. Ceteris
paribus, the larger the amount of debt issued, the smaller the debt price. There are two reasons for
this. First, there is the traditional risk mechanism in which an increase in debt issuance increases
the probability of default and lowers debt prices. Second, if the aggregate safety premium is
positive, larger issuance decreases the firm’s perceived safety and thereby decreases its safety
premium and price.
14
Model Mechanics
To illustrate the mechanics of the model, Figure 1.2 shows how the total value varies with the
amount of bonds issued for different levels of the aggregate safety premium. Consider first the
case in which ξ = 0, i.e., there is no bankruptcy cost. If the aggregate safety premium is also zero,
ϕt = 0, corporate debt does not carry a safety premium either, and the value of the firm would be
invariant to debt issuance. This is the Modigliani-Miller benchmark.
If safety services are valuable in this economy, ϕt > 0, the total value of the firm has two
components: the value of the normal business operation and the value due to safe-asset creation.
In Figure 1.2a, the green area shows the value of a firm’s business operation, which is the firm’s
value if the aggregate safety premium is zero. The blue areas represent that additional value created
by issuing debt that carries a safety premium for different levels of aggregate safety premium ϕt.
The maximum value is achieved when the marginal safety premium received by issuing debt is
equal to the marginal decrease in safety value for making the firm more leveraged.
The second step is to introduce a bankruptcy cost greater than zero. In this case, the firm faces
an additional trade-off for issuing bonds: On one hand, issuing bonds creates value for the firm due
to the extra creation of safety services; on the other hand, it increases the probability of bankruptcy,
which increases expected bankruptcy cost. Again, for each level of ϕt, there is a unique investment-
and debt-level pair that maximizes the value of the firm. Figure 1.2b shows how the total value
of the firm varies with issuance for different levels of aggregate safety premium. The dotted lines
represent the optimal debt level b∗i,t+1 that maximizes the value of the firm for each ϕt.
1.3.3 Comparative Statics and Empirical Predictions
I want to understand how firms react to variations in the safety premium, both in the time
series and in the cross section. In the cross section, the objective is to understand how cross
sectional differences in initial perceived safety, {αi,t}i∈I , affect the optimal policy. In the time
series, instead, the objective is to understand how a single firm optimally adjusts its policy in
15
response to fluctuations in the aggregate safety premium, ϕt.
Armed with the main intuition of the model, I turn next to illustrate the numerical solutions the
model. Parameter choices are described in Table 1.1. Parameters, such as the decreasing returns to
scale, depreciation, the idiosyncratic and aggregate shock parameters, and the stochastic discount
factor parameters are standard and follow the literature closely in selecting them.
The model predictions depend on whether the firm is financially constrained or not. I define a
firm to be unconstrained at time t whenever the dividend constraint is slack, i.e., d∗i,t > 0.14 Notice
that I use the word dividends, but the reader should understand “payouts," since it is immaterial
whether the firm distributes these payouts in the form of dividends, equity repurchases, or some
combination of both. As an illustration, Figure A.2 plots the valuation as function of the actions
{ki,t+1, bi,t+1} and the optimal policy for an unconstrained and a constrained firm.
Consider first the implications of the model for the cross section. Figure 1.3 shows optimal
bond issuance, investment, and payouts as a function of the initial perceived safety, αi,t, for two
different firms, one constrained and another unconstrained, for three different levels of the ag-
gregate safety premium, ϕt. As shown in panels (a) and (b), for both the unconstrained and the
constrained firms, as long as ϕt > 0, the higher the initial perceived safety, the higher the bond
issuance. The difference between these two firms lies on how they use the proceeds from debt
issuance. Unconstrained firms, even if the aggregate safety premium is zero, can always achieve
their optimal capital scale. Therefore, the money borrowed mostly translates into higher payouts.
Instead, constrained firms with higher perceived safety are less financially constrained than oth-
erwise identical companies with lower perceived safety, thus the higher investment of the former
relative to the later. Intuitively, payouts are equal to zero in this case. I summarize these results in
the following prediction.
Prediction 1.1 (Cross Section) In the cross section, if the aggregate safety premium is positive
(ϕt > 0), ceteris paribus, optimal bond issuance, b∗i,t+1, is increasing in the firm’s initial perceived
14Strictly speaking, there could be firms that have d∗i,t = 0 and are not financially constrained, because theyachieved their optimal scale exactly at the boundary. A small perturbation in the parameters, of course, places this firmat one side or the other of the constraint.
16
safety, αi,t. Furthermore, if a firm is financially unconstrained, investment increases by less than
the proceeds from bond issuance, with the remainder being distributed to equity holders.
The predictions are similar for the time series. Figure 1.4 shows the effect of the aggregate
safety premium on bond issuance, investment, and payouts for two different firms, one constrained
and another unconstrained, for three different levels of the firm-specific perceived safety, αi,t. I
summarize these predictions next.
Prediction 1.2 (Time Series) In the time series, for a firm with positive perceived safety, αi,t > 0,
ceteris paribus, optimal bond issuance, b∗i,t+1, is increasing in the aggregate safety premium, ϕt.
Furthermore, if the firm is financially unconstrained, investment increases by less than the proceeds
from bond issuance, the remainder being distributed to equity holders.
There are obviously interaction effects between the two components of the safety premium.
For instance, debt issuance of firms with higher initial level of perceived safety will respond more
to variation in the aggregate safety premium than otherwise equal firms with lower initial level of
perceived safety. In Figure 1.5, I plot the first derivative of optimal bond issuance with respect
to ϕt as a function of initial perceived safety. An equivalent effect exists for variation of the first
derivative of optimal bond issuance with respect to αi,t as a function of aggregate safety premium.
This result thus generates the next prediction.
Prediction 1.3 (Heterogeneous Effects A) Firms with higher perceived safety respond to an in-
crease in the aggregate safety premium by increasing bond issuance more than firms with lower
perceived safety. Furthermore, the difference in bond issuance among firms with different levels of
initial perceived safety is larger when the aggregate safety premium is higher.
Finally, there are also interactions between the two components of the safety premium and
firms’ initial net worth, wi,t. Consider two firms that are financially constrained, one with higher
net worth than the other. Then, the marginal cost of issuing an additional dollar of debt in response
to an increase in, say, the aggregate safety premium is lower for the company with higher net worth.
17
The reason is that the expected bankruptcy cost is lower for this company than for the company
with lower net worth. Clearly this effect disappears when the net worth is sufficiently high and
the firms are no longer financially constrained. This phenomenon is illustrated in Figure 1.6 and
generates the following empirical prediction.
Prediction 1.4 (Heterogeneous Effects B) Firms that are financially unconstrained respond to a
higher perceived safety or the aggregate safety premium by increasing bond issuance more than
financially constrained firms.
There are implications of this model regarding the interaction between safety premium and
bankruptcy cost. Testing these implications requires proper time or cross sectional varying mea-
sures of the bankruptcy cost, which are notably hard to estimate, and is therefore out of the scope
of this paper.
1.3.4 Bringing the Model to the Data
The model yields several predictions regarding firms’ responses to variations in the safety pre-
mium. The rest of the paper is dedicated to testing them using data on US non-financial corpora-
tions. With the goal of mapping the predictions described in the previous subsection to reduced-
form linear regressions, I calculate a policy function linearization.
Let the state space be S := {wi,t, αi,t, xt, zi,t, ϕt ∈ R+ × (0, 1)×R×R×R+} and the action
space be A := {bi,t+1, ki,t+1 ∈ R+ ×R+}. Note that in order to be feasible, an action must satisfy
the budget constraint. Let π∗ be the optimal policy function, π∗ : S → A.
Consider the Taylor expansion of the policy function around the point ∫0 = {wt, αt, x, zt, ϕ},
where wt, αt, and zt are the time t cross sectional averages of firms’ net worth, perceived safety,
and idiosyncratic productivity shock, respectively; and x and ϕ are time series averages of the
aggregate productivity shock and the aggregate safety premium.
As will be discussed in the next section, it is difficult to observe αi,t or ϕt directly in the data.
18
A quantity that turns out to be empirically important is the cross-basis, defined as
CrossBasisi,t := (αi,t − αt)ϕt. (1.13)
Hence, the optimal policy around ∫0 is approximately
∆bi,t+1 ≈ β1,t1
ϕt−1
CrossBasisi,t−1 + β2,tzi,t + β3,twi,t + δt + δi, (1.14)
where βs are the partial derivatives evaluated in ∫0, and δt and δi collect variables that are constant
in the cross section and in the time series. An equivalent specification can be written for investment
ii,t and payout di,t.
Empirically estimating how bond issuance, investment, and payouts vary as a function of the
cross section allows me to identify how a firm’s decision changes as a function of perceived safety,
conditional to a constant aggregate safety premium, ϕt.
1.4 Data
I study the impact of variation in the safety premium on the behavior of non-financial firms in
the United States. To this end, I use four main data sets: (i) bond characteristics, from the Mergent
Fixed Income Securities Database (FISD) for academia, (ii) Treasury yields and corporate bond
yields, respectively from the CRSP US Treasury Fixed-Term Indexes and WRDS Bond Returns
databases (iii) CDS spreads for single-name CDS composites from Markit, and (iv) firm balance
sheet data from Compustat quarterly data. The empirical tests focus on the period from January
2003 to September 2020. The starting date coincides with Markit’s CDS data starting date and the
end data with the last updated of WRDS Bond Returns database.
The bond-level data set is created by merging corporate bond characteristics, bond prices data,
and single-name CDS data. For bonds, I apply standard filters and exclude bonds not listed or
traded in the US public market, not traded in US dollars, whose issuers are not in the jurisdiction
19
of the United States, with convertible or floating rates, with non senior-unsecured claims, with
issuance size of less than 100 thousand dollars, or with time to maturity less than 1 year. For CDS
spreads, I select only CDS spreads for US dollar contracts that refer to senior unsecured debt and
with the documentation clause type “No Restructuring" (XR).15 The final data set contains infor-
mation about corporate yields, duration, bid and ask spreads, volume traded, bond characteristics,
and CDS spreads quoted in basis points per annum for a notional value of $10 million.
The original Markit data set provides a CDS-spread term structure incorporating maturities of
1y, 2y, 3y, 4y, 5y, 7y, 10y, 15y, 20y, and 30y. I use a locally constant hazard rate interpolation
of CDS spreads to match the bonds’ duration. To mitigate the concern that the 5y maturity is the
most liquid, I only consider CDS spreads that have valid quote rating; this guarantees that the CDS
spread has passed several tests ran by Markit to assure the quality of the quote.16
The firm-level data set is formed by merging the bond-level data set with firms’ balance sheet
data from Compustat quarterly data. The sample includes all Compustat firms that have publicly
traded equity in one of the three main stock exchanges (NYSE, NASDAQ, and Amex), except
regulated utilities (SIC codes 4900-4999), financial firms (SIC codes 6000-6999), and firms cate-
gorized as public service, international affairs, or non-operating establishments (SIC codes 9000+).
Finally, following standard data-cleaning methodology applied in the literature, I also exclude firms
with missing or non-positive book value of equity or sales and firms with less than $1 million in
total assets. For firm-level analyses, I aggregate yields, CDS spreads, and bases at the firm level
by calculating the face-value weighted averages.
All the empirical results use the universe of US firms in the Compustat sample with successful
merges with non-missing CDS spread, yields, and bonds outstanding. I winsorize all yields, CDS
15This option excludes restructuring altogether from the CDS contract, eliminating the possibility that the Protec-tion Seller suffers a “soft” Credit Event that does not necessarily result in losses to the Protection Buyer. Since theimplementation of SNAC in 2009, CDS with this clause are the most traded in North America. For more detail see,e.g., Boyarchenko et al. (2019)
16The documentation on Markit quote ratings can be found at Markit.com Guide Version 14.4 (here). The manualsays: “Ratings are assigned based on both quantitative criteria - of which the most important is the number of distinctpassing contributions - and qualitative measures: how competitive, liquid, and transparent the market is; and whetherthe trades are time stamped, frequently updated tradable quotes. To achieve a rating at all, our composites must havepassed stringent standards on these criteria."
20
spreads, CDS-bond bases, and financial ratios at 1% and 99% to remove outliers. The final data set
for bond prices is monthly, the same frequency as the corporate bond prices data set. The firm-level
data is quarterly, the same frequency as Compustat.
The coverage per year is reported in Table 1.2. The final sample covers on average 2793
bonds and 395 firms per year. It is worth noting that coverage is not concentrated in a few rating
buckets and is rather representative of the credit-risk spectrum. Table 1.3 reports the quarterly data
summary statistics.
1.5 Measuring the Corporate Safety Premium
The first empirical challenge to test the model of corporate safety creation is to measure the
safety premium in corporate liabilities. So far I have been speaking of corporate liabilities or debt,
but for measuring non-financial corporate safety premia, I focus on corporate bonds. This is due to
data availability. Data on corporate bond instruments is more readily available and comprehensive
than other forms of corporate debt. Moreover, for simplicity in notation, while explaining the
safety premium measurement construction, I assume that each firm in the sample has only one
bond outstanding. I discuss the empirical implementation of multiple bonds per firm in the next
subsection.
From equation (1.3), the safety premium of a particular bond is the difference in prices of this
bond and of a benchmark asset with the same cash flows, but no safety services. This benchmark
is not readily available. I overcome this issue by constructing, for each bond in the sample, a
synthetic asset which is a portfolio that combines the corporate bond and the maturity-matched
credit default swap (CDS). I call this synthetic asset the hedged bond. Under certain assumptions,
which are discussed below, the cash flows of the hedged bonds are the same among all bonds. Then,
by comparing the yields of the hedged bonds, I am able to quantify the relative safety premium
between different bonds.
The building blocks of the hedged-bond construction are the CDS contracts. A CDS contract
21
is a derivative instrument that can be used to hedge against default risk of the reference entity. If
there exists a CDS contract that perfectly hedges the default risk of a corporate bond, investors can
create a hedged bond that closely replicates the cash flow of a risk-free bond by buying a corporate
bond and the maturity-matched CDS.
To formally see how one can use the difference in yields of hedged bonds to measure the
relative safety premium, let yi,t = − ln(Pi,t) ≈ 1−Pi,t be the yield of bond i at time t. From (1.3),
yields are approximately
yT,t = 1− Et [Mt+1XT,t+1]− ϕt for Treasuries,
yi,t = 1− Et [Mt+1Xj,i,t+1]− αi,tϕt for bond i.
I make three assumptions, which are discussed further below. First, the CDS perfectly hedges
against credit risk; second, the CDS does not provide any safety services; and third, the US Trea-
sury bond is risk-free. Consider a hedged bond constructed by buying a bond j and a corresponding
CDSj . Under the three assumptions, the hedged bond has exactly the same payoff as the Treasury.
I define the CDS-bond basis as the difference in yields between the UST bond and the hedged
bond. Hence, the CDS-bond basis is
Basisi,t = yT,t − (yi,t − CDSi,t) = (αi,t+1 − 1)ϕt ∀i, (1.15)
where the bond i and UST bond T are of equal maturity and coupons. The basis is thus a measure
of the safety premium differential between the UST bond and the bond i. If the bond offers safety
services similar to UST, then αi,t+1 is close to one and the basis will be close to zero.
As discussed in Section 1.3, the variables of interest for testing the model of corporate safety
creation are αi,t+1 and ϕt, which are not observable directly in the data. Therefore, I define cross-
basis, which is the dependent variable of interest in equation (1.13). The cross-basis of bond i is
the difference in the yields of this hedged bond and of the average hedged bond in the sample,
22
which I denote by Basist.
CrossBasisi,t = Basisi,t −Basist = (αi,t+1 − αt+1)ϕt (1.16)
Equation (1.16) yields three testable predictions for the cross-basis and its connection with the
safety premium. First in the cross section, the cross-basis is monotonic in perceived safety (αi,t+1);
second, one factor, the US Treasury safety premium (ϕt), fully explains the time series variation
of the cross-basis; third, loadings on the US Treasury safety premium are monotonic in bonds’
perceived safety. I test these predictions below and find considerable support for them, which
validates my interpretation of the cross-basis as a measure of relative safety premium.
1.5.1 Empirical construction of the CDS-bond basis
I now map the theoretically defined CDS-bond basis, cross-basis and basis index to the non-
financial US corporate bond data. I begin by following the standard methodology (Oehmke and
Zawadowski (2017), Kim et al. (2016), among others), and for each bond j with maturity τ of firm
i, I calculate the CDS-bond basis at time t as
Basisj,τ,i,t = CDSτ,i,t − CreditSpreadj,τ,i,t (1.17)
where CDSi,τ,t is the CDS spread for company i, interpolated to have the same maturity τ as the
bond. CreditSpreadj,τ,i,t is the difference in yields between the bond j and the duration-matched
Treasury yield. The firm-level CDS-bond basis at each time t is the face-value weighted average
Basisj,i,τ,t across all bonds j outstanding of firm i in the sample.
The cross-basis calculation follows directly from equation (1.16), and it is defined as
CrossBasisi,t = Basisi,t −Basisindex,t, (1.18)
where Basisi,t is firm i CDS-bond basis and Basisindex,t is the face-value weighted bases for
23
all companies in the sample. Considering the value weighted average instead of simple averages
reduces the influence of small issuers with extreme basis values.
Table 1.4 reports summary statistics for cross-basis, CDS-bond basis, yields, and CDS spreads
in my sample; and Figure 1.7 shows the face-value weighted average CDS-bond basis by rating
category for corporate bonds of US non-financial firms. The CDS-bond basis is on average neg-
ative, reaching points as low as −10% during the peak of the financial crisis. This indicates that
investors are willing to forgo yields to hold a US Treasury rather than a hedged bond. In light of
the model of demand for safety, I interpret this result as evidence that US Treasuries provide more
safety services than corporate bonds.
In the absence of frictions, the CDS-bond basis and the cross-basis should be zero. The preva-
lence of negative CDS-bond bases in the market is a well-known empirical regularity in the cor-
porate bond literature (e.g. Longstaff et al. (2005), Oehmke and Zawadowski (2017), Bai and
Collin-Dufresne (2019)). The cross-basis captures the cross sectional dispersion in the CDS-bond
basis.
I interpret the cross-basis as capturing the premium attached to the services associated with the
ownership of high-quality bonds, such as collateral value, regulatory relief, or simply psychologi-
cal relief. All these interpretations are consistent with the model in Section 1.3. But it also may be
capturing frictions not associated with safety such as counterparty risk (Giglio (2014)), illiquidity
(Longstaff et al. (2005), Oehmke and Zawadowski (2015, 2017)), restructuring uncertainty (Berndt
et al. (2007)), or mismatch in the payoff structure of bonds (Duffie (1999)). In Section 1.7.1, I ar-
gue that none of these confounders are large enough to explain the cross sectional variation of the
cross-basis.
The innovation of this paper is, first, to show that cross sectional variation in the cross-basis
captures cross sectional variation in the safety premium of different corporate bonds, and, sec-
ond, that firms respond to variation in the cross-basis by issuing bonds. I turn next to the first
contribution and leave the second to Section 1.6.
24
1.5.2 The Validity of Cross-Basis as the Relative Safety Premium Measure
To validate the connection between the CDS-bond basis and the safety premium, I test the three
predictions from the model. First, I run the following Fama-MacBeth regressions to test whether
the cross-basis is monotonic in firms’ perceived safety
CrossBasisi,t = β0 + β1αi,t + εi,t, (1.19)
where αi,t are proxies for the perceived safety of firm i at time t. I measure safety in several ways:
rating category buckets (AA and above, A, BBB, BB, B and below); rating rank (1 for AAA,
2 for AA+, 3 for AA, etc.); interest coverage ratio (ICRi,t), measured as interest expenses over
EBITA; and the structurally estimated αi,t.17
Column (1) and (2) of Table 1.5 shows that, on average, the basis is monotonic on ratings.
Moreover, ratings alone are able to explain 25% of the cross sectional variation of cross-basis. I
also test the explanatory power of ICR and the structurally estimated αi,t. The results are reported
in columns (3) and (4). The highly statistically significant coefficient for ICR means that the
cross-basis is monotonically increasing in the inverse of the ICR. The highly significantly signifi-
cant coefficient for αi,t is yet another evidence that the cross-basis is monotonically increasing in
perceived safety. I interpret these results as supporting evidence for the predictions that the cross-
basis is monotonic in firms’ perceived safety and that perceived safety explains a lot of the cross
sectional variation in of the cross-bases.
Next, I turn to time series analyses to test the two remaining predictions. I run the following
regression
CrossBasisr,t = β0,r + β1,rUST SPt + εr,t, (1.20)
where CrossBasisr,t is the value-weighted average of the basis for the rating category r and
UST SPt is a proxy for the safety premium of Treasury.
17Details of this estimation are in A.2.
25
There is no consensus in the literature about how to measure the US Treasury safety premium.
I use four distinct measures: two measures inspired by Krishnamurthy and Vissing-Jørgensen
(2012a) (henceforth KV-J): (i) AAA−Treasury and (ii) BBB−(AAA and AA) basis spread;18 (iii)
the box-trade spread as in Binsbergen et al. (2019); and (iv) the structurally estimated safety pre-
mium based on the model in this paper. A more detailed discussion about each of the measures is
presented in A.2.
Figure 1.8 shows the time series of each one of the safety premium measures, and Table 1.6
shows the summary statistics and correlation matrix between all these measures. They are all
closely related. All of the measures of the US Treasury safety premium, except the one estimated
from the model, are a relative premium of Treasuries with respect to a benchmark. The only
measure that attempts to properly capture the correct level is ϕt, and this is the reason why it is
relatively higher than the others.
Table 1.7 shows the estimation results for equation (1.20). Results are qualitatively similar
across all measures. The loading on the safety premium should capture (αi − α), therefore we
expect it to be monotonically decreasing in how safe the bonds are. The loadings are indeed
monotonic in ratings for all four proxies of the US Treasury safety premium. Furthermore, the
UST safety premium should explain a large fraction of the time series variation of the cross-basis.
As shown in Panel A, for ϕt, the r-squared of the regressions range between 43% and 90%, for a
mean of 60%. This means that one factor explains a large portion of the time series variation of the
cross-basis. Results are similar for the two K-VJ safety premium measures. The lowest r-squared
is reported for the box-trade spread. This is expected at least for one reason: the box-trade is
calculated from the put-call parity relationship for European-style option contracts and the longest
18Krishnamurthy and Vissing-Jørgensen (2012a) make the simplifying assumption that the AAA−Treasury spreadreflects liquidity premium whereas the BBB−AAA spread reflects safety premium. Their assumption is that, AAA-rated securities and UST have the same safety but different liquidity, whereas AAA- and BBB-rated securities havedifferent safety but roughly the same liquidity. In my paper, I do not focus on differentiating liquidity and safetypremium. Nevertheless, to get the best possible measures of the Treasury safety premium, I also construct the twomeasures. There are two issues in using the BBB−AAA spread: (i) In recent years, there are only two US corporationsthat are rated AAA, Johnson & Johnson and Microsoft; (ii) a large component of the BBB−AAA spread is due tocredit risk. In order to minimize the influence of company-specific shocks, I use the face-value weighted CDS-bondbasis spread between “BBB” and “AAA and AA.” The difference in credit risk is controlled by the CDS correction.
26
maturity available is 18 months, whereas the average maturity of the corporate bond is 7 years in
my sample. It could be that the drivers of short-term UST convenience yield are different the the
long-term safety premium. In summary, these are evidences in support for the close connection
between the basis and corporate bonds safety premium.
1.6 Firms’ Response to Safety Premium
This section studies how firms’ decisions relate to the safety premium in corporate bonds. I
present evidence that supports the predictions of the model of corporate safety creation presented in
Section 1.3. In the cross section of US non-financial firms, high perceived safety, measured by high
cross-basis, forecasts high net debt issuance. Net debt issuance is not reverted into real investment
but is instead used for net payouts, measured as the sum of dividends and equity repurchases.
These results suggest that companies that can create safety services are, on average, not financially
constrained, and that bond issuance can be a financial maneuver that benefits equity holders.
1.6.1 Impact of Safety Premium on Net Debt Issuance
The first set of empirical tests aims to identify how variation in a firm’s safety premium affects
net debt issuance. Since αi,t is not directly observed in the data, the first empirical specification
includes the cross-basis, which is a proxy of a firm’s relative safety premium with respect to the
market and the dependent variable of interest after the linearization described in (1.14). For each
time t, the cross-basis captures cross section variation in perceived safety across companies.
Prediction 1 from the model says that firms with higher perceived safety issue more debt than
otherwise similar firms with low perceived safety. I test this prediction by running the following
regression
NDIi,t+1 = β1CrossBasisi,t + β2Xi,t + δi + δt + εi,t, (R1)
where NDIi,t+1 is long-term net debt issuance as a share of lagged total assets, CrossBasisi,t
is the CDS-bond basis minus the basis index, the basis index is the corporate bond market value-
27
weighted average of Basis, Xi,t are controls, and δi and δt are firm and time fixed effects, respec-
tively.
Based on equation (1.14), it is clear that controls should capture firm net worth (wi,t) and
investment opportunities (zi,t). In the baseline specification, the controls are log(TotalAssets) and
cash normalized by assets, to account for firms’ net worth, and Tobin’s Q to control for firms’
investment opportunities. Due to the limitations of those control variables, I also include the CDS
spread as a control. The CDS price captures any factor that affects a firm’s credit risk in a way that
is not related to the safety provision of the firm’s bonds. Net debt issuance is measured in quarter
t + 1, and all independent variables are measured in quarter t in order to avoid the “bad controls
problem" (Angrist and Pischke (2009a)).
The identification assumption to correctly estimate the impact of firms’ safety premium on debt
issuance is that the error term in (R1), εi,t, is orthogonal to the measure of relative safety premium,
CrossBasisi,t. This assumption is violated if there are factors correlated to the cross-basis that
affect a firm’s net debt issuance and are not fully captured by the controls. The most salient
confounder is the possibility that the controls are not good enough to fully account for investment
opportunities. If investment opportunities are the main confounder, cross-basis should then be a
strong predictor of investment. As will become clear in the next subsection, on average, firms do
not use the funds raised from issuing safe debt for investment. The results are robust to different
measures of investment: capital investments, intangible investments, and acquisitions. Therefore,
not properly controlling for investment opportunities should not be the major concern. Still, the
lack of a natural experiment or a valid instrument leaves space for possible confounders that can
threaten the identification. I alleviate this concern by showing that the regression results are robust
to the inclusion of several extra controls, and in Section 1.7, I develop a myriad of tests to rule out
other possible alternative hypotheses.
Table 1.8 shows the regression estimated for model R1. Column (1) shows that the cross-
basis forecasts a positive net debt issuance for the average firm. The effect of cross-basis on debt
issuance is statistically and economically significant. The point estimate means that a 1 percentage
28
point increase in the cross-basis forecast an increase of net debt issuance by 10 basis points as
a percentage of total assets. This represents an increase of $27.4 million (= β2× mean(atq)) in
debt issuance, which is a 31%(
= β2mean(NDI) × 100
)increase relative to the quarterly average debt
issuance.
To assess the magnitude of the results, it is useful to compare the elasticity of leverage to
the cross-basis with capital structure literature. Heider and Ljungqvist (2015) estimate that a 1
percentage point increase in taxes leads to a 40 basis points increase in the long-term leverage ratio.
The semi-elasticity coefficient estimated in Column (1) of Table 1.8, suggests that 1 percentage
point increase in the cross-basis forecasts a 35 basis points(
= β2mean(long-term leverage) × 104
)increase
in long-term leverage ratio. The two estimates are in the same order of magnitude, but it is worth
noting that the quarterly standard deviation in the cross-basis is 0.96%, whereas tax changes are
relatively infrequent. The magnitude of the point estimates is evidence that the safety premium is
an important economic force in determining firms’ leverage ratios.
To ensure results are robust, I consider three extra controls: ratings fixed effects, leverage
ratios, and return on assets (ROA). Credit ratings are intrinsically related to firm default probability
and expected cost of bankruptcy, forces that impact firm leverage decisions in many traditional
corporate theories, such as the trade-off theory. Although the CDS spread should largely capture
this effect, there could be time-varying frictions, systematically correlated with ratings, that affect
a firm’s access to credit and are not related to the firm’s perceived safety. Since credit rating is one
of the main drivers of cross sectional variations in the cross-basis, those omitted factors could be of
concern. I control for credit ratings by re-estimating (R1) including rating buckets fixed effects.19
The results are reported in column (2) of Table 1.8. The cross-basis has a significant impact on
net debt issuance even within a rating bucket. The point estimate is 8 basis points. As expected,
the point estimate is slightly smaller than the baseline specification, reflecting the fact that ratings
are intrinsically related to perceived safety, as shown in Section 1.5.2, and the rating fixed effects
subsume this variation. Nevertheless, the results are qualitatively unchanged.
19I consider 5 rating buckets: AAA and AA, A, BBB, BB, and B and below. All notches are included in theassociated bucket.
29
In dynamic models of firm capital structure, leverage can be path dependent (see, e.g., Hen-
nessy and Whited (2005) and Admati et al. (2018)). One concern is that the cross-basis is capturing
variation in the leverage ratio in the cross section. To alleviate this concern, in column (3) of Table
1.8, I include leverage ratio as one of the control variables. After controlling for the leverage ratio,
the impact of cross-basis on net debt issuance remains significant. The point estimate is 8 basis
points, which means that a 1 percentage point increase in the cross-basis forecasts a 24% increase
in debt relative to the average quarterly net issuance. The slightly smaller point estimate is ex-
pected because, like ratings, leverage ratio is one of the drivers of the cross sectional variation in
the cross-basis; consequently, it subsumes part of the firms’ safety premium variation.
One interesting difference between the baseline specification and the one that includes leverage
ratio as a control is the impact of the CDS spread on net debt issuance. Whereas a decrease in
the CDS spread forecasts larger issuance in the main specification, this is not robust to including
leverage ratio as a control. The credit premium measured by the CDS spread has a small impact
on debt issuance after controlling for leverage ratios. This result is probably related to the strong
correlation between the leverage ratio and the CDS spread.
Previous literature has documented the impact of profitability on leverage. Theoretically, how
profitability should impact net debt issuance is not straightforward. Under the trade-off theory,
profitable firms face lower expected costs of financial distress and find interest tax shields more
valuable, therefore high profitability should be related to higher debt issuance (Myers (1984)).
Under the pecking order theory of capital structure, firms should rely on external finance only if
the internal funds are not enough to meet the financing needs (Myers and Majluf (1984)). In this
case, everything else constant, firms with high profitability should issue less debt. In any case,
the source of concern for identifying the impact of the cross-basis on net debt issuance is that the
cross-basis is systematically correlated with firms’ profitability in a way that is not captured by
the controls and is not related to firms’ safety premium. To alleviate this concern, I control for
return on assets as a measure of profitability. Column (4) reports the results. The effect issuance
response to cross-basis variation remains almost unaltered. The ROA regression coefficient is not
30
statistically significant. Due to the relatively recent period that my sample covers compared to
other studies of firms’ capital structure, this result is consistent with Goyal and Frank (2009), who
show that the impact of profitability on leverage has been diminishing over time.
All together, the results reported in Columns (1) to (4) of Table 1.8 provide strong support for
the response in net debt issuance due to cross sectional variation in perceived safety, as described
in Prediction 1.1.
I now turn to explore the direct effect of the aggregate safety premium on issuance. Prediction
2 says that net debt issuance should respond to variation in the the aggregate safety premium.
Moreover, Prediction 3 says that this response should be stronger for firms with higher perceived
safety. I test these predictions by running the following regression
NDIi,t+1 = β1UST SPt × αHi,t + β2αHi,t + β3Xi,t + δi + δt + εi,t, (R2)
where USTSPt is the UST safety premium and αHi,t is a dummy variable equal to 1 if the firm has
high αi,t and 0 otherwise. I construct αHi,t in two ways. First, I set αHi,t to one if the firm belongs to
the highest quintile of the quarterly cross-basis distribution. Second, I set αHi,t to one if the firm is
rated A- and above in the quarter. “UST SP" is a proxy for the US Treasury safety premium. The
baseline estimation uses the structurally estimated US Treasury safety premium.20 The controls
are the same as in (R1).
The results are reported in columns (5)-(8) of Table 1.8. In all specifications, firms with high
safety premium respond to an increase in the aggregate safety premium by issuing relatively more
debt. This result is robust to including rating buckets fixed effects and/or extra controls as shown
in columns (6) and (8). It is noteworthy that estimating the aggregate safety premium coefficient is
not possible in this specification, since it is subsumed by the time fixed effects. Nevertheless, the
interaction coefficient provides evidence in support to Prediction 2 and 3.
This specification also alleviates concerns that noise in the cross-basis measure is systemat-
ically correlated with firm decisions and could be biasing the results from regression R1. The
20Results considering other proxies for the aggregated safety premium are reported in the appendix.
31
results in columns (5)-(8) of Table 1.8 provide strong evidence for the cross sectional effects of
safety premium variation on the net debt issuance, that they are not driven by idiosyncratic noise
in the firm-level cross-basis measure.
In summary, I find strong evidence that firms respond to higher safety premia by issuing more
debt than their comparable peers with lower safety premia. This result is robust to the inclusion
of ratings fixed effects and extra controls. The impact of the cross-basis on net debt issuance is
statistically and economically significant.
1.6.2 Impact of Safety Premium on Firms’ Real Decisions
The second set of empirical tests aim to identify how firms use the proceeds from issuing safe
debt. Let DebtIssuance be an indicator variable equal to 1 if the firm has strictly positive net debt
issuance value and 0 otherwise. I run the following empirical model
yi,t+1 =β1CrossBasisi,t ×DebtIssuancei,t+1 + β2CrossBasisi,t+
β3DebtIssuancei,t+1 + β4Xi,t + δi + δt + εi,t,
(R3)
The cross-basis and controls are the same as in regression (R1). The main y-variables of interest are
net payouts and investment. I measure payouts as the sum of dividends and equity repurchases. The
proper measure of investment must consider the increasing share of intangible investment among
corporate investment (Crouzet and Eberly (2020)) and also acquisitions. To this end, I measure
investment in three different ways: (1) the traditional capital investment, defined as CAPEX plus
net PPE bought; (2) intangible investment, measured as the sum of R&D and 30% of SG&A
expenses, as in Peters and Taylor (2017); and (3) acquisitions.
Although the model presented in Section 1.3 does not cover the impact of safety premium vari-
ation on liquid assets accumulation, this is an important margin to be empirically tested. To this
end, I include ∆Cash and financial investment in the set of y-variables. Using financial invest-
ments instead of Compustat CHE changes is important. It captures the increasing relevance of the
financial assets portfolio in non-financial firms, which is often not properly accounted for in the
32
Compustat CHE variable. Those issues are described in Darmouni and Mota (2020).
Table 1.9 shows the regression results. Interestingly, only payouts respond to the cross-basis
conditional on positive debt net issuance. The impact on payouts is statically and economically
significant. The point estimate signifies that 1 percentage point increase in the cross-basis forecasts
8 basis points (= β1 + β2) increase in total net payouts as a percentage of total assets. This is
an increase of 8%(
= β1+β2mean(payouts | DebtIssuance)
)to firms’ average quarterly net payout conditional
on positive net debt issuance. In dollar amounts, 1 percentage point increase in the cross-basis
forecasts $23.2 million, a number very close to the effect of the cross-basis on net debt issuance,
$27.4 million.
Investment and liquid assets accumulation do not respond to the cross-basis conditional on
positive issuance. The proceeds from issuing safe debt are largely transformed into equity payouts
rather than investment. This result is consistent with the hypothesis that firms that benefit from a
safety premium are not likely to be financially constrained. It is also consistent with Stein (1996),
who says that firms with decreasing returns to scale will not respond to cheap financing by investing
more as long as they are already at their optimal scale.
The lack of response in cash accumulation or financial investment differentiates the safety
premium mechanism from the market timing described in Bolton et al. (2013) and Eisfeldt and
Muir (2016). In case of a stochastic cost of external finance, firms should raise external finance
when it is cheap, guaranteeing liquidity if future adverse shocks happen in periods when external
finance is expensive. Under this theory, firms should issue debt in times of high safety premium
and accumulate liquid assets. The results in this paper suggest instead that firms that benefit from
a high safety premium are not likely to face financial constraints in raising funds, thus the liquidity
accumulation response is not observed.
In summary, the results of this subsection show that the proceeds from issuing debt in response
to variation in the safety premium are most converted into equity payout, rather than real invest-
ments. Based on Predictions 1 and 2, this is strong evidence that companies most affected by the
safety premium are not likely to be financially constrained. Furthermore, the results described in
33
this subsection are robust to including rating fixed effects, leverage ratio, and past profitability as
controls. The results are reported in Table A.1 in A.5.
1.6.3 Heterogeneity across Firms’ Characteristics
According to the model’s predictions, responses to variation in the safety premium vary across
firms’ initial conditions. First, according to Prediction 4 the extent to which a firm can increase
its leverage in response to an increase in the safety premium depends on its debt capacity and its
expected bankruptcy cost. Effectively, its default risk acts as a constraint on its ability to take
advantage of the discount in debt financing provided by the safety premium. Second, accord-
ing to Predictions 1 and 2, the impact on investment or payouts is related to the firm’s financial
constraints. Unconstrained firms are more likely to operate at their optimal scale. Therefore, an
increase in the safety premium should have a stronger payout response than in real investment. The
opposite should be true for constrained firms.
I examine the heterogeneity across different firms by running the following regression
Yi,t+1 = β1CrossBasisi,t×UNCi,t+β2CrossBasisi,t+β3UNCi,t+β4Xi,t+δi+δt+εi,t, (R4)
where UNC is a dummy variable equal to one if the firm is likely to be unconstrained and 0
otherwise. I group firms by five relevant characteristics: ratings, profitability, cash, payouts, and
size. For each characteristic and quarter, I set UNCi,t = 1 for firms that are in the largest 20%
quantile. For ratings, I consider investment grade ratings (BBB− and above) to be unconstrained.
To study a firm’s response conditional on issuing, I select the sample for which net debt issuance
is strictly positive.21
Table 1.10 reports the results for each one of the five characteristics. Column (1) shows that
the issuance response of investment grade and large firms to the cross-basis is stronger than other
firms, suggesting that they have a smaller marginal cost of increasing leverage. Investment grade
21Ideally, the triple interaction of CrossBasis × UNC × DebtIssuance should be considered. Due to samplesize restrictions, I consider instead the selected sample in which net debt issuance is strictly positive.
34
firms also engage in higher payouts in response to the cross-basis, as shown in column (2) of Panel
A. As predicted by the model, in all specifications, the impact on capital investment is smaller for
unconstrained firms, as shown in column (3). The differential impact in intangible investment for
investment grade, profitable, and high-payout firms is solely driven by SG&A expenses. Columns
(8) and (9) show that there are no differential effects in liquidity accumulation. Finally, one in-
triguing result emerges from the heterogeneous analysis, reported in column (7). Investment grade
and large firms engage in acquisitions in response to an increase in the cross-basis. Although spec-
ulative, this last result suggests that the safety premium can act as a financial advantage for firms
that can benefit from it, potentially having consequences for product market competition.
In summary, the results presented in this subsection are largely consistent with the corporate
safety-creation model. Firms that are likely to be financially unconstrained, in the sense that they
could achieve their optimal investment and scale even in the absence of a safety premium, respond
to the cross-basis by issuing debt and engaging in payouts. The impact of the cross-basis on capital
investment is smaller than for the contained group. These are in accordance with Predictions 1 and
2. Furthermore, in accordance with Prediction 4, unconstrained firms respond to higher cross-basis
by issuing more debt than constrained firms.
1.6.4 Summary
The results in this section show two notable patterns governing firms’ activities. First, the
cross-basis, a measure of relative safety premium in corporate bonds, strongly forecasts net bond
issuance. The results are robust to adding rating fixed effects and several extra controls. Second,
the proceeds from issuing safe debt are not converted into investment measured either as capital
investment or intangible investment. Instead, the proceeds from issuing debt in response to the
cross-basis are used to finance payouts in the form of equity repurchases or dividends. The results
suggest that firms that benefit from a safety premium embedded in the price of their liabilities are
likely to be financially unconstrained.
35
1.7 Robustness and Additional Tests
1.7.1 Is the Cross-basis Really Capturing Variation in the Safety Premium?
To validate the cross-basis as measure of the relative safety premium in corporate bonds, it is
important to consider factors that could influence the cross-basis that are not related to the aggre-
gate safety premium or the firm specific perceived safety. The first point worth noting is that any
frictions that affect all bonds or CDSs equally affect the CDS-bond basis, but they do not affect
the cross-basis. Second, frictions that are not systematically correlated with firms’ fundamentals
would make the cross-basis measurement noisy, but would not jeopardize the validity of the anal-
yses on how firms respond to safety premium variation. The frictions of concern are then those
likely to exhibit strong cross sectional correlation with the reference firm’s fundamentals, such as
credit quality.
Bai and Collin-Dufresne (2019) present a list of factors that could explain the cross sectional
variation of CDS-bond basis. From this list, the factors of concern for my study are counterparty
risk and bond liquidity. I add to that the restructuring uncertainty and mismatch in the payoff
structure of bonds. In this section, I discuss in detail why each one of these factors is unlikely to
be a first-order concern in validating cross-basis as a measure of the safety premium.
Before I start, it is worth noting that, after a thorough study of the cross section of the CDS-bond
basis, Bai and Collin-Dufresne (2019) conclude that only credit rating is consistently significant
in explaining the cross sectional variations of the basis, indicating that collateral quality is always
relevant in explaining the cross sectional variation in the CDS-bond basis. Since collateral value is
one of the safety services of interest, this result is reassuring of the interpretation of the cross-basis
as a relative safety premium measure.
36
Can it be counterparty risk?
In case of a credit event, the protection seller of the CDS contract must deliver the face value
of the bond in exchange for, typically, a bond from an eligible pool. Though, if the protection
seller counterparty defaults (or has defaulted) when the underlying firm defaults, then the CDS
protection expires worthless. This is called counterparty risk.
The evidence is that counterparty risk is small in CDS contracts. Arora et al. (2012) use the
Lehman default to assess the premium associated with counterparty risk. In the authors’ own
words, they find that counterparty effects on CDS prices are “vanishingly small." The modest
size of counterparty risk is also documented by Du et al. (2017). There are some reasons that
rationalize why the counterparty risk is likely to be small. First, CDS are highly collateralized;
second, derivative contracts are senior liabilities in case of counterparty default; third, the typical
counterparty is a large bank, or more recently, very often a central counterparty,22, all of which have
a low probability of default. The combination of a high concentration of counterparty entities for
single-name CDS, together with the small counterparty risk, makes it unlikely that the counterparty
risk is the main driver of the cross sectional variation in the CDS-bond basis.
Can it be restructuring risk?
Bond investors might incur losses due to credit restructuring events that do not trigger the CDS
payment under the “No Restructuring" (XR) CDS contract. This friction would make the hedged
bond carry a credit risk. The evidence though is that restructuring risk is also small. I am able
to measure the premium that investors are willing to pay for restructuring risk by comparing the
prices for different restructuring clauses. By comparing the difference in prices to buy protection
for the same entity at the same time, I find that the difference in prices accounts for less than few
basis points of the CDS spread, and moreover it has small explanatory power for cross sectional
regressions. The small premium paid for restructuring risk is consistent with the magnitude found
22Following the great financial crisis, regulatory changes moved the market to become more centrally clearedthrough a CCP, as recommended by the Dodd-Frank Act in 2009.
37
by Berndt et al. (2007).
Can it be mismatch between the payoff structure of the bond and that of the CDS?
Another issue that potentially affects the CDS-bond basis is the mismatch between the payoff
structure of the bond and that of the CDS. For instance, the typical corporate bond has a fixed
coupon with semiannual coupon payments, whereas a CDS has fixed spreads paid quarterly. It
is also typical that in case of default, the CDS protection buyer has to pay the accrued interest
from the last coupon payment to the CDS protection seller, whereas the holder of the bond would
not necessarily receive the last coupon. Furthermore, the credit spread might not be the ideal
comparison to the CDS spread, since the typical bond is fixed rate rather than floating.23
The CDS-spread Par Equivalent CDS (PECS) method to calculate the CDS-bond basis is a
well-known methodology that accommodates the differences in payoff structure of the bond and
the CDS.24 In the appendix, I recalculate the basis using the PECS methodology and I show the
assumptions necessary to achieve the equivalence between equation (1.15) and the PECS basis.
The result is that the CDS-bond basis calculated with the PECS methodology is very similar to
the simplified method described in equation (1.15). The disadvantage of the PECS methodology
is that it is more vulnerable to outliers. For this reason, I use the CDS-bond basis introduced in
equation (1.17) as my benchmark measure. As shown in A.6, results are qualitatively unchanged
when using PECS.
Can it be liquidity?
Finally, differences in the cross-basis could be driven by differences in market liquidity of the
underlying bond. One could think that bond yields are noisy proxies for the true price because of
lack of trading or high bid-ask spreads, and that this noise is correlated with bond characteristics
such as ratings. I deal with this concern by testing how much of the cross sectional variation of
23Duffie (1999), the ideal corporate spread to compute the CDS-bond basis would be that of a floating rate bond.This issue is also studied by Longstaff et al. (2005).
24PECS was developed by JP Morgan. For further details see Elizalde, Doctor, and Saltuk (2009). PECS is alsothe methodology used in Bai and Collin-Dufresne (2019).
38
the CDS-bond basis is explained by bid-ask spread or turnover. As shown by the r-squares of
regressions in columns (5)−(7) of Table 1.5, the two variables together add very little explanatory
power. These results alleviate concerns related to the mis-measurement in the cross-basis due to
bond iliquidity.
Clearly, the notion of liquidity goes beyond measures of bid-ask spreads and turnover. For
example, in Holmstrom and Tirole (2001), assets earn a liquidity premium whenever they are good
“reserve assets," simply because they offer better insurance than others against income shortfalls
and other liquidity needs. Liquidity is also related to assets’ exposure to adverse selection, and
information-insensitive assets are likely to be more liquid (see, e.g. Dang et al. (2015)). In both
cases, assets with stable cash flows are more likely to be liquid.
Indeed the regulatory development of Dodd-Frank has induced a demand for safety directly
linked to liquidity considerations. Banking institutions are now required to hold in their balance
sheet a particular fraction of assets deemed to be liquid (the liquidity coverage ratio or LCR).
Amongst the assets that can meet the LCR is high quality corporate debt as level 2B assets.25
In my terminology this is akin to an increase in the demand for safety, which translates into an
increase in demand for corporate debt. Liquidity and safety are thus fundamentally intertwined.
1.7.2 Delayed Reactions: Effect of Safety Premium in Different Time Hori-
zons
There is large evidence that firms’ financial and investment decisions can be lumpy and de-
layed. In Section 1.6, I found that the cross-basis forecasts higher debt issuance and does not
forecast investment in the span of one quarter. It is interesting to check whether these results are
robust when considering longer response periods. To this end, I re-estimate regressions in Model
(R1) and Model (R3) considering different horizons of the y-variable.
25For details see the Federal Register Vol.79 No.197., Department of the Treasury (2014). The directive allows forcorporate debt of non-finanacial firms that meet the definition of “investment grade” under 12 CFR to be part of Level2B high-quality liquid assets (HQLA). According to the agencies, “meeting this standard is indicative of lower overallrisk and, therefore, higher liquidity for a corporate debt security." (pg. 61459)
39
Figure 1.9 shows regression coefficients and 5% confidence intervals for dependent variables 1
to 8 quarters ahead. Panel (a) plots β1 coefficient of Model (R1). This picture shows that the effect
of cross-basis on net issuance is concentrated in the first quarter, and there is no evidence of lagged
responses.
Panels (b)−(g) of Figure 1.9 show β1 coefficients for Model (R3). The dependent variables
are the same as in Table 1.9. In this case, coefficients are interpreted as firms’ future response to
a variation on the cross-basis conditional on positive net debt issuance at t. I do not find evidence
that firms that issue debt in response to a high cross-basis respond by investing more in any period
ahead. The response is concentrated in net payouts in the one quarter ahead.
In summary, by looking at different horizons, I do not find evidence of pronounced delay in
firms’ behavior that contradicts the previous section’s conclusions.
1.7.3 Limits to Arbitrage and the Demand for Safety
If we depart from the representative investor economy, there could be investors that value
safety services and investors that do not. Investors that do not value safety services are natural
arbitrageurs that can supply safety services by shorting safe assets. In this economy a positive
safety premium will only exist in equilibrium if there are arbitrage costs related with supplying
safe assets. Furthermore, the equilibrium aggregate safety premium must be both the marginal
utility of consuming one extra unit on safety services and the marginal cost of arbitrageurs of
supplying this unit.
Clearly violations of the law of one price cannot be too high. In A.7, I develop an alternative
model that explicitly incorporates arbitrageur along the lines of Gârleanu and Pedersen (2011). I
also develop an example on how an arbitrageurs can exploit the negative CDS-bond basis trade,
and specifically link it to the implicit cost of capital of the arbitrageur (see also Boyarchenko et al.
(2018) and Bai and Collin-Dufresne (2019)).26 As it is intuitive, this cost of capital places a upper
26I would like to thank Aref Bolandnazar for helpful discussions about the CDS contract margins requirements,which are necessary to properly calculate the cost of arbitrage of the negative CDS-bond basis trade.
40
bound on the CDS-bond basis, and thus how much prices can deviate from the discounted cash
flows on account of the demand for safety.
More broadly, the higher regulatory cost imposed on intermediaries since the Great Financial
Crisis have forced many of them on the side of the demand for safety rather than on the supply.
Intermediaries now have to hold particular securities in order to meet liquidity or capital require-
ments, for example. When these constraints bind, their activities as arbitrageurs are curtailed.27.
Thus the high correlation in the different measures of violations of arbitrage relations that have
been observed since the passage of the new, more stringent regulatory framework for financial in-
stitutions around the world. For instance, in my case the average cross-basis for IG bonds is highly
correlated with the magnitude of violations of other apparent arbitrage trades such as the dollar
CIP-deviation described in Du et al. (2018).
1.8 Conclusion
In this paper, I study the role of non-financial corporations in the supply of safe assets. I argue
that corporate debt of highly rated firms, while not completely insulated from credit risk, has some
of the safety features needed to function as a store of value, as collateral, or as regulatory capital.
Thus, corporate debt can serve as imperfect substitutes for traditional safe securities such as US
Treasuries, other developed countries’ sovereign debt, and highly rated asset-backed securities. In
this case, by issuing debt, corporate managers may capture the premium investors are willing to
pay for safe assets.
The paper introduces a model of the supply of safety services by non-financial corporates. The
model generates testable predictions regarding the safety premium component in corporate debt
prices and about the firm’s response to variation in the safety premium. The paper innovates in
modeling corporate debt as supplying safety services to varying degrees; that is, safety is not bi-
27A rapidly growing literature explores how the balance sheet cost of financial intermediaries can address violationsof the law of one price in a variety of markets, as well as the effect on market liquidity and volume. Some examplesare Du et al. (2018), Duffie (2018),Andersen et al. (2019), Fleckenstein and Longstaff (2020), Bolandnazar (2020),among others.
41
nary, as has been traditionally assumed in the literature, but rather it varies smoothly between the
safety provided by US Treasuries and that of an asset that provides no safety services whatsoever.
This innovation allows me to exploit cross sectional differences in bond prices to identify firm spe-
cific components of the safety premium without the need to estimate the aggregate safety premium,
an estimation which is often contentious.
I introduce a novel measure of this relative safety premium, the cross-basis, and I show that
firms with a higher cross-basis issue more debt. I argue that this is because firm managers cre-
ate additional shareholder value, above the value associated with standard business operations, by
engaging in the supply of safety services. The supply of safety services by non-financial corpo-
rates, through corporate debt issuance, only occurs when the supply of safety services is in limited
supply relative to the demand for safety. This paper is the first to offer a model of the supply of
safety services and to show the existence of an upward sloping supply curve among non-financial
corporates.
Much remains to be done to understand the market for safety services, in particular what de-
termines the time series variation in the demand and supply of safety. First, as already mentioned,
a key building block of my framework is the observation that different securities provide different
degrees of safety services. US Treasury officials are on record as stating that they do not take into
account the level of the demand for safety in their decisions regarding the supply of Treasuries.
Thus one can safely assume that the sources of variation in the supply of safety services is exoge-
nously driven by the funding needs of the US government, as has been traditionally assumed in the
literature. Moreover, informal accounts of the years leading up to the global financial crisis suggest
that the financial services sector was in the business of providing safety services. However, regu-
lation after the financial crisis seems to have greatly impaired the ability of the financial sector to
increase the supply of safety services. Is this in fact the case? And, is this the reason non-financial
corporations are in the business of supplying safety services? The image that my model suggests is
that there are multiple suppliers of safety services with different marginal costs of supplying these
services, and that the non-financial corporate sector is one such supplier.
42
In addition, progress needs to be made on the determinants of the demand for safety. The
literature, and this paper is no exception, takes the demand for safety services as a primitive, and
models it in reduced form. But these safety services are tangible. For example, the ability of
a particular asset to relieve liquidity or regulatory constraints, while challenging to measure, in
principle could be observed and measured. Thus, it would be helpful to link exogenous sources of
variation in liquidity or capital requirements to changes in asset premia in a way that establishes
the presence of a particular channel in the demand for safety. Moreover, it might be that agents
experience a particular form of psychological relief when holding certain assets that is not captured
by the cash flow characteristics of the asset in question. This consideration may suggest the need
for further development of a behavioral theory of taste for safety.
This paper shows that the safety premium affects the yields of a much broader class of financial
assets than has been recognized. Additionally, safety may explain part or all of a puzzling present
phenomenon. Yields on financial assets, across classes and jurisdictions, have been extraordinarily
low for years. Why should this be so? The safety premium may contribute to such consistently and
extraordinarily low yields, as investors who would otherwise have demanded higher risk premia
have instead been constrained in holding assets that offer some safety services. As markets and
contracts develop greater complexity in collateral requirements, insurance considerations, and reg-
ulation, we can expect the safety premium to be even more central in explaining the cross section
of asset prices.
43
Figures
Figure 1.1: Corporate Safety Premium and Bond Price
(a) Corporate safety premium (b) Corporate bond price
This figure shows how, for a fixed level of investment, the corporate safety premium and corporate bond price varywith the amount of bonds issued. Each line shows the value for different levels of aggregate safety premium denotedby ϕ.
44
Figure 1.2: Firm’s Total Value as a Function of Debt Issuance
(a) No bankruptcy cost (ξ = 0) (b) Positive bankruptcy cost (ξ = 0.3)
This figure shows how, for a fixed level of investment, the total value of the firm varies with the amount of bondsissued. Each area shows the value for different levels of UST safety premium denoted by ϕt. The dashed line is thevalue of b that maximizes the value of the firm for each value of ϕt.
45
Figure 1.3: Response to Perceived Safety
(a) Unconstrained optimal debt issuance (b) Constrained optimal debt issuance
(c) Unconstrained optimal investment (d) Constrained optimal investment
(e) Unconstrained optimal dividends (f) Constrained optimal dividends
This figure shows optimal debt issuance, optimal investment, and optimal dividends as a function of the firm-specificperceived safety, αi,t, for different levels of the aggregate safety premium, ϕt. The plots on the left are for a firm thatis financially unconstrained, and the plots on the right are for a firm that is financially constrained.
46
Figure 1.4: Response to Aggregate Safety Premium
(a) Unconstrained optimal debt issuance (b) Constrained optimal debt issuance
(c) Unconstrained optimal investment (d) Constrained optimal investment
(e) Unconstrained optimal dividends (f) Constrained optimal dividends
This figure shows optimal debt issuance, optimal investment, and optimal dividends as a function of the aggregatesafety premium, ϕt, for different levels of perceived safety, αi,t. The plots on the left are for a firm that is financiallyunconstrained, and the plots on the right are for a firm that is financially constrained.
47
Figure 1.5: Interaction Effects of Bond Issuance Response to Safety Premium
0.00 0.01 0.02 0.03 0.04 0.05φt
0.05
0.10
0.15
∂bt+1
∂αt
(a) Bond issuance response to αi,t
0.0 0.2 0.4 0.6 0.8 1.0αt0
2
4
6
8
∂bt+1
∂φt
(b) Bond issuance response to ϕt
This figure shows how optimal bond issuance responds to perceived safety αi,t as function of ϕt, and how optimalbond issuance responds to perceived safety ϕt as function of αi,t.
Figure 1.6: Heterogeneous Effects on Bond Issuance Due to Initial Net Worth
0.0 0.1 0.2 0.3 0.4 0.5wt
0.02
0.04
0.06
0.08
∂bt+1
∂αt
constrained firm unconstrained firm
(a) Bond issuance response to αi,t
0.0 0.1 0.2 0.3 0.4 0.5wt
2
4
6
8
∂bt+1
∂φt
constrained firm unconstrained firm
(b) Bond issuance response to ϕt
This figure shows how the optimal bond issuance responds to perceived safety αi,t and ϕt as a function of the initialnet worth wi,t. Firms with low net worth are financially constrained, and firms with high net worth are not financiallyconstrained. These curves are calculated from applying the implicit function theorem to firms’ first-order conditions.
48
Figure 1.7: The CDS-bond Basis
−10.0
−7.5
−5.0
−2.5
0.0
2004 2006 2008 2010 2012 2014 2016 2018 2020
CD
S−
bond
bas
is (
%)
AAA and AA A BBB BB B and Below
This figure shows the times series of the CDS-bond basis across ratings. The CDS-bond basis is the difference betweenthe CDS spread and the bond’s implied credit spread. For each rating class, the CDS-bond basis is the face-valueweighted average.
Figure 1.8: US Treasury Safety Premium.
0
1
2
3
4
5
6
2004 2006 2008 2010 2012 2014 2016 2018 2020
Val
ue (
%)
UST SP ( ϕt ) AAA credit−spread (K−VJ) BBB − (AAA and AA) basis−spread Box (BDM)
This picture shows the time series of different measures of the US Treasury safety premium. All measure definitionsare described in detail in A.2.
49
Figure 1.9: Effect of Cross-Basis on Firms’ Decisions for Different Time Horizons.
−0.1
0.0
0.1
1 2 3 4 5 6 7 8Quarter
Est
imat
e
(a) Net debt issuance
−0.1
0.0
0.1
1 2 3 4 5 6 7 8Quarter
Est
imat
e
(b) Payout
−0.1
0.0
0.1
1 2 3 4 5 6 7 8Quarter
Est
imat
e
(c) Capital investment
−0.1
0.0
0.1
1 2 3 4 5 6 7 8Quarter
Est
imat
e
(d) Intangible investment
−0.1
0.0
0.1
1 2 3 4 5 6 7 8Quarter
Est
imat
e
(e) Acquisitions
−0.1
0.0
0.1
1 2 3 4 5 6 7 8Quarter
Est
imat
e
(f) Financial investment
−0.1
0.0
0.1
1 2 3 4 5 6 7 8Quarter
Est
imat
e
(g) ∆Cash
This picture shows regression coefficients in the y-axis and 1 to 8 quarters ahead in the x-axis. Panel (a) plots the cross-basis regression coefficients, β1, of Model (R1). Panels (b) - (g) plots the interaction cross-basis and debt issuancedummy coefficient, β1, of Model (R3) for different dependent variables. The shaded area is the estimated coefficient95% confidence interval. Standard errors are clustered by both firm and time. Data is quarterly from 2003Q1 to2019Q3.
50
1.9 Tables
Table 1.1: Calibration
Parameter Description Value Target
ζ Decreasing returns to scale 0.65 Kuehn and Schmid (2014)
δ Depreciation rate 0.03 Kuehn and Schmid (2014)
ξ Bankruptcy costs 0.30 Crouzet (2018)
ρz Idiosy. shock persistence 0.85 Kuehn and Schmid (2014)
σz Idiosy. shock volatility 0.15 Kuehn and Schmid (2014)
ρx Agg. shock persistence 0.89 Begenau and Salomao (2019)
σx Agg. shock volatility 0.0093 Begenau and Salomao (2019)
β Rate of time preference 0.996 Kuehn and Schmid (2014)
γ Relative risk aversion 7.5 Kuehn and Schmid (2014)
51
Table 1.2: Number of Bonds and Firms with Valid CDS-Bond Basis
Number of Bonds Number of Firms
Year AAA and AA A BBB BB B and Below Total AAA and AA A BBB BB B and Below Total
2003 114 676 1054 301 197 2342 18 85 128 64 37 332
2004 103 634 1023 376 272 2408 16 92 146 79 60 393
2005 106 653 1006 485 317 2567 16 100 166 106 79 467
2006 117 641 900 413 361 2432 19 105 174 95 82 475
2007 144 620 896 363 408 2431 19 91 168 95 103 476
2008 130 609 886 348 352 2325 19 78 159 102 94 452
2009 128 637 979 324 335 2403 17 79 171 82 75 424
2010 166 648 1038 317 341 2510 18 79 171 79 75 422
2011 180 789 1078 362 311 2720 17 84 174 89 59 423
2012 253 922 1106 364 297 2942 21 90 167 87 63 428
2013 273 944 1213 347 267 3044 21 89 162 76 54 402
2014 288 931 1263 332 227 3041 21 85 159 71 40 376
2015 326 987 1435 360 212 3320 22 82 164 78 41 387
2016 365 936 1514 319 219 3353 23 73 166 71 46 379
2017 380 927 1550 275 203 3335 23 68 159 59 39 348
2018 339 951 1628 248 179 3345 22 69 153 52 34 330
2019 286 1010 1572 255 148 3271 19 73 138 50 32 312
2020 279 1076 1566 341 125 3387 15 70 131 47 26 289
avg 221 811 1206 341 265 2843 19 83 159 77 58 395
This table shows the number of distinct bonds and distinct firms in the sample per year and rating bucket. The last rowshows the average annual numbers during the sample. Data is from January 2003 to September 2020.
52
Table 1.3: Firm-Level Summary Statistics
Statistic N Mean St. Dev. Pctl(25) Median Pctl(75)
Basis (%) 19,227 −1.149 1.168 −1.393 −0.850 −0.536
Cross basis (%) 19,227 −0.228 0.942 −0.418 −0.052 0.220
Credit-spread (%) 19,227 2.590 2.391 1.191 1.839 3.251
CDS-spread (%) 19,227 1.461 1.792 0.482 0.874 1.724
Net Debt Issuance (% lag assets) 19,227 0.324 3.329 −0.555 −0.009 0.232
I{ DebtIssuance } 19,227 0.307 0.461 0 0 1
Net Payout (% lag assets) 19,227 0.012 1.362 0 0 0
ST Debt Net Issuance (% lag assets) 19,227 1.090 1.644 0.102 0.595 1.601
CAPEX (% lag assets) 19,227 1.287 1.321 0.496 0.899 1.576
Capital Investment (% lag assets) 19,227 1.224 1.255 0.464 0.864 1.529
R&D (% lag assets) 19,227 0.387 0.791 0.000 0.000 0.452
.3 × SGA (% lag assets) 19,227 1.057 1.046 0.362 0.733 1.362
Intangible Investment 19,227 1.444 1.300 0.463 1.026 2.187
Acquisitions (% lag assets) 19,227 0.515 2.289 0 0 0.1
Financial Investment (% lag assets) 19,227 0.016 1.145 −0.003 0.000 0.012
∆ Cash (% lag assets) 19,227 0.152 2.991 −0.869 0.044 1.094
Net Operating Cash Flows (% lag assets) 19,227 4.051 3.095 2.173 3.674 5.578
Other Cash Flows (% lag assets) 19,227 0.068 2.431 −0.174 0.004 0.214
Total Assets ($ Bi) 19,227 27.339 46.642 5.810 12.107 27.952
CHE (% assets) 19,227 8.718 8.807 2.547 5.782 11.986
ROA (%) 19,227 3.449 2.023 2.381 3.314 4.377
Leverage Ratio (%) 19,227 30.997 13.776 20.878 29.177 39.575
Long-term Leverage Ratio (%) 19,227 27.574 13.492 17.678 25.648 35.545
This table shows the firm-level quarterly data summary statistics. Mean, median, standard deviation, and selectedpercentiles are presented. For comparability, the statistics for the Compustat sample are presented based on the sametime period. Data is quarterly from 2003Q1 to 2019Q3. See A.1.1 for the details on the construction of each variable.
53
Table 1.4: CDS-bond Basis Summary Statistics
Panel A: Full Sample
Statistic N Mean St. Dev. Pctl(25) Median Pctl(75)
Cross-basis 68,463 −0.256 1.183 −0.453 −0.052 0.239
Basis 68,463 −1.179 1.404 −1.417 −0.851 −0.513
Yield 68,463 5.231 3.130 3.395 4.806 6.267
Credit-spread 68,463 2.815 3.101 1.212 1.921 3.477
CDS-spread 68,463 1.666 2.416 0.491 0.914 1.924
Panel B: Pre-GFC (January 2003 – November 2007)
Statistic N Mean St. Dev. Pctl(25) Median Pctl(75)
Cross-basis 19,026 −0.114 0.468 −0.295 −0.054 0.143
Basis 19,026 −0.887 0.501 −1.095 −0.810 −0.587
Yield 19,026 6.036 1.583 5.084 5.798 6.749
Credit-spread 19,026 2.055 1.526 1.055 1.562 2.599
CDS-spread 19,026 1.201 1.571 0.292 0.572 1.543
Panel C: During GFC (December 2007 – June 2009)
Statistic N Mean St. Dev. Pctl(25) Median Pctl(75)
Cross-basis 6,535 −0.783 3.013 −1.085 −0.245 0.398
Basis 6,535 −3.067 3.255 −3.555 −2.191 −1.563
Yield 6,535 9.117 6.654 5.827 7.319 9.620
Credit-spread 6,535 6.544 7.018 2.859 4.546 7.250
CDS-spread 6,535 3.492 5.474 0.741 1.639 3.943
Panel D: Post-GFC (July 2009 – September 2020)
Statistic N Mean St. Dev. Pctl(25) Median Pctl(75)
Cross-basis 42,902 −0.239 0.837 −0.504 −0.034 0.277
Basis 42,902 −1.021 0.904 −1.330 −0.775 −0.428
Yield 42,902 4.282 2.071 2.950 3.780 5.132
Credit-spread 42,902 2.585 2.094 1.213 1.868 3.373
CDS-spread 42,902 1.594 1.745 0.581 0.976 1.867
This table shows the summary statistics for the cross-basis, defined as the basis minus the basis index, where thebasis index is the face-value weighted average of all basis in the sample; the basis, defined as the difference betweencredit spread and maturity-matched CDS spread; corporate bond yield; credit spread (over US Treasury); and the CDSspreads. Data is monthly and the full sample is from January 2003 to September 2020. Panels B, C, and D shows thesame summary statistics for different sample windows. 54
Table 1.5: CDS-Bond cross section Analyses
Dependent variable:
Cross-basis
(1) (2) (3) (4) (5) (6) (7)
A −0.169∗∗∗ −0.165∗∗∗ −0.167∗∗∗ −0.162∗∗∗
(0.011) (0.011) (0.011) (0.010)
BBB −0.573∗∗∗ −0.538∗∗∗ −0.582∗∗∗ −0.547∗∗∗
(0.032) (0.031) (0.032) (0.031)
BB −0.947∗∗∗ −0.907∗∗∗ −0.977∗∗∗ −0.935∗∗∗
(0.045) (0.044) (0.047) (0.045)
B and Below −1.132∗∗∗ −1.060∗∗∗ −1.187∗∗∗ −1.114∗∗∗
(0.084) (0.080) (0.086) (0.082)
Rating rank −0.102∗∗∗
(0.007)
ICR −0.671∗∗∗
(0.056)
αi 1.159∗∗∗
(0.073)
Bid-ask spread −0.219∗∗∗ −0.213∗∗∗
(0.018) (0.019)
Turnover 0.008∗∗∗ 0.008∗∗∗
(0.001) (0.001)
Constant 0.349∗∗∗ 0.718∗∗∗ −0.113∗∗∗ −0.418∗∗∗ 0.451∗∗∗ 0.297∗∗∗ 0.397∗∗∗
(0.020) (0.055) (0.011) (0.023) (0.025) (0.018) (0.023)
Observations 66,549 66,549 62,964 62,964 66,549 66,549 66,549R2 0.255 0.249 0.119 0.105 0.269 0.264 0.278
Note: ∗p<0.1; ∗∗p<0.05; ∗∗∗p<0.01
This table presents Fama-MacBeth regression results of cross-basis on bond characteristics, as specified in equation(1.19). In Column (1), the proxy for safety is the rating buckets categorical variables: AAA and AA, A, BBB, BB,and B and below, the first category is omitted due to multicollinearity. In Column (2), the proxy for safety is ratingrank, which is equal to 1 if the bond is rated AAA, 2 if the bond is rated AA+, 3 if the bond is rated AA, etc. InColumn (3), the proxy for safety is the interest coverage ratio (ICR) at the firm level, which is the total long-term debtdivided by EBITA; both variables are quarterly and extracted from Compustat. In column (4), the proxy for safety isthe structurally estimated perceived safety αi,tas described in A.2. Data is monthly from January 2003 to September2020. Standard errors are shown in parenthesis.
55
Table 1.6: Treasury Safety Premium Proxies
(a) Summary Statistics
Statistic N Mean St. Dev. Pctl(25) Median Pctl(75)
UST SP 213 1.299 0.845 0.859 1.060 1.394
AAA credit-spread (K-VJ) 213 0.800 0.331 0.617 0.718 0.857
AAA and AA - BBB basis-spread 213 0.440 0.324 0.255 0.338 0.506
Box (BDG) 171 0.371 0.204 0.250 0.325 0.420
(b) Correlation Matrix
UST SP AAA credit-spread (K-VJ) BBB - (AAA and AA) basis-spread Box (BDG)
UST SP 1
AAA credit-spread (K-VJ) 0.887 1
BBB - (AAA and AA) basis-spread 0.900 0.697 1
Box (BDG) 0.573 0.650 0.286 1
This table shows the summary statistics and correlation matrix of different proxies for US Treasury safety premium.A.2 describes the details of the estimation of each of those proxies. Data is monthly from January 2003 to September2020 if available.
56
Table 1.7: CDS-Bond Time Series Analyses
Panel A: UST SP (ϕT )
rating β0 βr t-stat(β0) t-stat(βr) R2
AAA and AA -0.146 0.393 -10.329 43.112 0.898
A -0.094 0.227 -7.045 26.397 0.768
BBB -0.028 -0.073 -3.355 -13.253 0.454
BB -0.092 -0.285 -2.842 -13.581 0.466
B and Below 0.131 -0.551 1.946 -12.689 0.433
Panel B: AAA−Treasury Spread
rating β0 βr t-stat(β0) t-stat(βr) R2
AAA and AA -0.294 0.823 -7.429 17.998 0.606
A -0.171 0.465 -6.080 14.332 0.493
BBB 0.020 -0.178 1.585 -12.362 0.420
BB 0.077 -0.674 1.560 -11.873 0.400
B and Below 0.384 -1.212 3.661 -9.989 0.321
Panel C: BBB−(AAA and AA) CDS-Bond Basis Spread
rating β0 βr t-stat(β0) t-stat(βr) R2
AAA and AA -0.070 0.989 -4.249 32.680 0.835
A -0.056 0.585 -4.410 25.058 0.748
BBB -0.039 -0.191 -5.025 -13.380 0.459
BB -0.154 -0.702 -4.929 -12.222 0.415
B and Below -0.029 -1.265 -0.432 -10.300 0.335
Panel D: Box-Trade Spread
rating β0 βr t-stat(β0) t-stat(βr) R2
AAA and AA 0.100 0.765 1.780 5.779 0.165
A 0.106 0.299 2.889 3.460 0.066
BBB -0.050 -0.206 -3.585 -6.282 0.189
BB -0.384 -0.212 -6.644 -1.556 0.014
B and Below -0.290 -0.776 -2.504 -2.837 0.045
This table shows the results of the time series regressions specified in equation (1.20). The dependent variable is theface-value weighted average cross-basis for each rating bucket. Each panel corresponds to a different proxy for theUS Treasury safety premium. A.2 describes the details of the construction of each of those proxies. Data is monthlyfrom January 2003 to September 2020 if available.
57
Table 1.8: Impact of Safety Premium on Net Debt Issuance
Dependent variable:
Net Debt Issuance(% of Lag Assets) at t+ 1
(1) (2) (3) (4) (5) (6) (7) (8)
Cross-basis 0.100∗∗∗ 0.090∗∗ 0.079∗∗ 0.077∗∗
(0.032) (0.035) (0.034) (0.034)
USTreas SP × HighCBB 0.120∗∗ 0.115∗∗
(0.051) (0.050)
USTreas SP × A and Above 0.134∗∗ 0.155∗∗∗
(0.055) (0.055)
HighCBB 0.041 −0.021(0.102) (0.100)
A and Above 0.383∗∗∗ 0.156(0.134) (0.133)
CDS-spread −0.106∗∗∗ −0.095∗∗∗ −0.043∗ −0.039 −0.112∗∗∗ −0.042 −0.084∗∗∗ −0.011(0.025) (0.029) (0.026) (0.026) (0.024) (0.026) (0.021) (0.022)
log(Total Assets) −0.905∗∗∗ −0.936∗∗∗ −0.829∗∗∗ −0.815∗∗∗ −0.892∗∗∗ −0.806∗∗∗ −0.887∗∗∗ −0.800∗∗∗
(0.154) (0.148) (0.138) (0.138) (0.151) (0.136) (0.151) (0.144)
CHE (% assets) −0.024∗∗∗ −0.025∗∗∗ −0.027∗∗∗ −0.027∗∗∗ −0.025∗∗∗ −0.027∗∗∗ −0.025∗∗∗ −0.027∗∗∗
(0.008) (0.008) (0.008) (0.008) (0.008) (0.008) (0.007) (0.008)
Tobin’s Q 0.005 0.006 0.028∗∗∗ 0.027∗∗∗ 0.006 0.027∗∗∗ 0.006 0.026∗∗∗
(0.005) (0.005) (0.007) (0.007) (0.005) (0.007) (0.005) (0.007)
Leverage Ratio (%) −0.059∗∗∗ −0.058∗∗∗ −0.058∗∗∗ −0.056∗∗∗
(0.008) (0.008) (0.008) (0.007)
ROA (%) 0.020 0.021 0.020(0.014) (0.014) (0.014)
Firm FE Yes Yes Yes Yes Yes Yes Yes YesTime FE Yes Yes Yes Yes Yes Yes Yes YesRating FE No Yes Yes Yes No Yes No No
Observations 19,227 19,227 19,227 19,227 19,227 19,227 19,227 19,227R2 0.065 0.066 0.077 0.077 0.065 0.077 0.066 0.077Adjusted R2 0.031 0.031 0.043 0.043 0.031 0.043 0.031 0.043
Note: ∗p<0.1; ∗∗p<0.05; ∗∗∗p<0.01
This table presents regression results of net debt issuance on different measures of the safety premium in corporatedebt, as described in (R1) and (R2). The y-variable is net debt issuance normalized by lag total assets in quarter t+ 1.The x-variables of interest are the cross-basis, defined as the CDS-bond basis minus the basis index; HighCBB, anindicator variable equal to 1 if the firm belongs to the highest quintile of cross-basis and 0 otherwise; “A and Above",an indicator variable equal to 1 if the firm is rated A- and above and 0 otherwise; and the US Treasury safety premium(UST SP). All independent variables are measured in quarter t. Standard errors are reported in parenthesis and areclustered by time. Data is quarterly from 2003Q1 to 2019Q3. See A.1.1 for the details on the construction of variablesand controls.
58
Table 1.9: Impact of Safety Premium on Firms’ Decisions
Dependent variable:
Net PayoutCapital
InvestmentR & D SG & A
Intangible
InvestmentAcquisitions
Financial
Investment∆ Cash
(1) (2) (3) (4) (5) (6) (7) (8)
Cross-basis × DebtIssuance 0.044∗∗∗ 0.018 −0.002 0.003 0.001 −0.080 0.015 −0.052(0.016) (0.016) (0.005) (0.004) (0.006) (0.056) (0.021) (0.051)
Cross-basis 0.041∗∗ 0.035∗∗ 0.002 0.005∗ 0.007∗ 0.035 0.008 −0.016(0.018) (0.015) (0.003) (0.002) (0.004) (0.023) (0.008) (0.022)
DebtIssuance 0.301∗∗∗ 0.193∗∗∗ 0.003 0.011∗∗ 0.014∗ 0.885∗∗∗ 0.114∗∗∗ 0.891∗∗∗
(0.031) (0.013) (0.007) (0.005) (0.008) (0.081) (0.024) (0.089)
CDS-spread −0.085∗∗∗ −0.085∗∗∗ −0.005∗∗ −0.002 −0.007∗∗ −0.033∗∗ −0.010∗ −0.007(0.019) (0.018) (0.002) (0.002) (0.003) (0.014) (0.005) (0.018)
log(Total Assets) −0.229∗∗∗ −0.124∗∗∗ −0.109∗∗∗ −0.341∗∗∗ −0.450∗∗∗ −0.274∗∗∗ −0.024 −0.651∗∗∗
(0.041) (0.023) (0.010) (0.008) (0.012) (0.077) (0.033) (0.095)
CHE (% assets) 0.024∗∗∗ 0.001 −0.0003 −0.004∗∗∗ −0.005∗∗∗ 0.083∗∗∗ −0.004 −0.180∗∗∗
(0.003) (0.001) (0.001) (0.0005) (0.001) (0.009) (0.003) (0.009)
Tobin’s Q 0.017∗∗∗ 0.008∗∗∗ 0.001 0.002∗∗∗ 0.002∗∗ 0.002 −0.002 0.009(0.004) (0.002) (0.001) (0.001) (0.001) (0.004) (0.002) (0.007)
Firms FE Yes Yes Yes Yes Yes Yes Yes YesTime FE Yes Yes Yes Yes Yes Yes Yes Yes
Observations 19,227 19,227 19,227 19,227 19,227 19,227 19,227 19,227R2 0.397 0.680 0.765 0.939 0.901 0.116 0.058 0.137Adjusted R2 0.375 0.668 0.757 0.937 0.897 0.083 0.023 0.105
Note: ∗p<0.1; ∗∗p<0.05; ∗∗∗p<0.01
This table presents regression results of firms’ decisions on the safety premium in corporate debt, measured by thecross-basis, as described in equation (R3). The y-variables are (1) net payout, defined as dividends plus net equityrepurchase, (2) capital investment, defined as CAPEX plus net PPE bought, (3) R&D expenses, (4) 30% of SG&Aexpenses, (5) intangible investment, defined as R&D plus 30% of SG&A expenses, (6) acquisitions, (7) financialinvestments, and (8) change in cash from the cash flow statement. All independent variables are measured in quartert+ 1 and normalized by lag total assets. The x-variables of interest are the cross-basis, defined as the CDS-bond basisminus the basis index; and DebtIssuance, an indicator variable equal to 1 if net debt issuance is strictly positive and0 otherwise. All independent variables are measured in quarter t. Standard errors are reported in parenthesis and areclustered by time. Data is quarterly from 2003Q1 to 2019Q3. See A.1.1 for the details on the construction of variablesand controls.
59
Table 1.10: Heterogeneous Impact of Cross-Basis on Firms’ Decisions
Panel A: Investment Grade
Dependent variable:
Net Debt
IssuanceNet Payout
Capital
InvestmentR & D SG & A
Intangible
InvestmentAcquisitions
Financial
Investment∆ Cash
(1) (2) (3) (4) (5) (6) (7) (8) (9)
Cross-basis × IG 0.145∗∗ 0.114∗ −0.104∗∗∗ 0.011 0.025∗∗ 0.036∗∗ 0.224∗ 0.021 −0.104
(0.057) (0.058) (0.030) (0.009) (0.012) (0.015) (0.115) (0.047) (0.152)
Cross-basis 0.048 0.046∗ 0.104∗∗∗ −0.008∗ −0.001 −0.009 −0.021 0.007 −0.067
(0.036) (0.023) (0.025) (0.004) (0.004) (0.006) (0.045) (0.022) (0.052)
IG 0.511∗∗∗ 0.483∗∗∗ 0.198∗∗ 0.021 0.051∗∗ 0.072∗∗ 0.396 0.072 0.293
(0.102) (0.123) (0.075) (0.025) (0.024) (0.036) (0.281) (0.081) (0.235)
Controls Yes Yes Yes Yes Yes Yes Yes Yes Yes
Firms FE Yes Yes Yes Yes Yes Yes Yes Yes Yes
Time FE Yes Yes Yes Yes Yes Yes Yes Yes Yes
Observations 19,227 5,905 5,905 5,905 5,905 5,905 5,905 5,905 5,905
R2 0.066 0.450 0.765 0.772 0.947 0.907 0.244 0.192 0.233
Adjusted R2 0.032 0.384 0.737 0.744 0.940 0.896 0.153 0.095 0.141
Note: ∗p<0.1; ∗∗p<0.05; ∗∗∗p<0.01
Panel B: Cash Rich
Dependent variable:
Net Debt
IssuanceNet Payout
Capital
InvestmentR & D SG & A
Intangible
InvestmentAcquisitions
Financial
Investment∆ Cash
(1) (2) (3) (4) (5) (6) (7) (8) (9)
Cross-basis × CashRich −0.021 0.020 −0.073∗∗∗ 0.001 −0.007 −0.006 0.065 −0.088 −0.137
(0.077) (0.066) (0.026) (0.010) (0.012) (0.016) (0.194) (0.056) (0.156)
Cross-basis 0.104∗∗∗ 0.090∗∗∗ 0.095∗∗∗ −0.005 0.009∗∗ 0.004 0.041 0.031 −0.062
(0.038) (0.023) (0.021) (0.005) (0.004) (0.007) (0.059) (0.021) (0.053)
CashRich −0.296∗∗ 0.095 −0.071 0.005 −0.040∗∗ −0.035 −0.003 −0.123 −0.291
(0.140) (0.113) (0.048) (0.034) (0.018) (0.035) (0.315) (0.111) (0.299)
Controls Yes Yes Yes Yes Yes Yes Yes Yes Yes
Firms FE Yes Yes Yes Yes Yes Yes Yes Yes Yes
Time FE Yes Yes Yes Yes Yes Yes Yes Yes Yes
Observations 19,227 5,905 5,905 5,905 5,905 5,905 5,905 5,905 5,905
R2 0.066 0.448 0.764 0.772 0.947 0.907 0.243 0.192 0.233
Adjusted R2 0.031 0.381 0.736 0.744 0.940 0.896 0.152 0.095 0.141
Note: ∗p<0.1; ∗∗p<0.05; ∗∗∗p<0.01
60
Panel C: High Profitability
Dependent variable:
Net Debt
IssuanceNet Payout
Capital
InvestmentR & D SG & A
Intangible
InvestmentAcquisitions
Financial
Investment∆ Cash
(1) (2) (3) (4) (5) (6) (7) (8) (9)
Cross-basis × Profitable 0.087 −0.024 −0.149∗∗ 0.009 0.030∗ 0.039∗ −0.032 0.098 0.135
(0.094) (0.073) (0.067) (0.020) (0.016) (0.022) (0.150) (0.081) (0.160)
Cross-basis 0.087∗∗ 0.083∗∗∗ 0.085∗∗∗ −0.007∗ 0.003 −0.004 0.052 0.007 −0.106∗∗
(0.033) (0.020) (0.020) (0.004) (0.004) (0.006) (0.049) (0.024) (0.048)
Profitable 0.282∗∗∗ 0.465∗∗∗ 0.285∗∗∗ 0.054∗∗∗ 0.099∗∗∗ 0.153∗∗∗ 0.156 0.011 0.341∗∗
(0.086) (0.070) (0.062) (0.017) (0.013) (0.019) (0.162) (0.052) (0.144)
Controls Yes Yes Yes Yes Yes Yes Yes Yes Yes
Firms FE Yes Yes Yes Yes Yes Yes Yes Yes Yes
Time FE Yes Yes Yes Yes Yes Yes Yes Yes Yes
Observations 19,227 5,905 5,905 5,905 5,905 5,905 5,905 5,905 5,905
R2 0.066 0.453 0.767 0.772 0.948 0.908 0.243 0.192 0.233
Adjusted R2 0.031 0.387 0.739 0.745 0.941 0.897 0.152 0.095 0.141
Note: ∗p<0.1; ∗∗p<0.05; ∗∗∗p<0.01
Panel D: High Payout
Dependent variable:
Net Debt
IssuanceNet Payout
Capital
InvestmentR & D SG & A
Intangible
InvestmentAcquisitions
Financial
Investment∆ Cash
(1) (2) (3) (4) (5) (6) (7) (8) (9)
Cross-basis × HighPayout 0.112 −0.070 −0.014 0.016 0.031∗∗ 0.048∗∗∗ 0.255∗ −0.029 −0.009
(0.087) (0.066) (0.034) (0.017) (0.014) (0.018) (0.145) (0.056) (0.204)
Cross-basis 0.087∗∗ 0.085∗∗∗ 0.082∗∗∗ −0.006 0.004 −0.002 0.037 0.019 −0.082
(0.034) (0.019) (0.021) (0.004) (0.004) (0.006) (0.049) (0.025) (0.053)
HighPayout 0.220∗∗∗ 0.720∗∗∗ 0.021 −0.006 0.028∗∗∗ 0.022 −0.420∗∗∗ −0.051 −0.200
(0.074) (0.062) (0.027) (0.014) (0.010) (0.016) (0.117) (0.047) (0.131)
Controls Yes Yes Yes Yes Yes Yes Yes Yes Yes
Firms FE Yes Yes Yes Yes Yes Yes Yes Yes Yes
Time FE Yes Yes Yes Yes Yes Yes Yes Yes Yes
Observations 19,227 5,905 5,905 5,905 5,905 5,905 5,905 5,905 5,905
R2 0.066 0.463 0.764 0.772 0.947 0.907 0.245 0.192 0.233
Adjusted R2 0.031 0.399 0.736 0.744 0.940 0.896 0.154 0.095 0.141
Note: ∗p<0.1; ∗∗p<0.05; ∗∗∗p<0.01
61
Panel E: Large
Dependent variable:
Net Debt
IssuanceNet Payout
Capital
InvestmentR & D SG & A
Intangible
InvestmentAcquisitions
Financial
Investment∆ Cash
(1) (2) (3) (4) (5) (6) (7) (8) (9)
Cross-basis × Large 0.165 −0.073 −0.184∗∗ 0.008 −0.002 0.006 0.431∗ 0.007 −0.054
(0.115) (0.100) (0.074) (0.025) (0.014) (0.030) (0.242) (0.085) (0.194)
Cross-basis 0.091∗∗∗ 0.099∗∗∗ 0.095∗∗∗ −0.005 0.008∗ 0.003 0.022 0.014 −0.083
(0.033) (0.023) (0.020) (0.004) (0.004) (0.006) (0.049) (0.022) (0.053)
Large −0.118 −0.136 −0.138∗ −0.011 −0.014 −0.025 0.128 0.037 −0.213
(0.106) (0.100) (0.074) (0.020) (0.018) (0.028) (0.203) (0.087) (0.271)
Controls Yes Yes Yes Yes Yes Yes Yes Yes Yes
Firms FE Yes Yes Yes Yes Yes Yes Yes Yes Yes
Time FE Yes Yes Yes Yes Yes Yes Yes Yes Yes
Observations 19,227 5,905 5,905 5,905 5,905 5,905 5,905 5,905 5,905
R2 0.065 0.448 0.765 0.772 0.947 0.907 0.244 0.192 0.233
Adjusted R2 0.031 0.382 0.737 0.744 0.940 0.896 0.153 0.094 0.140
Note: ∗p<0.1; ∗∗p<0.05; ∗∗∗p<0.01
This table presents regression results of firms’ heterogeneous response to the safety premium, measured by the cross-basis, as described in equation (R4). The y-variables are (1) net debt issuance, (2) net payout, defined as dividendsplus net equity repurchase, (3) capital investment, defined as CAPEX plus net PPE bought, (4) R&D expenses, (5)30% of SG&A expenses, (6) intangible investment, defined as R&D plus 30% of SG&A expenses, (7) acquisitions,(8) financial investments, and (9) change in cash from the cash flow statement. All independent variables are measuredin time t+ 1 and normalized by lag total assets. The x-variable of interest is the cross-basis, defined as the CDS-bondbasis minus the basis index. UNC is an indicator variable equal to one if the firm belongs the 20% highest quantileof each one of the firm characteristics: CHE, profits, payout (all three as share of the total assets), and size. IG is adummy variable equal to 1 if the firm is rated BBB- or above, 0 otherwise. Standard errors are reported in parenthesisand are clustered by time. Data is quarterly from 2003Q1 to 2019Q3. See A.1.1 for the details on the construction ofvariables and controls.
62
Chapter 2
The Cross-Section of Risk and Return 1
2.1 Introduction
A common practice in the academic finance literature has been to create characteristic portfo-
lios (CPs) by sorting on characteristics positively associated with expected returns. The resulting
set of zero-investment CPs, which go long a portfolio of high characteristic firms and short a port-
folio of low characteristic firms, then serve as a model for returns in that asset space. Fama and
French (1993, 2015) are prominent examples of this approach, but there are numerous others, de-
veloped both to explain the equity market anomalies, and also the cross-section of returns in other
asset classes.2
Consistent with this, Fama and French (2015, FF) argue that a standard dividend-discount
model implies that a combination of firm characteristics based on valuation, profitability and in-
vestment should forecast firms’ average returns. Based on this they develop a five factor model—
consisting of the MktRF, SMB, HML, RMW, and CMA characteristic portfolios—and argue that
this model does well in explaining the cross-section of average excess returns for a variety of test
1This chapter is based on Daniel et al. (2020). We thank Stefano Giglio, Ravi Jagannathan, Sonia Jimenez-Garcès,Ralph Koijen, Lars Lochstoer, Maurizio Luisi, Suresh Sundaresan, Paul Tetlock, Brian Weller, Michael Wolf, DachengXiu, Leifu Zhang, as well as the participants of seminars at Amsterdam, BI Oslo, CEMFI, Cincinnati, Columbia,Kellogg/Northwestern, Michigan, TU München, Münster, UCLA, Washington University, Zürich, AQR, Barclays,Bloomberg, and the participants of conferences at the AFA, AFFI, EFA, EEA, Fordham, HKUST, Imperial College,“New Methods for the Cross Section of Returns” in Chicago, and Villanova for helpful comments and suggestions,and Dan Mechanic for his support with the computing cluster.
2Examples are: UMD (Carhart, 1997); LIQ (Pastor and Stambaugh, 2003); BAB (Frazzini and Pedersen, 2014);QMJ (Asness et al., 2019); PMU (Novy-Marx, 2013); ISU (Daniel and Titman, 2006) and RX and HML-FX (Lustiget al., 2011).
63
portfolios, based on a set of time-series regressions like:
rp,t = αp + bp,mrMktRF,t + bp,HMLrHML,t + bp,SMBrSMB,t
+bp,CMArCMA,t + bp,RMW rRMW,t + εp,t (2.1)
SMB, HML, RMW, and CMA are characteristic portfolios, formed by sorting on various com-
binations of firm size, valuation ratios, profitability and investment respectively. Fama and French
(1993, 2015) refer to these characteristic portfolios as “mimicking portfolios” or “factors”.3
Standard projection theory shows that the intercepts (αs) from these regressions will be zero
for all test assets if and only if the mean variance efficient (MVE) portfolio is in the span of the
CPs, or equivalently, if the maximum Sharpe ratio in the economy is the maximum Sharpe ratio
achievable with the CPs alone. Despite several critiques of this methodology, it remains popular in
the finance literature.
This paper is concerned with the standard procedure employed when constructing these CPs.
We show that, if characteristics are a good proxy for expected returns, then forming CPs by sorting
on characteristics alone will generally not explain the cross-section of returns in the way proposed
in the literature. The argument is based on the early insights of Markowitz (1952) and Roll (1977).
Suppose a set of characteristics are positively associated with expected returns, and a correspond-
ing set of long-short CPs are constructed by buying high characteristic stocks and shorting low
characteristic stocks. This set of portfolios will explain the returns of portfolios sorted on the same
characteristics, but are unlikely to span the mean variance efficient frontier of all assets, because
they do not take into account the asset covariance structure.
A simple example with a single characteristic and a single priced factor helps to illustrate this
intuition (we describe this example in detail in Section 2.2.1). Consider an economy with N assets
3As emphasized by Cochrane (2005, p.174), the word “factor” is used with different meanings in the asset pricingliterature. In this paper we use “characteristic portfolio” to refer to a zero-investment portfolio formed on the basis ofone or more firm characteristics. We use the term “factor” to refer to a latent economic force (see, e.g., equation (2.2))but not the return on an investment portfolio. Fama and French (1996, p.57) refer to these latent economic forces asrisk factors or “state variables of special hedging concern to investors.”
64
and let µµµ be the N × 1 vector of expected excess returns on these assets. Premia are driven by
exposure to a single risk factor, which is unobserved. Assume finally that there is a linear relation
between expected excess returns and a single characteristic, that is, µµµ = xxxλc, where xxx is the
corresponding N × 1 vector of stock characteristics and λc is some constant. Researchers are
interested in identifying the underlying risk factor. To do so they construct a CP, a zero investment
portfolio that goes long high characteristic stocks and short low characteristic stocks. Since the
CP earns a large excess return, it must also have a large exposure to the risk factor. Further, the
literature effectively argues that exposure to the CP should price the cross-section, in the spirit of
regressions like the one in equation (2.1). Of course, this will only be the case if the resulting CP
is mean variance efficient.
We show that, in general, this standard procedure will not produce a mean variance efficient
portfolio. The reason is that, while variation in the characteristic does indeed pick up variation
in the loading with respect to the priced risk factor, it also captures variation in the loadings with
respect to unpriced sources of common variation in returns. As a result, exposure to the CP com-
mands premium but the volatility of returns is too high because the portfolio also loads on these
unpriced sources of common variation. It follows that the Sharpe ratio of the CP is lower than the
Sharpe ratio of the projection of the risk factor on the space of returns: the CP is not mean-variance
efficient. We show how to improve on the CP by removing from it unpriced sources of common
variation in returns.
We extend these ideas to the empirically relevant case where average excess returns are ex-
plained by many characteristics, such as size, book-to-market, profitability, and investment. We
introduce the concept of a characteristic efficient portfolio (CEP), which has the smallest return
variance amongst the portfolios that has characteristic equal to one for one characteristic and zero
to all other characteristics. We further show that the complete set of CEPs spans the mean variance
frontier.
The CEPs are the solution to an optimization problem that takes into account the covariance
matrix of returns. Were the covariance matrix known, the calculation of the CEP weights would
65
be straightforward. However, there are numerous problems associated with using an estimated
covariance matrix to construct portfolios and no accepted way of correcting a sample covariance
matrix to fully resolve the problems associated with optimal portfolio construction.4 We instead
develop an empirically feasible strategy to get close to the CEPs. Our starting point is a set of
CPs—in our empirical implementation we start with the five FF CPs.5 We then introduce the
concept of a hedge portfolio: a characteristic balanced portfolio designed to pick up variation
in the loadings with respect to unpriced sources of common variation in returns, and with zero
loading on the priced factors. Characteristic balanced here means that the long- and the short-side
of the hedge portfolio have identical characteristics, and therefore according to our characteristic
model, also have zero expected return. In our theory section, we show how to select the optimal
hedge portfolio: It is the characteristic balanced portfolio that maximizes the loading with respect
to the CP. Finally we show how an optimal combination of the original CPs and the optimal hedge
portfolios delivers the CEPs.
Based on this theoretical development, we construct hedge portfolios for each of the five FF
CPs. There are two key empirical challenges: the construction of the optimal hedge portfolios, and
the calculation of the optimal hedge ratios. For the construction of the optimal hedge portfolios
we build on Daniel and Titman (1997), but improve on their procedure on multiple dimensions.
Through the use of higher frequency data and differential windows for calculating volatilities and
correlations, we are able to construct hedge portfolios that are highly correlated with the FF CPs,
but which have approximately zero expected returns. Importantly, like the FF CPs themselves, our
hedge portfolios are highly tradable: we form value-weighted portfolios once per year, at the end
of June, and hold their composition fixed for 12 months. Based on robustness considerations, we
also calculate the hedge ratios only once per year, also at the end of June, and based only on data
that are in the investor’s information set at that time. Thus our procedure is out-of-sample in the
4Black and Litterman (1991) describe this problem and a suggest shrinking the expected return estimates towardan equilibrium-based prior as a partial solution. Ledoit and Wolf (2003),Ledoit and Wolf (2004),Ledoit and Wolf(2012),Ledoit and Wolf (2017) each propose alternative covariance matrix estimators.
5We concentrate on the factors of Fama and French (2015). However, the critique we develop in Section 2.2applies to any factors constructed using this method.
66
sense that, given knowledge of the five FF characteristics, an investor could have hedged the FF
portfolios in exactly the way we do here.
Empirically, our hedge portfolios behave in a way that is consistent with our theory: except for
the size (SMB) hedge portfolio, they all earn economically and statistically significant five-factor
alphas.6 We combine each of the original five FF CPs with our hedge portfolios in an ex-ante
optimal way, i.e., we forecast the optimal hedge ratio, and generate the five FF CEPs. The optimal
combination of the five CEPs yields a squared Sharpe ratio of 2.13 versus 1.17 for the optimal
combination of the five FF CPs.
Our procedure has the important advantage that it does not require us to identify the sources of
unpriced risk. In fact, we are completely agnostic as to what these unpriced sources of common
variation in returns represent. We do argue, though, that one source of unpriced common variation
may be industry exposure, and present evidence that the standard FF CPs load on industry returns.
We compare the performance of the characteristic efficient FF portfolios with the performance of
a strategy in which we only hedge out the industry component of the original five FF CPs. The
squared Sharpe ratio of the ex-post optimal combination of the industry-neutral five FF CPs is
1.37, which is lower than what we obtain with our methodology, 2.13: There are unpriced sources
of common variation beyond industry and thus the industry-neutral CPs do not span the MVE
portfolio.
Our results are important for several reasons. First, they increase the hurdle for standard asset
pricing models. Following the logic of Hansen and Jagannathan (1991), the pricing kernel variance
that is required to explain the returns of our CEPs is 82% higher than what is required to explain
the returns of the FF CPs.
Second, in order to find economic explanations for the premia associated with characteristics
such as size and value, it is important to start out with portfolios that capture the factor premia with
the minimum possible return variance. In the context of rational models, recall that the ultimate
purpose behind this literature is to find the underlying risk factors that are the source of premia.
6Note that over this sample period, the SMB characteristic portfolio has the lowest Sharpe ratio of the five FF CPs.
67
As FF (page 3) suggest, building on the ICAPM logic of Merton (1973), “. . . the factors are just
diversified portfolios that provide different combinations of exposures to the unknown state vari-
ables” driving the marginal rate of substitution of the marginal investor. CPs then should correlate
with proxies for the marginal utility of the representative investor. But if, by construction, as we
argue, these CPs load on unpriced sources of common variation this correlation with the marginal
rate of substitution is bound to be biased towards zero and thus may lead to the wrong inferences
regarding the suitability of the proposed asset pricing model.7
Third, our CEPs are better benchmarks for the performance evaluation of managed portfolios.
While the characteristics approach to measure managed portfolio performance (see, e.g., Daniel
et al., 1997, DGTW) has gained popularity, the regression based approach initially employed by
Jensen (1968) (and later by Carhart (1997), Fama and French (2010) and numerous others) remains
the more popular. A good reason for this is that the characteristics approach can only be used
to estimate the alpha of a portfolio when the holdings of the managed portfolio are known, and
frequently sampled. In contrast, the Jensen-style regression approach can be used in the absence
of holdings data, as long as time series of portfolio returns are available.
However, as pointed out originally by Roll (1977), the regression approach requires that the
benchmark used in the regression test be efficient; otherwise the conclusions of the regression test
will be invalid. What we show in this paper is that, with the historical return data, efficiency of
the proposed CPs can be rejected. However, our CEPs incorporate the information both from the
characteristics and from the historical covariance structure and thus improve on their FF counter-
parts. Thus, if the CEPs are used as benchmarks and loadings can be estimated accurately, alphas
equivalent to what would be obtained with the DGTW characteristics-approach can be generated
with the regression approach without the need for portfolio holdings data.
Our paper connects to the recent vintage of papers that revisits the question of how to combine
characteristics into tradable portfolios (see Gu, Kelly, and Xiu, 2018; Huang, Li, and Zhou, 2018;
7We thank our discussant, Ralph Koijen, for emphasizing this point to us. Indeed, a recent literature studies theconnection between characteristic premia and risk. See Lewellen, Nagel, and Shanken (2010), and Daniel and Titman(2012) for summaries of the literature. One example is the study by Golubov and Konstantinidi (2019), which focuseson the value premium.
68
Freyberger, Neuhierl, and Weber, 2019; Kozak, Nagel, and Santosh, 2019; Liu, Tsyvinski, and
Wu, 2019). These papers all take as their starting point a set of characteristics that explain average
excess returns. Our focus instead is on improving the efficiency of the characteristic portfolios by
using individual asset loadings on the CPs. Another paper related to ours is Kelly, Pruitt, and Su
(2018), who develop a method they label Instrumented Principal Components Analysis (IPCA),
which they argue allows them to determine the set of priced factors that describe the returns of a
set of 36 characteristic-sorted portfolios with a small set of factors. Our empirical findings strongly
suggest that the characteristic-sorted portfolios employed by Kelly, Pruitt, and Su (2018), which
they refer to as latent factors, are inefficient as a result of ignoring information about the (future)
covariance structure that can be derived from historical covariances.
Finally, our work also connects to another set of papers which identify the priced components
of book-to-market CPs (see Gerakos and Linnainmaa, 2018; Golubov and Konstantinidi, 2019),
but our point is much broader and refers to the general procedure used to construct characteristic
portfolios.
2.2 Theory and examples
Fama and French (1993) and numerous subsequent studies construct characteristic portfolios
as a proxy for the priced risk associated with characteristic premia.8 These papers construct a
zero-investment CP by going long a unit-investment portfolio of high characteristic assets, and
short a unit-investment portfolio of low characteristic assets (where average returns are positively
correlated with the characteristic). Then, each paper proceeds to examine whether the returns of a
set of test assets are explained by a combination of well-known benchmark portfolios and the new
CP, often using regressions like the one in equation (2.1). The implicit argument here is that the
such a characteristic portfolio, in combination with the other benchmark portfolios, will span the
mean variance efficient portfolio.
8See footnote 2 for examples.
69
This paper makes two contributions. We first show that the standard characteristic portfolio
construction procedure is unlikely to yield the mean variance efficient (MVE) portfolio, because
the so-constructed CP will load on unpriced risk. Second, we show how to improve on this standard
procedure by constructing a hedge portfolio which captures the unpriced risk in the CP.
To illustrate, we start with a simple example. The example makes two key assumptions: ex-
cess returns are described by a two-factor structure and expected excess returns are linear in a
single characteristic. Section 2.2.1 further illustrates our results in the context of the popular HML
portfolio. Section 2.2.2 generalizes the simple example to the empirically relevant case in which
multiple characteristics are needed to fully describe the cross-section of average excess returns.
2.2.1 A simple example
Characteristic portfolios and mean variance efficiency
We consider a single period economy with N assets. Realized excess returns are determined
by a two-factor structure, so for asset i:
ri = βi (f + λ) + γig + εi, (2.2)
where E[f ] = E[g] = E[εi] = 0 for all i = 1, 2, · · · , N . Further, suppose that var (f) = σ2f ,
var (g) = σ2g , var (εi) = σ2
ε for all i = 1, 2, · · · , N , and that f , g, and εi are mutually orthogonal
for all i 6= j.
Let rrr denote the (N × 1) column vector of individual excess returns,
rrr> ≡ [r1 r2 · · · rN ] ,
where > denotes transpose. Taking expectations of equation (2.2) gives:
µµµ ≡ E [rrr] = βββλ, (2.3)
70
where βββ is the (N × 1) column vector of individual assets’ exposures to f .
The standard interpretation of f is that it is a proxy for shocks to the marginal rate of substi-
tution; the two canonical examples are that f is (some function of) consumption growth or that
(f + λ) is the return on the market portfolio (Cochrane, 2005, page 78). g is the unpriced source
of common variation. That there is only one factor that is the source of premia is without loss of
generality: For any factor structure there is always a rotation of the factor space in which there is
only one priced factor. Accurately determining f is important in assessing macroeconomic theo-
ries. Its projection onto the space of returns has the maximal Sharpe ratio, so financial economists
attempt to identify f by constructing portfolios with the highest possible Sharpe ratios.
Studies in this literature begin with the observation that expected excess returns in the cross-
section are a function of a set of characteristics. For instance, Fama and French (1993, page 4),
state that “two empirically determined variables, size and book-to-market equity, do a good job
explaining the cross-section of average returns on NYSE, Amex, and NASDAQ stocks for the
1963-1990 period,” and then build the characteristic portfolios SMB and HML based on the these
characteristics.
We follow the literature but go a step further. We assume that expected excess returns are
perfectly described by a linear function of characteristics. To make this example as simple as
possible we assume that expected excess returns are described by a single characteristic, xxx, an
N × 1 column vector and that this characteristic lines up perfectly with expected excess returns,
µµµ = xxxλc, (2.4)
where λc is the characteristic premium.
In order for equations (2.3) and (2.4) to hold simultaneously, it must be the case that:
βββ =
(λcλ
)xxx (2.5)
In this simple setting the characteristic is a perfect proxy for the exposure to the priced factor.
71
6
- γi
βi(=(λcλ
)xi)
A1, A2
��
A3
@@R
A4@
@I
A5, A6���
1−1
1
−1
Figure 2.1: Six assets in the space of loadings on priced and unpriced factors.
Thus, sorting on the characteristic will pick up variation in β. This is the motivation for the
standard procedure in the literature, first developed in Fama and French (1993), of constructing a
zero investment portfolio that goes long stocks with a high value of the characteristic x and short
stocks with low value of the characteristic.
A portfolio is defined by an N -dimensional column vector of portfolio weights,
www> ≡ [w1 w2 · · · wN ] , (2.6)
where wi is asset i’s weight in the portfolio for i = 1, 2, · · · , N .
To continue, suppose that there are only six stocks (N = 6) with equal market capitalizations.
The six stocks have characteristics and loadings on the priced and unpriced factors as illustrated in
Figure 2.1. Notice that assets 1 and 2 have identical loadings and characteristics. The same holds
for assets 5 and 6.
We now construct a specific characteristic portfolio, or CP, which we label c, on the basis of
72
characteristic x, by going long a value-weighted portfolio of the high characteristic stocks A1, A2,
and A3, and short a value-weighted portfolio of the low characteristic stocks A4, A5, and A6.9
Specifically, the weights on individual stocks in the characteristic portfolio c are given by:
www>c =
[1
3
1
3
1
3− 1
3− 1
3− 1
3
], (2.7)
and the return of portfolio c is:
rc = www>c rrr =1
3×
[3∑j=1
rj −6∑j=4
rj
]= 2(f + λ) +
2
3g +
1
3
[3∑j=1
εj −6∑j=4
εj
]. (2.8)
The CP’s return rc does indeed capture the common source of variation in expected excess
returns, since it loads on f . However, our point here is that CPs so constructed are likely to also
load on unpriced factors, and will therefore not be mean-variance efficient. This is the case in this
example: because of the cross-sectional correlation between the characteristic and the loading on
the unpriced factor—i.e., the fact that most high characteristic firms also have a high loading on
the unpriced factor—the constructed CP also loads on the unpriced source of common variation
g.10 Specifically, the CP loads on the factor f with βc = 2 and on g with γc = 23. The value of
the characteristic for this portfolio is xc = 2 λλc
and thus expected excess return is E [rc] = 2λ. The
variance of the returns is given by
σ2c = 4σ2
f +4
9σ2g +
2
3σ2ε , (2.9)
giving the CP a Sharpe ratio of
SRc =2λ√
4σ2f + 4
9σ2g + 2
3σ2ε
. (2.10)
9Because in this simple example all stocks have equal weight there is no difference between equal and valueweighting. The usual Fama-French construction uses value-weighted portfolios.
10Note that a cross-sectional correlation between the characteristic and the loading on the unpriced factor of exactlyzero constitutes the knife-edge case, i.e., it is extremely unlikely.
73
If σ2ε is small relative to the variance of the systematic factors f and g, then it is clear that the
CP is not MVE because it is exposed to both priced and unpriced risk. In this example then a single
characteristic lines up perfectly with expected excess returns and still the CP fails to deliver the
mean variance efficient portfolio. Can we improve on the CP?
Consider the following portfolio h with weights:
www>h =
[1
4
1
4− 1
2
1
2− 1
4− 1
4
]. (2.11)
This portfolio goes long stocks with high loadings on g and short stocks with low loadings on g.
The return of portfolio h is given by
rh =1
2
[r3 +
r5
2+r6
2
]− 1
2
[r1
2+r2
2+ r4
]= 2g +
1
2
[ε3 +
ε5
2+ε6
2
]− 1
2
[ε1
2+ε2
2+ ε4
].
(2.12)
The loading of the h portfolio on g is γh = 2. Notice that this portfolio is characteristic balanced
in that xh = www>hxxx = 0, so βh = 0 and E [rh] = 0 (see (2.4)).
We can use the portfolio h to improve on the CP by reducing its variance without changing its
expected excess returns. For this reason we refer to h as a hedge portfolio. Indeed, given that the
characteristic and hedge portfolios have loadings on g of γc = 23
and γh = 2, respectively, we can
form a portfolio for which for every dollar invested long in portfolio c we also invest $13
(short) in
the hedge portfolio h. This combined portfolio has the same expected return as the CP (which is
2λ) but its exposure to g is eliminated. The variance of this portfolio is
4σ2f +
3
4σ2ε (2.13)
11For a well-diversified portfolio for which residual variance is zero, this problem is the same as setting the loadingon the unpriced factor to zero; with residual risk it is not. In this example the Sharpe ratio is higher as long asσ2g >
(316
)σ2ε .
74
and thus it has a Sharpe ratio of2λ√
4σ2f + 3
4σ2ε
, (2.14)
which is higher than the Sharpe ratio of the CP, SRc (see equation (2.10)), whenever diversification
is large enough so that idiosyncratic risk vanishes.11
We can do better by combining the hedge portfolio with the characteristic portfolio in order
to maximize the Sharpe ratio. Given that the hedge portfolio has zero expected excess return this
is equivalent to finding the combination of the characteristic portfolio and the hedge portfolio that
minimizes the variance of the resulting portfolio, that is,
minδ
var (rc − δrh) ⇒ δ∗ = ρc,hσcσh, (2.15)
where σh is the standard deviation of the returns of the hedge portfolio, h, and ρc,h is the correlation
coefficient between the returns of the characteristic portfolio, c, and the hedge portfolio, h. We refer
to δ∗ as the optimal hedge ratio. It can be shown that this procedure improves the Sharpe ratio of
the characteristic portfolio bySR’SRc
=1√
1− ρ2c,h
, (2.16)
where SR’ is the Sharpe ratio of the improved characteristic portfolio.
Notice that there are several ways of constructing the hedge portfolio h so as to remove expo-
sure to g from the characteristic portfolio c. Equation (2.16) shows though that the optimal hedge
portfolio is the one that is maximally correlated with the CP. In Section 2.2.2 we extend these in-
sights to the empirically relevant case in which a full description of the cross-section of expected
excess returns requires multiple characteristics. Before showing these result formally, we illustrate
the ideas of the example in the context of a popular characteristic portfolio, the HML portfolio of
Fama and French (1993).
75
The simple example in practice: Industry portfolios as g
Book-to-market is one characteristic that has been shown to align with average returns in the
cross-section and HML is a popular characteristic portfolio.12 Asness et al. (2000), Cohen and
Polk (1995) and others13 have shown that if book-to-market ratios are decomposed into an across-
industry component and a within-industry component, then only the within-industry component—
that is, the difference between a firm’s book-to-market ratio and the book-to-market ratio of its
corresponding industry portfolio—forecasts future returns. This literature then suggests that the
exposure of HML to industry returns is unpriced, that is, that industry is one unpriced source of
common variation, g. Therefore, if the industry exposure of HML was hedged out, it would result
in a characteristic portfolio with lower risk, but the same expected return, i.e., with a higher Sharpe
ratio. But, does HML really load on industries?
Figure 2.2 plots the R2 from 126-day rolling regressions of daily HML returns on the twelve
daily Fama and French (1997) value-weighted industry excess returns. The time period is 1963/07
- 2019/12.14 The plot shows that, while there are short periods where the realized R2 dips below
50%, there are also several periods where it exceeds 90%. The R2 fluctuates considerably but the
average is well above 70%. The upper Panel of Figure 2.3 plots, for the same set of daily, 126-day
rolling regressions, the regression coefficients for each of the 12 industries. As it is apparent, these
coefficients display considerable variation: sometimes the HML portfolio loads more heavily on
some industries than on others.
The behavior of the ‘Money’ industry during and after the Great Recession of 2008 is a striking
example of the large industry effect on HML. The lower Panel of Figure 2.3 shows that the regres-
sion coefficient associated with ‘Money’ increased dramatically between 2007 and early 2009,
as stock prices for firms in this segment collapsed and those firms quickly became classified as
12Fama and French (1993, 2015) refer to HML as well as to the other portfolios, as factors or factor portfolios. Weinstead use the expression characteristic portfolios throughout, in order to further distinguish between the underlyingfactor, f , and the portfolio formed on characteristic sorts.
13See also Lewellen (1999), Cohen et al. (2003), and Golubov and Konstantinidi (2019).14The industry classification follows Ken French’s data library at http://mba.tuck.dartmouth.edu/
pages/faculty/ken.french/Data_Library.
76
value.15 As shown in Figure 2.4, the volatility of returns also increased dramatically. As a re-
sult of these two effects, ‘Money’ explained a substantial amount of the variation of HML returns
during those years. Indeed Figure 2.5 plots the R2 of a regression of the return on HML on the
‘Money’ industry excess returns alone. Between late 2008 and late 2010, the R2 was well above
60%. The reason for this was that as of December 2007, the top 4 firms by market capitalization
in the ‘Money’ industry were J.P. Morgan, Bank of America, Citigroup and Wells Fargo. Three
of these four were in the large value portfolio (Big/High-BEME to use the standard terminology).
While the market capitalization of these firms fell dramatically through 2008, they remained large
and, particularly as the volatility of the returns on the ‘Money’ industry increased, these firms and
others like them drove the returns both of the HML portfolio and the ‘Money’ industry portfolio.
However, there were firms in the ‘Money’ industry that did not have high book-to-market ratios,
even in the depths of the financial crisis. For example, in 2008 American Express (AXP) and
UnitedHealth Group (UNH) were both “L” (low book-to-market) firms. Yet both AXP and UNH
had large positive loadings on HML at this point in time (see Table 2.1). The reason is that, at this
time, both AXP and UNH covaried strongly with the returns on the ‘Money’ industry, as did HML.
We can exploit this variation within the ‘Money’ industry to construct a characteristic balanced
hedge portfolio wwwh as illustrated in the example in the previous section. The short side of the
characteristic balanced portfolio features firms with high loadings on HML and low and high book-
to-market, such as American Express and Citi, respectively. Loosely speaking, in the example in
Figure 2.1, Citi would be likeA1 (i.e., a value stock in the finance industry), and American Express
would be like asset A4 (a growth stock in the finance industry). The characteristic balanced hedge
portfolio goes long both value and growth stocks with low loadings on HML, and goes short value
and growth firms with high loadings, such as Citi and Amex.16
15As shown in Laeven and Huizinga (2009) banks during the crisis used accounting discretion to avoid writingdown the value of distressed assets. As a result the value of bank equity was overstated. The market knew better andas a result the book-to-market ratio of bank stocks shot up during the crisis.
16By maximizing the negative loading on HML, subject to the constraint that the the portfolio be book-to-marketneutral, we pick up the unpriced part of the HML-exposure. In this simple example the unpriced component of HMLis money-industry return.
77
2.2.2 The general case
We now show that the insights of the previous section extend to the more general case in which
there are multiple factors and characteristics that drive excess returns.
As in the example in Section 2.2.1, we consider a single period economy with a large number
of assets N but in which now realized excess returns are determined by a factor structure in which
the number of factors is K. Recall that for any multifactor representation there is always a rotation
with only one priced factor f and a vector of (K − 1) of unpriced factors ggg. We can then write
realized excess returns as
ri = βi (f + λ) + γγγiggg + εi, (2.17)
where E[f ] = E[gk] = E[εi] = 0 for all k = 1, 2, · · · , K − 1 and i = 1, 2, · · · , N . Further,
suppose that var (f) = σ2f , var (ggg) = Σg, cov (f,ggg) = 000, cov (εi, f) = 0, cov (εi, ggg) = 000 for
i = 1, 2, · · · , N and cov (εi, εj) = 0 for all i 6= j. γγγi is the (1 × (K − 1)) vector of asset i’s
exposure to the unpriced factors ggg.
As before we assume that there is a linear relation between expected excess returns and char-
acteristics
µµµ = Xλλλc, (A1)
where µµµ is again an (N × 1) vector of expected excess returns, X is now an (N ×M) matrix of
characteristics, and λλλc is an (M × 1) vector of characteristic premia.
Assumption (A1) is consistent with model (2.17) as long as
βββ =1
λXλλλc, (2.18)
where βββ is an (N × 1) vector of loadings on f . Thus, under assumption (A1), asset i’s exposure to
f is a linear combination of the M characteristics that describe expected excess returns.
This setting captures, in somewhat simplified form, the current state of the asset pricing litera-
ture, where a set of characteristics explains average returns. The asset pricing tests in the literature
78
(e.g., Fama and French, 1993, 2015) construct a set of CPs, one for each of the characteristics
that are shown to capture variation in average excess returns in the cross-section, and then examine
whether the cross-section of returns is explained by the CPs’ returns, for example using time-series
regressions like that in equation (2.1). The hope is that the projection of f on the space of returns
(the MVE portfolio) will be in the span of those CPs. If this were the case, then the factor model
with the CPs as factors would be a valid multi-factor asset pricing model. We now examine when,
for CPs constructed in this way, the MVE portfolio will indeed be in the span of the CPs.
Our starting point is the set of M CPs, one for each characteristic. The (N × 1) vector of
weights for the m-th CP, wwwc,m, will have positive values for firms with a high value of the m-th
characteristic, and negative values for firms with a negative characteristic. The return of the m-th
CP is then:
rc,m ≡ www>c,mrrr for m = 1, 2, · · · ,M. (2.19)
We further define the (N ×M) matrix of CP weights as:
Wc = [wwwc,1 wwwc,2 · · · wwwc,m] . (2.20)
This paper is concerned with, first, whether the CPs span the MVE frontier, and, second, if they
do not, whether and how we can improve on the CPs. A key concept in what follows is that of
characteristic efficient portfolios or CEPs.
Definition 2.1 (Characteristic efficient portfolios) The weight-vector of the m−th characteristic
efficient portfolio is the solution to the program
minwwwc,m
1
2www>c,mΣwwwc,m subject to www>c,mX = eeem. (Pm)
In program (Pm), Σ is the (N ×N) return covariance matrix and eeem is an (M × 1) vector with
the m−th entry equal to 1 and all others equal to 0. Intuitively the m−th CEP selects among the
portfolios that have the m−th characteristic equal to one and all other characteristics equal to zero,
79
the one with the minimum variance possible.
Our main results are that, first, the M CEPs span the mean variance efficient frontier and,
second, that the asset loadings with respect to CEPs line up perfectly with asset characteristics.
Finally we show how to adjust any set of CPs to transform them into CEPs.
Characteristic efficient portfolios
As shown in the Appendix B.2.1, the solution to program (Pm) is
www∗c,m = Σ−1X(X>Σ−1X
)−1eeem. (2.21)
Let
W ∗c ≡
[www∗c,1 www∗c,2 · · · www∗c,M
]= Σ−1X
(X>Σ−1X
)−1, (2.22)
be the (N ×M) matrix of CEP weights.
Let B∗, an (N × M) matrix, be the projection coefficient of rrr on rrr∗c , where each column
bbb∗m corresponds to the vector of individual stocks’ loadings on the m-th CEP, that is, B∗ ≡
[bbb∗1 bbb∗2 · · · bbb∗M ]. Armed with this we can prove the following:
Proposition 2.1 Under assumption (A1)
1. The returns of the CEPs span the mean-variance-efficient portfolio, that is,
SR∗2 = µµµ∗>c Σ∗−1c µµµ∗c = µµµ>Σ−1µµµ (2.23)
where
µµµ∗c ≡ W ∗>c µµµ = λλλc and Σ∗c ≡ var
(W ∗>c rrr)
=(X>Σ−1X
)−1. (2.24)
2. Asset loadings with respect to the CEPs line up with the characteristics
B∗ = X (2.25)
80
Proof: See Appendix B.2.2. �
Proposition 2.1 says that given (A1), there is an optimal way of constructing portfolios linked
to the characteristics so that they span the mean variance efficient frontier. One property of these
portfolios is that the loadings of any test portfolio on the CEPs will equal the vector of portfolio
characteristics for that test portfolio. That is, if the portfolios are the CEPs there is no distinction
between characteristics and covariances.
Notice that any rotation of the CEPs, W ∗c = W ∗
c A where A is (M ×M) and full rank, will also
span the MVE portfolio of excess returns. But for any such rotation the loadings will no longer be
the corresponding characteristic but a linear combination of them.17
We are interested in constructing CEPs rather than CPs. However, Σ is difficult to estimate,
which may justify the implicit choice in the literature to use simple characteristic sorting proce-
dures to construct CPs, but in general these CPs will not span the same space as the CEPs.
There is though a particular case of interest in which the CPs span the mean variance efficient
frontier. It is when K = M , that is, when the number of characteristics equals the number of
factors that explain the covariance matrix. In this case, adding the hedge portfolios would not
increase the maximum Sharpe ratio achievable with the CPs. Our view though is that this case is
of limited practical interest. The number of factors that capture common variation in stock returns
is likely large (at least the number of industries!) whereas the number of characteristics that have
been found to explain the cross-section of expected excess returns is smaller. In particular, it is
easy to show that as long as K >> M and the characteristics are correlated with the loadings on
the unpriced factors γγγ in the cross-section, the CPs will not span the MVE portfolio. We proceed
next by showing how to recover CEPs from the CPs.
17That the loadings are a linear function of the characteristics follows from the fact that the loadings with respectto any rotation of the CEPs are given by
B∗ = ΣW ∗c A(A>W ∗>c ΣW ∗c A
)−1= X
(A>)−1
,
where the last equality uses (2.22).
81
Characteristic portfolios and hedge portfolios
Our starting point is a set of CPs, for example the five portfolios in Fama and French (2015).
Let B, an (N × M) matrix, be the matrix of projection coefficients of rrr on rrrc, where each
column bbbm corresponds to the vector of loadings of individual assets on the m-th CP, that is,
B ≡ [bbb1 bbb2 · · · bbbM ]. The empirical counterpart of B is a matrix of a multivariate time series
regression coefficients of each asset’s excess return on rrrc.
We show next that there exists a set of optimal hedge portfolios, with weights given by the
columns of the (N × M) matrix W ∗h , that can be combined with the original CPs to obtain (a
rotation of) the CEPs. That is,
W ∗c A = Wc −W ∗
h∆∗, (2.26)
where A is an (M ×M) rotation matrix, and ∆∗ is an (M ×M) matrix of optimal hedge ratios.
Definition 2.2 (Optimal hedge portfolio) The weight-vector of the m−th characteristic hedge
portfolio is the solution to the program
maxwwwh,m
www>h,mbbbm subject to www>h,mX = 000 and1
2www>h,mΣwwwh,m = σ2 (Ph,m)
Program (Ph,m) delivers a portfolio weight-vector www∗h,m so as to maximize the correlation of
the returns of the hedge portfolio, rh,m ≡ www∗>h,mrrr, with the returns of the corresponding CP, rc,m,
conditional on having zero characteristic exposure. Define
W ∗h =
[www∗h,1 www∗h,2 · · · www∗h,M
].
Proposition 2.2
1. The weights of the optimal hedge portfolios are given by
W ∗h =
(Wc −W ∗
cX>Wc
)Σ−1c E−1 (2.27)
82
where E is an (M ×M) diagonal matrix specified in the Appendix B.2.3 and W ∗c is given
by (2.22).
2. A and ∆∗ in expression (2.26) are given by
A = X>Wc and ∆∗ = EΣc (2.28)
Proof: See Appendix B.2.3 �
To understand the intuition of Proposition 2.2 start by noticing that W ∗c A is a rotation of the
CEPs’ weights such that these rotated CEPs have the same characteristic as the original CPs. The
corresponding optimal hedge portfolios have zero expected excess returns,
Errrh = 0 where rrrh = W ∗>h rrr (2.29)
Finally, there is the interpretation of the optimal hedge ratios. A bit of algebra, reported in the
Appendix B.2.4, shows that18
∆∗ = Σ−1h W ∗>
h ΣWc, (2.30)
that is, for each CP, the optimal hedge ratios are the coefficients of a multivariate regression of
its return rc,m on the returns of all the optimal hedge portfolios. The intuition of this result is
straightforward. The hedge portfolios command zero premia, but their returns are correlated with
rrrc. Hence, the optimal hedge ratios are such that the return of the CEP is orthogonal to rrrh. That
is, consistent with exactly the intuition in the example in Section 2.2.1, each CEP is the residual
from a projection of the CP on the set of hedge portfolios, meaning that each CEP is equal to the
corresponding CP, orthogonalized to the set of hedge portfolios.
In sum, the optimal hedge portfolios do not remove any of the premia from the CPs but remove
sources of variation that do not command any premium. In other words, each of the optimal hedge
18The reason why we write ∆∗, rather than ∆, is because, as it was the case in the example (see equation (2.15)),the optimal hedge ratios are the solution of an optimization problem that results in an optimal combination of the CPsand the optimal hedge portfolios.
83
portfolios has zero expected excess return, and hence zero loading on the priced risk factor f .
The only reason that the optimal hedge portfolios load on the CPs is because they all load on the
unpriced risk factors.19 All optimal hedge portfolios together then form a basis for the unpriced
components in the CPs and can be used to hedge out all the exposure to unpriced risk factors. This
is the source of the improvement in the Sharpe ratio when going from CPs to CEPs.
An important implication of this analysis is that whenever we have a set of characteristics
that explain expected excess returns, we can always find a set of portfolios that span the MVE
portfolio. These portfolios lack economic content and thus so do the loadings with respect to
those portfolios, which are simply the characteristics (see Proposition 2.1). These CEPs though
can help in discriminating amongst alternative economic models: if a particular economic variable
is uncorrelated with the CEPs, then it cannot be a candidate for a state variable that drives the
marginal rate of substitution of the marginal investor. But the validity of such an inference depends
on using the CEPs rather than the CPs; the correlation of an economic variable with a CP could
result from a correlation of the variable with the priced factor, or with the unpriced factors on
which the CP loads.
2.3 Empirical results
2.3.1 Hedge portfolio construction
Recall that our starting point is any given set of CPs on which we want to improve. To do so
our methodology involves two steps. First, we construct the hedge portfolios. Second we find the
optimal hedge ratios.
In our empirical exercise, we focus on the FF five-factor model and we follow these authors in
the construction of their CPs. The empirical goal is to construct the best possible hedge portfolios,
as introduced in (Ph,m). The empirical procedure to construct the hedge portfolios builds on Daniel
and Titman (1997). The idea is to use ex-ante forecasts for the loadings for each stock i on the
19We assume that N is large enough and we can ignore idiosyncratic risk.
84
returns of the CPs, rc,m, in order to construct hedge portfolios with maximum loadings on the CPs.
At the same time, these hedge portfolios are constructed in such a way that they have characteristics
as close as possible to zero.
More precisely, our empirical approach is based on the first order conditions of the program (Ph,m).
We show in the Appendix B.2.3 that the weights of each optimal hedge portfolio are given by
www∗h,m =1
κ2,m
Σ−1(bbbm −Xκκκ>1,m
), (2.31)
them−th column ofWh in (2.27). In (2.31)κκκ1,m, which is (1×M), and κ2,m > 0 are the Lagrange
multipliers associated with the first and second constraints in program (Ph,m).
Roughly, equation (2.31) says, holding fixed the characteristics, the hedge portfolio goes long
stocks with high loadings and short stocks with low loadings with respect to the CP. Intuitively,
one can think about stocks’ loadings with respect to the CPs as a combination of exposure to priced
and unpriced risk. When we control for the characteristics, we control for cross-sectional variation
in the exposure to the CEPs, the sole source of variation in premia. Thus, holding characteristics
constant, sorting on CP loadings captures the remaining variation: the one with respect to the
unpriced sources of common variation.
Empirically, we construct the optimal hedge portfolios by sorting individual stocks into charac-
teristic bins and then within each bin sort again on the forecast loading with respect to a particular
CP. We form the portfolio by buying the high loading stocks and shorting the low loading stocks.
There are two challenges in constructing optimal hedge portfolios. First, our theory requires
that we control for all characteristics. Roughly, within each characteristic bin stocks have the same
characteristic values. But if there are, for example, five characteristics and we sort stocks into three
bins for each of them, this would result in 243 portfolios. Some of these portfolios would surely
contain very few stocks and thus would not be sufficiently diversified. It turns out that, empirically,
controlling for size and one additional characteristic at a time is enough to deliver hedge portfolios
that have close to zero exposure to all characteristics, while obtaining well-diversified portfolios.
85
We return to this issue when we discuss the characteristic properties of the hedge portfolios.
Second, notice that construction of the optimal hedge portfolios requires use of the full covari-
ance matrix (Σ; see equation (2.31)). We instead construct an approximation to the optimal hedge
portfolio by, for a set of firms with roughly equal characteristics, going long a value-weighted port-
folio of stocks with low loadings and short a value-weighted portfolio of stocks with high loadings
with respect to the CPs. This results in a hedge portfolio that we can combine with the CPs to get
close to the CEPs. Indeed, because we are not using the theoretically optimal hedge portfolios we
cannot exactly recover the CEPs from Definition 2.1. We still refer to these “approximate CEPs”
as CEPs in order to avoid the need to introduce additional terminology. Finally, value-weighting
stocks in each of the portfolios sorted on characteristics and loadings guarantees that our portfolios
do not overweight small stocks; this avoids the inherent difficulties in trading small stocks because
of a lack of liquidity.
We describe next the exact procedure to construct the hedge portfolios based on the example
of HML. We first calculate book-to-market (BEME) and market capitalization (ME) break points
at the marks of 33.3% and 66.7% based on NYSE firms. For BEME we use data from the end of
December of the previous year and for ME we use data from the end of June of each year. Then,
at the end of June of a given year, all NYSE, AMEX and NASDAQ stocks are placed into one of
the nine resulting bins. Next, within these nine bins, each of the stocks is sorted into one of three
additional bins formed based on the stocks’ forecast future loading on the HML CP. This last sort
results in portfolios of stocks with similar characteristics (BEME and ME) but different loadings on
HML.20 The firms remain in those portfolios between July and June of the following year. Finally,
we construct our hedge portfolio for HML by going long an equal weighted combination of all
high loading portfolios and short an equal weighted combination of all low loading portfolios.
The hedge portfolios for RMW and CMA are constructed in exactly the same way, simply by
replacing BEME with operating profitability (OP) and investment (INV). For SMB, we follow FF
20A potential concern with independently triple-sorted portfolios is sparse portfolio population. The number oftraded firms has varied substantially over time, reaching a “listing peak” in 1996 when it started declining (see Doidgeet al., 2017). We show in Appendix B.4.1 that even in periods of relatively few listed firms, the resulting portfolios aresufficiently diversified.
86
and construct three different hedge portfolios: the first sorts are based on BEME and ME, and then
within these 3x3 bins, we conditionally sort on the loading on SMB. The second and third versions
use OP and INV instead of BEME in the first sort. Then, an equal weighted portfolio of the three
different SMB hedge portfolios is used as the hedge portfolio for SMB. We do exactly the same for
the hedge portfolio for the market (MktRF), using forecast loadings on MktRF instead of forecast
loadings on SMB.
Clearly a key ingredient of the last step of the sorting procedure is the estimation of the future
loading on the corresponding characteristic portfolio. Our purpose is to obtain forecasts of loadings
in the five-factor FF model:21
ri,t = αp + bi,MktRF rMktRF,t + bi,HMLrHML,t + bi,SMBrSMB,t
+ bi,CMArCMA,t + bi,RMW rRMW,t + εp,t
(2.32)
For each stock, we instrument future loadings with pre-formation loading forecasts. The result-
ing estimation method is intuitive and is close to the method proposed by Frazzini and Pedersen
(2014) to estimate individual-firm market loadings. These authors build on the observation that
correlations are more persistent than variances22 and propose estimating correlations and variances
separately. They then combine these estimates to produce the pre-formation loadings. Specifi-
cally, correlations are estimated using a five-year window with overlapping log-return observa-
tions aggregated over three trading days, to account for non-synchronicity of trading. Variances
of characteristic portfolios and stocks are estimated on daily log-returns over a one-year horizon.
Furthermore, we introduce an additional intercept in the pre-formation regressions for returns in
the six months preceding portfolio formation, i.e., from January to June of the rank-year (see Fig-
ure 1 in Daniel and Titman (1997) for an illustration). Further, we use constant-allocation and
constant-weight pre-formation characteristic portfolio returns, as in Daniel and Titman (1997).23
The accuracy of loading forecast impacts the efficacy of the hedge portfolios. Intuitively, if
21We write, say, rHML,t instead of rc,BEME,t to simplify the notation.22See, e.g., De Santis and Gerard (1997)23See Appendix B.3.2 for details.
87
our forecasts of future loadings are very noisy, then sorting on the basis of forecast loadings will
not capture variation in the actual post-formation loadings of the sorted portfolios. In contrast, if
the forecasts are accurate, then our hedge portfolio—which goes long the high forecast loading
portfolio and short the low forecast loading portfolio—will indeed have large loading with respect
to the corresponding FF CP. Notice that this relates to statistical power of rejecting the benchmark
asset pricing model. Under the null hypothesis, αs are equal to zero for all stocks. Given our
theory, the alternative hypothesis is that the hedge portfolios have zero expected returns and strong
positive loadings, which translates into large negative αs. The larger the ex-port loadings, the
higher is the power of the test designed to reject the null hypothesis that the benchmark model is
true. We show in the Appendix B.4.2 that using a low power methodology that follows Daniel and
Titman (1997) and Davis et al. (2000) leads to different results than the ones presented in the next
section. Indeed, with hedge portfolios constructed using the low power method we are not able to
reject the FF five-factor model.
2.3.2 Description of the sorted portfolios
Table 2.2 presents average monthly excess returns for the portfolios sorted on characteris-
tics and forecast-loadings, which we combine to form our hedge portfolios. Each panel presents
a set of sorts with respect to size and one characteristic—either book-to-market, profitability or
investment—and the loading on HML (Panel A), RMW (Panel B), CMA (Panel C), MktRF (Pan-
els D-F), or SMB (Panels G-I).
For each of the 27 portfolios in each subpanel, we report value-weighted monthly excess re-
turns. The column labeled “Avg.” gives the average across the 9 portfolios for a given charac-
teristic. First, note that the average returns in the “Avg.” column are consistent with empirical
regularities well-known in the literature: the average returns of value portfolios are higher than
those of growth, historically robust profitability firms beat weak profitability firms, and histori-
cally conservative investment firms beat aggressive investment firms.
In Table 2.3 we present the post-formation loadings and αs. These are the coefficients from
88
regressing the monthly excess returns of the BEME/OP/INV×ME×loading sorted portfolios on
the excess returns of the five FF CPs, in the sample period from 1963/07 to 2019/12. We see
that there are large differences between the post-formation loadings of the low-forecast-loading
(“1”) and high-forecast-loading (“3”) portfolios For the value, profitability, and investment sorts,
the average post-formation differences in loading of the “3” and “1” portfolios are 0.8, 0.69, and
0.96 respectively. Given these large differences in loadings, it is remarkable that the difference in
the average monthly returns for the high- and low-loading portfolios are 6, 7, and -4 basis points
per month for the value, profitability and investment-loading sorts, respectively (see the last rows,
labeled “Avg.” of Panels A-C in Table 2.2).24 This is consistent with the Daniel and Titman (1997)
conjecture that average returns are a function of characteristics, and are unrelated to the loadings
on the FF-CPs after controlling for the characteristics.
In Figures 2.6, 2.7 and 2.8 we analyze the average characteristics of the sorted portfolios. Each
dot in these plots represents one of the 27 portfolios from the 3×3×3, BEME/OP/INV×ME×loading
sort. The dotted lines connect all portfolios within the same BEME/OP/INV×ME bucket. The x-
axis is the respective post-formation loading and the y-axis the average characteristic value. Figure
2.6 shows the portfolios sorted on HML loadings (Panel A), the portfolios sorted on RMW load-
ings (Panel B) and the portfolios sorted on CMA loadings (Panel C). Figure 2.7 shows portfolios
that form the market hedge portfolio and Figure 2.8 shows portfolios that form the SMB hedge
portfolio.
Ideally, all the dotted lines in Figures 2.6, 2.7 and 2.8 should be horizontal straight lines. This
would mean that, within each characteristic bucket, forecast loadings were uncorrelated with any
characteristic. However, our method uses coarse characteristic sorts and therefore we do not expect
the characteristics of the high and low loading portfolios to be identical. Rather, we expect that
the loading with respect to the CP will be correlated with the characteristic used to construct it.
For example, bHML is correlated with BEME in the cross-section. This correlation translates into
differences in the average characteristics of the low b and the high b portfolios. Last, we do not
24For comparison, the average excess returns of the HML, RMW, and CMA portfolios over the same period are 30,27, and 22 bp/month, respectively.
89
control for the two other characteristics, when sorting on a particular loading. For example, when
we form BEME×ME×bHML sorted portfolios, we do not control for OP or INV. To the extent
that OP and/or INV are cross-sectionally correlated with bHML, we might also pick up variation in
those characteristics.
One way to assess the magnitude of the deviation of our sorted portfolios from the ideal “char-
acteristic balanced” case, is to compare the spread in characteristics within and across characteristic
buckets. The former constitutes the vertical distance between red and green dots, that are connected
with a dotted line, which we call the “unintended characteristic spread”. The latter is the vertical
distance across the dotted lines for the cases where the characteristic on the y-axis corresponds to
the one used to form the CP (i.e. HML with BEME, RMW with OP, and CMA with INV). This is
the “intended spread” in the characteristic between high and low characteristic portfolios used to
form the CP. This gives us an idea of the magnitude of a large spread in the characteristic.
As one can see from the figures, in general, the unintended spreads are relatively small, com-
pared to the intended spreads. For example, in the case of portfolios sorted on bhml, the unintended
BEME spread within characteristic buckets is at most about 0.23 (among the small-value stocks).
When we compare that to the intended spread in BEME between small value and small growth
stocks, which amounts to 1.13, we can conclude that the unintended spread is relatively small.
We view these results as evidence that even a sorting procedure as simple and coarse as ours
does a reasonable job in forming hedge portfolios that are close to being characteristic balanced.
Furthermore, the small observed return differences presented in Table 2.2 may be related to the
characteristic spread observed above. In fact, our theory predicts that the characteristic spreads
across low loading and high loading portfolios should relate to the expected returns in the hedge
portfolios. For example, among the firms in the small-cap, low BEME bucket in Panel A of Fig-
ure 2.6, there is considerable variation in OP. This could partially explain the 19 bp difference in
returns between the high and low bHML portfolios, as documented in the top row in Panel A of
Table 2.2.
Finally, from Figures 2.6, 2.7 and 2.8 we can also see that we forecast future loadings quite
90
well. Ideally, the low forecast loading stocks also have a low post-formation loading on the CPs.
Therefore, the red dots should always be the farthest to the left, whereas the green dots (the high
forecast loading stocks) should end up to the right of those, within each characteristic bucket.
Indeed we observe this pattern for all portfolios. Moreover, the spread between the red and the
green dots, within a given characteristic bucket, should be as large as possible. Indeed the spread
generated here is far bigger, as compared to, e.g., the one that is generated using a loading forecast
methodology following Daniel and Titman (1997) or Davis et al. (2000).25
2.3.3 Pricing results
In this subsection we describe the two key empirical results of this paper. First, we show that
we can reject the FF five-factor model using the hedge portfolios as test assets. Second we show
how to improve the Sharpe ratios of the FF CPs by combining them optimally with the hedge
portfolios. We argue that such CEPs have a better chance of spanning the mean variance efficient
frontier than the standard CPs proposed in the literature.
Pricing the hedge portfolios
We run a single time series regression of the monthly excess returns of the hedge portfolios
rh,m, m ∈ {HML,RMW,CMA,SMB,MktRF}, on the excess returns of the five FF CPs.
Table 2.4 reports the average excess returns, alphas and loadings as well as the corresponding
t−statistics.
Two attributes are important to determine the ability of the hedge portfolios in hedging unpriced
risk: They must have zero expected excess returns and have large loadings with respect to the
corresponding CP.
We first assess the hedge portfolios’ expected excess returns. Column “Avg" in Table 2.4
reports the monthly average excess returns of all hedge portfolios. Ideally, all of these numbers
should be exactly zero. For all 5 hedge portfolios, average excess returns are slightly positive but
25We present evidence on this in Appendix B.4.2.
91
statistically indistinguishable from zero. This result mirrors the fact that the hedge portfolios have
close to zero characteristic exposures. The fact that the excess returns are all slightly negative,
albeit insignificantly so, reflects the earlier insight, that characteristics and corresponding loadings
are inherently cross-sectionally correlated. A coarse sort (such as 3 buckets) is thus always at risk
of picking up some variation in the corresponding characteristic. Hence, going long high (short
low) loading stocks mechanically also tends to slightly tilt towards high (low) characteristic values,
as pointed out in Section 2.3.2.
We then turn to the hedge portfolios’ ability to hedge out unpriced risk by looking at their
post-formation loading on their corresponding CP. As expected, each hedge portfolio exhibits a
strong significantly positive loading on their corresponding CP. For example, the hedge portfolio
for HML has a loading on HML of 0.8 with a t−statistic of 28.21.
This directly translates into pricing implications, as indicated by the alphas. The five FF CPs
fail to price four out of five long-short hedge portfolios, three of them (MktRF, RMW, and CMA)
at a significance level of 5%.26 The last lines of the Table constructs equal-weight combinations
of these portfolios. The alphas for all of them are strongly statistically significant. For instance,
when we consider the equal-weight combination of four hedge portfolios (the ones corresponding
to HML, RMW, CMA and MktRF), the monthly alpha is -0.18 with a t-statistic of -5.92.
Ex-ante determination of the optimal hedge-ratio
Having studied the hedge portfolios, the next step is to construct characteristic efficient portfo-
lios, i.e.,
r∗c,m,t = rc,m,t − rrrh,tδδδm,t−1 (2.33)
where m ∈ {HML,RMW,CMA,SMB,MktRF}.27
The optimal hedge ratio δδδm,t−1 is determined ex-ante, in the spirit of equation (2.15). We
26The only one for which the FF model cannot be rejected, even at the 10% level, is the SMB hedge portfolio. Thefact that the FF model succeeds in pricing the SMB hedge portfolio is consistent with the notion that there is little toprice there, as we know that the size premium has historically been relatively weak.
27To be consistent with our notation, the returns of, for example, the HML portfolio at time t should be denoted byrc,BEME,t. We simplify the notation by calling it rHML,t.
92
employ the same loading forecast techniques as described before to forecast loadings, i.e., we
first calculate five years of constant-weight and constant-allocation pre-formation returns of rc,m,t
and rh,t. We then calculate correlations over the whole five years of 3-day overlapping return
observations and variances by utilizing only the most recent 12 months of daily observations.
Note that this is done in a multi-variate framework, i.e., we consider the covariance of each CP
with all five hedge portfolios, to account for the correlation structure among the hedge portfolios.
Consequently, both δδδm,t−1 and rrrh,t are M−dimensional vectors, where M = 5 in the case of
the FF model examined here. Note further, that the returns of the CEPs r∗m,t are (approximately)
orthogonal to the returns of the hedge portfolios rrrh,t. The reason why they are only approximately
orthogonal is because the δδδm,t−1 is estimated ex-ante, i.e., up to t− 1.
Characteristic efficient Fama and French portfolios
The first column of Table 2.5 reports key statistics on the returns of each of the CPs (rc):
the annualized average returns in percentages, the annualized volatility of returns and the squared
annualized Sharpe ratio. The second column reports the same three quantities for the CEPs, r∗c .
These portfolios are constructed exactly as in expression (2.33).
When we move from rc,m to r∗c,m, we see that the mean return of all characteristic portfolios
decreases, but that the volatility decreases substantially more. This leads to an increase in the
Sharpe ratio for each of the individual Fama and French CPs. For example, the squared Sharpe
ratio of the improved version of CMA is 0.3, where the squared Sharpe ratio of the original CMA
is 0.16.
The right-side panel of Table 2.5 presents p-values for the differences in means based on a
t-test, and for the volatilities using a Levene (1961) test for equality of variances. To test for
differences in Sharpe-Ratios, we use a test based on Jensen (1968)’s alpha. Specifically, to assess
whether the portfolio performance increases when we move from the CP to the CEP, we run a
time-series regression of the returns of the CEP on the CP, and obtain a p-value for the regression
intercept. Consistent with the interpretation of Jensen (1968) we are testing whether there is a
93
statistically significant performance differential between the CP and the CEP.
While the result that we improve on each characteristic portfolio individually is promising, the
ultimate goal of the exercise was to construct a set of portfolios that gets closer to spanning the
mean variance efficient portfolio, as compared to the CPs. Hence, in the second-to-last panel of
Table 2.5, we compute the in-sample optimal combination of both the original FF CPs (column
rc,m) and the CEPs (r∗c,m). The maximum achievable squared Sharpe ratio with FF CPs in the
sample period covered in this paper (1963/07 - 2019/12) is 1.17. The squared Sharpe ratio of the
optimal combination of the CEPs is instead 2.13.
Notice that each individual CEP is perfectly tradable, as all information used to construct them
is known to an investor ex-ante. Only the weights of optimal combinations of the five CPs as well
as CEPs, as reported in the bottom panel of Table 2.5, are calculated in-sample. Additionally, we
want to emphasize that the way we construct our portfolios is very conservative, in that we only
rebalance once every year—in order to be consistent with the rules of the game set by Fama and
French.
We reiterate that our empirical approach does not in general deliver the theoretical CEPs. Com-
putation of the optimal hedge portfolios (see equation (2.31)) and optimal hedge ratios (described
in equation (2.30)) requires knowledge of Σ, which is difficult to estimate, as well as of the post-
formation loadings. Nevertheless, the CEPs deliver a large improvement over the CPs. Moreover,
our empirical method is robust and, at same time, delivers tradable hedge portfolios.
Redundancy of HML
FF find that HML is redundant, in that it is spanned by the other CPs. Table 2.6 shows that
we can replicate this result based on our extended sample. The weight of HML in the ex-post
optimal combination, based on Markowitz optimization, is -2.0 % when we use the original FF
CPs (column rc). However, if we use the CEPs (column r∗c ), the weight on HML increases to 8.0
%, close to the weight on MktRF .
We can confirm this result by running spanning regressions in Table 2.7. The return of HML,
94
rHML is indeed spanned by the other four CPs (column 1). It is similarly subsumed by the other
four CEPs (column 2). The return of the CEP version of HML, r∗HML (column 3), is not fully
spanned by the returns of the other four FF CPs: removing unpriced sources of variation from
HML makes it an unspanned portfolio, relative to the other four original FF CPs. The alpha of
a regression of the HML CEP on the other CEPs has a t-statistic of 1.72. We can thus reject
redundancy of HML∗ at the 10% significance level.
An important additional empirical finding is that the correlation between HML∗ and RMW ∗
is now strongly negative, −.52, whereas it was positive but very small for HML and RMW , .09
(see Table 2.8). This fact suggests that both CPs, HML and RMW , load on an unpriced source
of common variation. The implication is that an investor can capture the premium associated with
exposure to HML∗ and RMW ∗ while lowering the total variance of the portfolio.
2.3.4 Industry-neutral characteristic portfolios
In Section 2.2.1, we argued that industry was one potential source of common variation that
was likely to be unpriced. Since we know that there are periods in which the FF CPs strongly
load on industry portfolios, a natural exercise is to construct CPs that are industry-neutral. In this
section, we construct industry-neutral versions of CPs and compare their performance with the
performance of the CEPs constructed in this paper.
To construct industry-neutral CPs we ex-ante hedge any exposure to the 12 FF industries out of
the FF CPs, except for the market.28 Define the returns of the industry-neutral portfolio, rc−ind,m,t,
as:
rc−ind,m,t = rc,m,t − rrrind,tδδδindc,m,t−1 (2.34)
wherem ∈ {HML,RMW,CMA,SMB,MktRF}, rrrind,t is a (1×12) vector with excess returns
of all 12 industries, δδδindc,m,t−1 is the ex-ante optimal industry hedge-ratio. Analogous to the previous
exercises, δδδindc,m,t−1 is estimated every June 30th, using correlations over the previous five years of
28The market is a linear combination of all industries and thus, hedging out industries from the market using themethod described is not feasible.
95
3-day overlapping return observations and variances by using only the most recent 12 months of
daily observations.29
Table 2.5 reports the mean, volatility and squared Sharpe ratios for all rc−ind,m and the in-
sample optimal combination of the industry-neutral characteristic portfolios. Hedging out industry
risk leads to an improvement in the squared Shape ratio for HML, CMA and SMB, consistent
with the hypothesis that it is generally unpriced risk. However, the CEPs outperform the industry-
hedged CPs in the case of RMW and CMA, i.e., the use of our hedge portfolio results in a greater
Sharpe ratio improvement than simply hedging out industry exposure. In contrast, for HML the
industry-neutral version has a higher Sharpe ratio than CEP. A possible explanation is that, in
theory, unlike our procedure, the industry-hedging can change the characteristic of the resulting
portfolio and as a consequence the exposure to the priced factor. Recall that our CEPs have the
same characteristics as the CPs, but lower variance and therefore a higher squared Sharpe ratio.
Instead, industry-neutral portfolios do not need to have the same characteristic as the original CPs
and our theory does not have a prediction for this case.
Nevertheless, improving the squared Sharpe ratios for each of the CPs is not the goal. Rather
it is to construct CEPs that span the MVE portfolio. Indeed, the ex-post optimal combination
of the CEPs shows a far more dramatic improvement over the original FF CPs compared to the
ex-post optimal combination of industry-hedged portfolios. Based on our Jensen (1968) test, the
CEPs’ optimal combination significantly outperforms the industry-neutral one.30 Since the market
could not be included in the industry-hedging, we repeat the ex-post optimal combination exercise
excluding MktRF in the last panel of Table 2.5. The CEPs also achieve a higher Sharpe ratio
compared to the industry-neutral CPs in this specification, and that difference is also statistically
significant.
These results suggest that simply hedging out industry exposure is not optimal for two potential
reasons. First, some component of the industry factors might be priced. Second, there can be other
29We also employ constant-weight, constant-allocation (as of June 30th) pre-formation returns of the factor- andindustry-portfolios.
30Note that we test whether Jensen’s α of regressing the CEP on the industry-neutral portfolio is statistically largerthan zero. For CPs where the point estimate of that α is negative (such as HML and SMB), we report a “-”.
96
sources of common variation that are not related to industries and do not command a premium.
Our procedure is designed to only hedge out unpriced sources of common variation and does not
require us to identify those sources.
2.4 Conclusions
This paper makes two contributions to the asset pricing literature. First, we examine the stan-
dard procedure employed for constructing characteristic portfolios (CPs): zero-investment portfo-
lios for which the long side is a portfolio of high characteristic stocks, and the short side consists
of a portfolio of low characteristic stocks. This procedure, which has become standard since Fama
and French (1993), does not guarantee that the set of portfolios will span the mean variance ef-
ficient frontier. The reason is that, when sorting on a characteristic, the resulting portfolios are
likely to load on an unpriced sources of common variation. Our second contribution is to show
how to construct hedge portfolios that capture the unpriced risk in these portfolios, and which can
be combined with the CPs to form characteristic efficient portfolios (CEPs) that are free of expo-
sure to these unpriced sources of common variation. Our hedge portfolios are constructed to have
maximum loading on the CPs, subject to having zero characteristic. We show in particular that
if the model linking characteristics and average excess returns is correct, the CEPs will span the
mean variance efficient portfolio.
We illustrate the empirical relevance of our ideas in the context of the five-factor model of
Fama and French (2015). We take the five characteristic portfolios from that model and construct
hedge portfolios for each. Then we construct empirical counterparts to the CEPs, one for each
of the characteristics (market, size, market-to-book, profitability and investment) by optimally
combining the original CPs with our hedge portfolios. The in-sample squared Sharpe ratio of the
optimal combination of the FF CPs is 1.16 whereas it is 2.16 for the CEPs. Removing unpriced
sources of common variation from the original CPs is both empirically and economically relevant.
This paper sheds light on some of the debates in the cross-sectional asset pricing literature.
97
First, an important, if somewhat implicit, assumption in the literature is that there is a model
linking average excess return to characteristics. The existence of this model is also our starting
point. Our contribution is then to show how to construct the CEPs from the CPs so that they span
the MVE portfolio. It is a representation theorem: If a complete model of average excess returns
and characteristics is available, then average excess returns can be fully described with a “factor
model” in which the “factors” are the CEPs.
Economic theory is interested in understanding the economic forces that are the sources of
premia in asset returns. The CEPs we construct are important when discriminating between al-
ternative economic models of the marginal rate of substitution of the representative investor. The
reason is that only the return of the optimal combination of the CEPs—which is the maximum
Sharpe ratio portfolio—is maximally correlated with shocks to the marginal rate of substitution of
the representative investor. The returns of the CPs are not, as these portfolios also load on unpriced
sources of common variation. CEPs then provide a lens through which we can learn about the
economic shocks that matter for the representative investor.
Second, the loadings of any portfolio on the CEPs equal the portfolio characteristics. This
clarifies the characteristics versus covariance debate. To put it sharply: In the context of the asset
pricing models that spring from Fama and French (1993) there is no distinction between charac-
teristics and covariances when the portfolios that serve as factors are the CEPs.
Third, we emphasize the distinction between priced and unpriced sources of common variation.
A full description of the covariance matrix of returns requires at the very least the CEPs and
the hedge portfolios, but only the CEPs are needed for pricing. This speaks to the theoretical
distinction between the APT of Ross (1976) and the ICAPM of Merton (1973). The first is a
model of the covariance matrix of returns whereas the second is a model of sources of premia, that
is, of expected excess returns. Keeping in mind this distinction when building asset pricing models
out of characteristics is key to guaranteeing that the resulting portfolios span the MVE portfolio.
98
Figures
Figure 2.2: Rolling regression R2s – HML returns on industry returns
1970
1980
1990
2000
2010
2020
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
R2 (
126-da
y-rollin
g)
This figure shows the R2 from 126-day rolling regressions of daily HML returns on the twelve daily Fama and French(1997) industry excess returns. The time period is 1963/07 - 2019/12.
99
Figure 2.3: HML loadings on industry-portfolios
1970
1980
1990
2000
2010
2020
−0.6
−0.4
−0.2
0.0
0.2
0.4
0.6
Indu
stry lo
adings
(126
-day-ro
lling)
BusEqMoneyChemsDurblEnrgyHlthManufNoDurOtherShopsTelcmUtils
1970
1980
1990
2000
2010
2020
−0.4
−0.2
0.0
0.2
0.4
0.6
Money
-indu
stry lo
ading of H
ML (126
-day
-rollin
g)
The upper panel of this figure plots the loadings from rolling 126-day regressions of the daily returns to the HMLcharacteristic portfolio on the twelve daily Fama and French (1997) industry excess returns over the 1963/07-2019/12time period. The lower panel plots only the loading on the Money industry portfolio (including the 95% confidenceinterval) and hides the other 11 industry-portfolio loadings.
100
Figure 2.4: Volatility of the money industry-portfolios
1970
1980
1990
2000
2010
2020
0.0
0.2
0.4
0.6
0.8
1.0An
nualize
d Vo
latility
(126
-day
-rollin
g)
This figure shows 126-day volatility of the daily returns to the Money portfolio over the 1963/07 - 2019/12 timeperiod.
Figure 2.5: Rolling regression R2s – HML returns on Money industry returns
2002
2004
2006
2008
2010
2012
2014
2016
2018
2020
0.0
0.2
0.4
0.6
0.8
1.0
R2 (
126-da
y-rollin
g)
This figure shows the R2 from 126-day rolling regressions of daily HML returns on daily Money industry excessreturns from the 12 Fama and French (1997) industry returns. The time period is 2000/01 - 2019/12.
101
Figure 2.6: Ex-post HML/RMW/CMA loadings vs. characteristicsB
EM
EPanel A: HML
−1.5 −1.0 −0.5 0.0 0.5 1.0 1.5Post-formation bHML
0.00
0.25
0.50
0.75
1.00
1.25
1.50
1.75
2.00
BEME
Low bHMLMedium bHMLigh bHML
Panel B: RMW
−1.5 −1.0 −0.5 0.0 0.5 1.0 1.5Post-formation bRMW
0.00
0.25
0.50
0.75
1.00
1.25
1.50
1.75
2.00
BEME
Low bRMWMedium bRMWigh bRMW
Panel C: CMA
−1.5 −1.0 −0.5 0.0 0.5 1.0 1.5Post-formation bCMA
0.00
0.25
0.50
0.75
1.00
1.25
1.50
1.75
2.00
BEME
Low bCMAMedium bCMAigh bCMA
OP
−1.5 −1.0 −0.5 0.0 0.5 1.0 1.5Post-formation bHML
−0.4
−0.2
0.0
0.2
0.4
0.6
0.8
1.0
OP
Low bHMLMedium bHMLigh bHML
−1.5 −1.0 −0.5 0.0 0.5 1.0 1.5Post-formation bRMW
−0.4
−0.2
0.0
0.2
0.4
0.6
0.8
1.0
OP
Low bRMWMedium bRMWigh bRMW
−1.5 −1.0 −0.5 0.0 0.5 1.0 1.5Post-formation bCMA
−0.4
−0.2
0.0
0.2
0.4
0.6
0.8
1.0
OP
Low bCMAMedium bCMAigh bCMA
INV
−1.5 −1.0 −0.5 0.0 0.5 1.0 1.5Post-formation bHML
−0.2
0.0
0.2
0.4
0.6
0.8
INV
Low bHMLMedium bHMLigh bHML
−1.5 −1.0 −0.5 0.0 0.5 1.0 1.5Post-formation bRMW
−0.2
0.0
0.2
0.4
0.6
0.8
INV
Low bRMWMedium bRMWigh bRMW
−1.5 −1.0 −0.5 0.0 0.5 1.0 1.5Post-formation bCMA
−0.2
0.0
0.2
0.4
0.6
0.8
INV
Low bCMAMedium bCMAigh bCMA
ME
−1.5 −1.0 −0.5 0.0 0.5 1.0 1.5Post-formation bHML
2
4
6
8
10
12
14
log(ME)
Lo bHMLMedium bHMLigh bHML
−1.5 −1.0 −0.5 0.0 0.5 1.0 1.5Post-formation bRMW
2
4
6
8
10
12
14
log(ME)
Lo bRMWMedium bRMWigh bRMW
−1.5 −1.0 −0.5 0.0 0.5 1.0 1.5Post-formation bCMA
2
4
6
8
10
12
14
log(ME)
Lo bCMAMedium bCMAigh bCMA
This figure shows the time-series average of post-formation characteristic portfolio loading on the x-axis and the time-series average of each characteristic on the y-axis for each of the 27 portfolios formed on size, characteristic (book-to-market/operating profitability/investment) and HML/RMW/CMA-loading. The first column uses sorts on book-to-market and HML-loading, the second one operating profitability and RMW-loading and the last one investment andCMA-loading.
102
Figure 2.7: Ex-post MktRF loadings vs. characteristicsB
EM
EPanel A: MktRF (ME × BEME)
0.6 0.8 1.0 1.2 1.4Post-formation bMktRF
0.00
0.25
0.50
0.75
1.00
1.25
1.50
1.75
2.00
BEME
Low bMktRFMedium bMktRFigh bMktRF
Panel B: MktRF (ME × OP)
0.6 0.8 1.0 1.2 1.4Post-formation bMktRF
0.00
0.25
0.50
0.75
1.00
1.25
1.50
1.75
2.00
BEME
Low bMktRFMedium bMktRFigh bMktRF
Panel C: MktRF (ME × INV)
0.6 0.8 1.0 1.2 1.4Post-formation bMktRF
0.00
0.25
0.50
0.75
1.00
1.25
1.50
1.75
2.00
BEME
Low bMktRFMedium bMktRFigh bMktRF
OP
0.6 0.8 1.0 1.2 1.4Post-formation bMktRF
−0.4
−0.2
0.0
0.2
0.4
0.6
0.8
1.0
OP
Low bMktRFMedium bMktRFHigh bMktRF
0.6 0.8 1.0 1.2 1.4Post-formation bMktRF
−0.4
−0.2
0.0
0.2
0.4
0.6
0.8
1.0
OP
Low bMktRFMedium bMktRFHigh bMktRF
0.6 0.8 1.0 1.2 1.4Post-formation bMktRF
−0.4
−0.2
0.0
0.2
0.4
0.6
0.8
1.0
OP
Low bMktRFMedium bMktRFHigh bMktRF
INV
0.6 0.8 1.0 1.2 1.4Post-formation bMktRF
−0.2
0.0
0.2
0.4
0.6
0.8
INV
Low bMktRFMedium bMktRFHigh bMktRF
0.6 0.8 1.0 1.2 1.4Post-formation bMktRF
−0.2
0.0
0.2
0.4
0.6
0.8
INV
Low bMktRFMedium bMktRFHigh bMktRF
0.6 0.8 1.0 1.2 1.4Post-formation bMktRF
−0.2
0.0
0.2
0.4
0.6
0.8
INV
Low bMktRFMedium bMktRFHigh bMktRF
ME
0.6 0.8 1.0 1.2 1.4Post-formation bMktRF
2
4
6
8
10
12
14
log(ME)
Low bMktRFMedium bMktRFigh bMktRF
0.6 0.8 1.0 1.2 1.4Post-formation bMktRF
2
4
6
8
10
12
14
log(ME)
Low bMktRFMedium bMktRFigh bMktRF
0.6 0.8 1.0 1.2 1.4Post-formation bMktRF
2
4
6
8
10
12
14
log(ME)
Low bMktRFMedium bMktRFigh bMktRF
This figure shows the time-series average of post-formation characteristic portfolio loading on the x-axis and the time-series average of each characteristic on the y-axis for each of the 27 portfolios formed on size, characteristic (book-to-market/operating profitability/investment) and MktRF-loading. The first column uses sorts on book-to-market andMktRF-loading, the second one operating profitability and MktRF-loading and the last one investment and MktRF-loading.
103
Figure 2.8: Ex-post SMB loadings vs. characteristics.B
EM
EPanel A: SMB (ME × BEME)
−1.5 −1.0 −0.5 0.0 0.5 1.0 1.5Post-formation bSMB
0.00
0.25
0.50
0.75
1.00
1.25
1.50
1.75
2.00
BEME
Low bSMBMedium bSMBigh bSMB
Panel B: SMB (ME × OP)
−1.5 −1.0 −0.5 0.0 0.5 1.0 1.5Post-formation bSMB
0.00
0.25
0.50
0.75
1.00
1.25
1.50
1.75
2.00
BEME
Low bSMBMedium bSMBigh bSMB
Panel C: SMB (ME × INV)
−1.5 −1.0 −0.5 0.0 0.5 1.0 1.5Post-formation bSMB
0.00
0.25
0.50
0.75
1.00
1.25
1.50
1.75
2.00
BEME
Low bSMBMedium bSMBigh bSMB
OP
−1.5 −1.0 −0.5 0.0 0.5 1.0 1.5Post-formation bSMB
−0.4
−0.2
0.0
0.2
0.4
0.6
0.8
1.0
OP
Low bSMBMedium bSMBigh bSMB
−1.5 −1.0 −0.5 0.0 0.5 1.0 1.5Post-formation bSMB
−0.4
−0.2
0.0
0.2
0.4
0.6
0.8
1.0
OP
Low bSMBMedium bSMBigh bSMB
−1.5 −1.0 −0.5 0.0 0.5 1.0 1.5Post-formation bSMB
−0.4
−0.2
0.0
0.2
0.4
0.6
0.8
1.0
OP
Low bSMBMedium bSMBigh bSMB
INV
−1.5 −1.0 −0.5 0.0 0.5 1.0 1.5Post-formation bSMB
−0.2
0.0
0.2
0.4
0.6
0.8
INV
Low bSMBMedium bSMBigh bSMB
−1.5 −1.0 −0.5 0.0 0.5 1.0 1.5Post-formation bSMB
−0.2
0.0
0.2
0.4
0.6
0.8
INV
Low bSMBMedium bSMBigh bSMB
−1.5 −1.0 −0.5 0.0 0.5 1.0 1.5Post-formation bSMB
−0.2
0.0
0.2
0.4
0.6
0.8
INV
Low bSMBMedium bSMBigh bSMB
ME
−1.5 −1.0 −0.5 0.0 0.5 1.0 1.5Post-formation bSMB
2
4
6
8
10
12
14
log(ME)
Lo bSMBMedium bSMBigh bSMB
−1.5 −1.0 −0.5 0.0 0.5 1.0 1.5Post-formation bSMB
2
4
6
8
10
12
14
log(ME)
Lo bSMBMedium bSMBigh bSMB
−1.5 −1.0 −0.5 0.0 0.5 1.0 1.5Post-formation bSMB
2
4
6
8
10
12
14
log(ME)
Lo bSMBMedium bSMBigh bSMB
This figure shows the time-series average of post-formation characteristic portfolio loading on the x-axis and the time-series average of each characteristic on the y-axis for each of the 27 portfolios formed on size, characteristic (book-to-market/operating profitability/investment) and SMB-loading. The first column uses sorts on book-to-market andSMB-loading, the second one operating profitability and SMB-loading and the last one investment and SMB-loading.
104
Tables
Table 2.1: Low book-to-market stocks in the Money industry as of June 2008
Firm BE/ME βHML-portfolioAmerican Express 0.19 3United Health 0.27 3Aflac 0.29 3Charles Schwab 0.13 3Franklin Resources 0.27 3Cme Group 0.34 3Aetna 0.36 2Express Scripts Holding 0.04 1Northern Trust 0.27 3Price T. Rowe 0.17 3TD Ameritrade 0.18 2Cigna 0.34 1Navient 0.36 3Humana 0.32 2Nasdaq 0.32 2
The first column reports the largest fifteen stocks in the Money industry in the low book-to-market bin, sorted bymarket capitalization. The second column reports the book-to-market and the third reports the HML loading-portfolioto which the stock belongs as of June 30th, 2008.
105
Table 2.2: Average monthly excess returns for the sorted portfolios
Panel A: HML
Char-Portfolio bHML-PortfolioBEME ME 1 2 3 Avg.1 1 0.49 0.65 0.68 0.59
2 0.52 0.61 0.753 0.49 0.55 0.55
2 1 0.86 0.91 0.91 0.752 0.71 0.79 0.843 0.57 0.58 0.57
3 1 1.02 0.98 1.02 0.872 0.91 0.86 1.013 0.76 0.66 0.63
Avg. 0.71 0.73 0.77
Panel B: RMW
Char-Portfolio bRMW -PortfolioOP ME 1 2 3 Avg.1 1 0.63 0.84 0.79 0.61
2 0.58 0.71 0.713 0.26 0.49 0.48
2 1 0.88 0.95 0.82 0.712 0.72 0.79 0.763 0.51 0.45 0.5
3 1 0.89 1.04 0.97 0.82 0.77 0.84 0.933 0.61 0.58 0.59
Avg. 0.65 0.74 0.73
Panel C: CMA
Char-Portfolio bCMA-PortfolioINV ME 1 2 3 Avg.1 1 0.97 1 0.9 0.8
2 0.81 0.85 0.733 0.73 0.64 0.6
2 1 0.95 0.91 0.98 0.782 0.97 0.87 0.743 0.57 0.51 0.57
3 1 0.59 0.76 0.59 0.622 0.62 0.73 0.713 0.52 0.55 0.55
Avg. 0.75 0.76 0.71
Mkt
RF
Panel D: MktRF (ME × BEME)
Char-Portfolio bMktRF -PortfolioBEME ME 1 2 3 Avg.1 1 0.51 0.68 0.57 0.58
2 0.64 0.66 0.63 0.57 0.53 0.47
2 1 0.76 0.92 0.97 0.742 0.7 0.8 0.863 0.49 0.62 0.59
3 1 0.96 1.03 1.01 0.872 0.84 0.92 1.023 0.57 0.65 0.82
Avg. 0.67 0.76 0.77
Panel E: MktRF (ME × OP)
Char-Portfolio bMktRF -PortfolioOP ME 1 2 3 Avg.1 1 0.54 0.75 0.84 0.6
2 0.56 0.75 0.733 0.36 0.43 0.46
2 1 0.85 0.93 0.86 0.712 0.7 0.76 0.813 0.45 0.5 0.55
3 1 1.03 0.96 0.95 0.812 0.8 0.85 0.873 0.65 0.56 0.66
Avg. 0.66 0.72 0.75
Panel F: MktRF (ME × INV)
Char-Portfolio bMktRF -PortfolioINV ME 1 2 3 Avg.1 1 0.75 1 1.04 0.8
2 0.73 0.78 0.923 0.63 0.67 0.7
2 1 0.85 0.94 1.02 0.782 0.79 0.83 0.963 0.48 0.51 0.63
3 1 0.69 0.69 0.57 0.622 0.6 0.77 0.673 0.57 0.51 0.53
Avg. 0.68 0.74 0.78
SMB
Panel G: SMB (ME × BEME)
Char-Portfolio bSMB -PortfolioBEME ME 1 2 3 Avg.1 1 0.51 0.66 0.57 0.6
2 0.59 0.66 0.683 0.49 0.61 0.6
2 1 0.78 0.86 1.01 0.772 0.67 0.78 0.943 0.47 0.66 0.73
3 1 0.96 0.98 1.09 0.892 0.82 0.91 1.13 0.53 0.72 0.93
Avg. 0.65 0.76 0.85
Panel H: SMB (ME × OP)
Char-Portfolio bSMB -PortfolioOP ME 1 2 3 Avg.1 1 0.66 0.77 0.73 0.62
2 0.65 0.72 0.673 0.29 0.49 0.65
2 1 0.81 0.93 0.89 0.742 0.66 0.77 0.883 0.42 0.62 0.67
3 1 0.96 1.04 0.9 0.822 0.77 0.85 0.943 0.58 0.66 0.73
Avg. 0.64 0.76 0.78
Panel I: SMB (ME × INV)
Char-Portfolio bSMB -PortfolioINV ME 1 2 3 Avg.1 1 0.89 0.95 1 0.82
2 0.69 0.82 0.963 0.55 0.74 0.79
2 1 0.89 0.97 0.99 0.812 0.78 0.82 1.013 0.46 0.62 0.76
3 1 0.6 0.71 0.58 0.642 0.63 0.69 0.763 0.46 0.64 0.67
Avg. 0.66 0.77 0.84
Stocks are sorted into 3 portfolios based on the respective characteristic — book-to-market (BEME), operating profitability (OP) or investment (INV) — andindependently into 3 size (ME) groups. These are depicted row-wise and indicated in the first two columns. Last, within each bucket, stocks are sorted into 3further portfolios based on the loading forecast. These portfolios are displayed column-wise and in Panels A-C for HML, RMW, CMA, and Panels D-F for MktRF,and Panels G-I for SMB. The last column shows average returns of all 9 respective characteristic-portfolios. The last row shows averages of all 9 respectiveloading-portfolios. The sample period is 1963/07 - 2019/12.
106
Table 2.3: Alphas and loadings
Panel A: HML
Char-Portfolio pre-formation bHML-sorted portfolios
BEME ME 1 2 3 1-3 1 2 3 1-3
α t(α)
1 1 0.00 -0.03 -0.14 0.15 0.04 -0.47 -2.15 1.24
2 0.09 -0.09 -0.13 0.23 1.16 -1.43 -1.87 2.07
3 0.05 0.03 -0.02 0.07 0.83 0.48 -0.24 0.62
2 1 0.12 0.09 -0.02 0.13 1.79 1.68 -0.30 1.51
2 -0.11 -0.06 -0.04 -0.07 -1.56 -1.02 -0.62 -0.68
3 -0.06 -0.13 -0.14 0.08 -0.66 -1.85 -1.69 0.67
3 1 0.22 0.10 -0.07 0.29 3.08 2.07 -1.21 3.02
2 0.01 -0.04 0.01 -0.01 0.08 -0.63 0.15 -0.05
3 0.02 -0.16 -0.11 0.13 0.27 -2.04 -1.08 0.83
Avg. 0.04 -0.03 -0.07 0.11 1.07 -1.20 -2.12 1.86
post-formation bHML t(bHML)
1 1 -0.71 -0.23 0.08 -0.79 -15.22 -6.98 2.40 -13.93
2 -0.74 -0.19 0.29 -1.03 -19.12 -6.73 8.52 -19.71
3 -0.48 -0.18 0.17 -0.65 -16.67 -7.23 5.49 -12.98
2 1 -0.16 0.15 0.50 -0.66 -5.34 5.92 19.17 -15.97
2 -0.04 0.28 0.62 -0.66 -1.20 9.50 19.19 -14.59
3 -0.10 0.27 0.56 -0.66 -2.58 7.92 14.56 -11.56
3 1 0.07 0.45 0.84 -0.78 2.08 20.15 30.99 -17.32
2 0.24 0.51 1.01 -0.78 6.09 17.24 23.61 -12.09
3 0.16 0.65 1.33 -1.17 3.81 17.13 28.04 -15.66
Avg. -0.20 0.19 0.60 -0.80 -11.54 14.28 37.00 -28.21
Panel B: RMW
Char-Portfolio pre-formation bRMW-sorted portfolios
OP ME 1 2 3 1-3 1 2 3 1-3
α t(α)
1 1 0.03 0.07 -0.13 0.16 0.40 1.31 -2.22 1.61
2 0.22 0.05 -0.12 0.33 2.16 0.73 -1.76 2.75
3 0.11 0.01 -0.23 0.34 1.29 0.08 -2.99 2.60
2 1 0.09 0.07 -0.16 0.25 1.34 1.14 -2.78 2.80
2 0.01 -0.02 -0.14 0.15 0.19 -0.35 -2.11 1.65
3 0.15 -0.15 -0.20 0.35 1.99 -2.46 -2.86 2.98
3 1 0.03 0.07 -0.07 0.10 0.39 1.12 -0.95 0.91
2 -0.07 -0.09 -0.09 0.02 -1.05 -1.48 -1.13 0.19
3 0.16 0.01 -0.00 0.16 2.47 0.21 -0.05 1.53
Avg. 0.08 -0.00 -0.13 0.21 2.31 -0.00 -3.83 3.66
post-formation bRMW t(bRMW )
1 1 -0.89 -0.19 0.04 -0.92 -22.35 -7.54 1.26 -18.84
2 -1.09 -0.22 0.11 -1.19 -22.17 -6.74 3.27 -19.98
3 -1.22 -0.40 0.11 -1.33 -28.38 -11.44 2.82 -20.48
2 1 0.00 0.30 0.33 -0.32 0.13 10.52 11.53 -7.53
2 -0.03 0.30 0.37 -0.41 -1.10 10.28 11.78 -9.19
3 -0.51 0.16 0.29 -0.80 -13.98 5.18 8.53 -14.10
3 1 0.02 0.43 0.41 -0.39 0.54 14.70 11.56 -7.30
2 0.29 0.54 0.62 -0.32 8.92 17.94 15.80 -6.50
3 -0.07 0.27 0.42 -0.49 -2.11 10.17 13.84 -9.40
Avg. -0.39 0.13 0.30 -0.69 -22.51 9.79 18.56 -24.80
107
Panel C: CMA
Char-Portfolio pre-formation bCMA-sorted portfolios
INV ME 1 2 3 1-3 1 2 3 1-3
α t(α)
1 1 0.13 0.14 0.02 0.12 2.05 2.74 0.19 1.16
2 0.05 -0.00 -0.22 0.27 0.78 -0.05 -2.57 2.45
3 0.17 -0.11 -0.23 0.40 2.22 -1.71 -3.13 3.36
2 1 0.10 0.07 0.14 -0.04 1.64 1.22 2.15 -0.44
2 0.25 0.08 -0.13 0.39 3.42 1.36 -1.93 3.83
3 0.13 -0.07 -0.13 0.26 1.71 -1.21 -2.16 2.30
3 1 -0.22 -0.04 -0.18 -0.04 -3.10 -0.80 -2.82 -0.45
2 -0.01 -0.09 -0.01 -0.00 -0.13 -1.39 -0.15 -0.01
3 0.34 -0.00 -0.16 0.50 3.86 -0.06 -2.21 3.65
Avg. 0.10 -0.00 -0.10 0.20 2.91 -0.14 -3.01 3.39
post-formation bCMA t(bCMA)
1 1 0.06 0.25 0.68 -0.61 1.33 6.35 11.47 -8.14
2 -0.09 0.55 0.93 -1.02 -1.77 11.23 14.70 -12.38
3 -0.11 0.56 1.22 -1.33 -1.96 11.28 22.24 -15.03
2 1 -0.23 0.16 0.35 -0.58 -5.03 3.78 6.98 -8.27
2 -0.36 0.12 0.42 -0.78 -6.54 2.92 8.08 -10.34
3 -0.45 0.17 0.64 -1.09 -8.11 3.78 13.79 -12.85
3 1 -0.54 -0.11 -0.00 -0.54 -10.05 -2.77 -0.05 -7.55
2 -0.92 -0.15 0.24 -1.16 -13.88 -3.25 4.81 -13.70
3 -1.16 -0.23 0.33 -1.49 -17.41 -5.15 6.32 -14.59
Avg. -0.42 0.15 0.53 -0.96 -15.71 7.11 21.44 -21.13
Panel D: MktRF (ME × BEME)
Char-Portfolio pre-formation bMktRF-sorted portfolios
BEME ME 1 2 3 1-3 1 2 3 1-3
α t(α)
1 1 -0.10 0.01 -0.16 0.06 -1.25 0.10 -1.76 0.48
2 0.01 -0.05 -0.11 0.13 0.23 -0.79 -1.34 1.13
3 0.18 0.02 -0.14 0.32 2.94 0.47 -1.83 2.69
2 1 0.02 0.06 0.04 -0.02 0.33 1.09 0.62 -0.20
2 -0.01 -0.05 -0.16 0.15 -0.15 -0.74 -2.14 1.48
3 -0.06 -0.06 -0.25 0.19 -0.70 -0.82 -2.86 1.51
3 1 0.31 0.11 -0.12 0.43 4.82 2.14 -1.90 4.53
2 0.13 -0.01 -0.17 0.30 1.89 -0.14 -1.79 2.32
3 -0.06 -0.06 -0.12 0.06 -0.63 -0.75 -1.14 0.38
Avg. 0.05 -0.00 -0.13 0.18 1.21 -0.10 -2.94 2.37
post-formation bMktRF t(bMktRF )
1 1 0.86 1.01 1.18 -0.32 43.85 54.94 53.11 -10.35
2 0.90 1.08 1.23 -0.33 54.27 69.79 57.47 -11.38
3 0.88 1.01 1.17 -0.29 56.32 76.61 62.49 -9.79
2 1 0.74 0.94 1.13 -0.39 49.73 69.68 70.65 -15.97
2 0.79 1.02 1.24 -0.45 48.71 64.83 66.52 -17.74
3 0.79 1.02 1.22 -0.43 39.43 57.74 56.69 -13.55
3 1 0.65 0.91 1.21 -0.55 40.98 71.92 74.80 -23.35
2 0.78 1.07 1.33 -0.55 45.74 65.85 56.57 -17.11
3 0.83 1.05 1.29 -0.47 34.39 52.29 47.94 -11.33
Avg. 0.80 1.01 1.22 -0.42 81.52 152.09 108.71 -22.12
108
Panel E: MktRF (ME × OP)
Char-Portfolio pre-formation bMktRF-sorted portfolios
OP ME 1 2 3 1-3 1 2 3 1-3
α t(α)
1 1 -0.07 0.01 -0.03 -0.03 -1.00 0.25 -0.45 -0.33
2 0.03 0.15 -0.04 0.07 0.45 2.08 -0.37 0.52
3 0.00 0.06 -0.09 0.10 0.05 0.71 -0.99 0.66
2 1 0.16 0.05 -0.17 0.34 2.47 0.86 -2.84 3.60
2 0.05 -0.05 -0.14 0.20 0.82 -0.85 -1.94 1.92
3 0.00 -0.01 -0.18 0.18 0.03 -0.19 -2.22 1.44
3 1 0.21 0.02 -0.16 0.38 2.79 0.36 -2.00 3.17
2 0.04 -0.08 -0.21 0.25 0.66 -1.28 -2.56 2.36
3 0.23 -0.04 -0.02 0.26 3.66 -0.73 -0.28 2.10
Avg. 0.07 0.01 -0.12 0.19 1.92 0.49 -2.70 2.57
post-formation bMktRF t(bMktRF )
1 1 0.72 0.97 1.20 -0.48 42.47 75.49 62.94 -18.18
2 0.82 1.07 1.26 -0.44 44.25 59.05 52.21 -13.14
3 0.85 1.07 1.25 -0.41 40.39 54.58 54.08 -11.22
2 1 0.69 0.92 1.13 -0.45 41.23 63.28 74.10 -18.97
2 0.76 1.02 1.20 -0.44 47.92 69.03 64.49 -17.30
3 0.80 1.02 1.20 -0.40 43.36 66.72 59.18 -12.59
3 1 0.83 1.00 1.26 -0.43 43.66 66.31 61.01 -14.37
2 0.89 1.10 1.29 -0.39 57.68 67.83 61.62 -14.63
3 0.86 1.00 1.15 -0.29 53.33 74.98 58.93 -9.66
Avg. 0.80 1.02 1.22 -0.41 81.95 165.09 111.34 -22.10
Panel F: MktRF (ME × INV)
Char-Portfolio pre-formation bMktRF-sorted portfolios
INV ME 1 2 3 1-3 1 2 3 1-3
α t(α)
1 1 0.08 0.14 0.03 0.05 1.15 2.79 0.34 0.44
2 0.03 -0.06 -0.13 0.16 0.49 -1.01 -1.42 1.31
3 -0.01 -0.08 -0.15 0.15 -0.10 -1.19 -1.81 1.17
2 1 0.17 0.10 0.05 0.12 2.44 1.67 0.70 1.16
2 0.13 0.03 0.00 0.13 2.19 0.50 0.04 1.38
3 -0.00 -0.07 -0.08 0.08 -0.05 -1.23 -1.20 0.70
3 1 0.02 -0.11 -0.30 0.32 0.26 -1.91 -4.61 2.97
2 -0.02 0.02 -0.14 0.11 -0.34 0.35 -1.55 0.96
3 0.31 0.05 -0.08 0.39 4.63 0.87 -0.96 3.03
Avg. 0.08 0.00 -0.09 0.17 2.08 0.15 -2.10 2.28
post-formation bMktRF t(bMktRF )
1 1 0.74 0.98 1.23 -0.49 44.22 75.73 59.52 -17.70
2 0.82 1.05 1.31 -0.49 48.60 65.89 58.36 -15.97
3 0.87 1.08 1.23 -0.36 49.05 63.82 57.94 -11.48
2 1 0.67 0.89 1.11 -0.43 38.84 58.08 64.31 -16.62
2 0.77 0.99 1.20 -0.43 50.46 56.54 70.93 -17.96
3 0.79 0.96 1.14 -0.35 44.42 69.44 64.45 -12.15
3 1 0.81 1.00 1.20 -0.38 43.74 68.69 72.79 -14.16
2 0.89 1.09 1.25 -0.36 54.77 66.53 56.81 -12.16
3 0.86 1.07 1.24 -0.38 50.45 69.71 58.97 -11.72
Avg. 0.80 1.01 1.21 -0.41 84.05 167.65 113.64 -22.10
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Panel G: SMB (ME × BEME)
Char-Portfolio pre-formation bSMB-sorted portfolios
BEME ME 1 2 3 1-3 1 2 3 1-3
α t(α)
1 1 -0.16 -0.07 -0.03 -0.13 -2.23 -0.98 -0.29 -1.05
2 -0.08 -0.02 -0.01 -0.07 -1.33 -0.32 -0.15 -0.78
3 0.04 0.05 0.03 0.01 0.96 0.93 0.36 0.15
2 1 0.00 -0.06 0.12 -0.12 0.02 -1.12 1.59 -1.16
2 -0.09 -0.12 -0.01 -0.08 -1.33 -2.04 -0.13 -0.85
3 -0.12 -0.07 -0.13 0.01 -1.57 -1.08 -1.63 0.10
3 1 0.17 -0.00 0.02 0.16 2.77 -0.09 0.26 1.57
2 0.04 -0.03 -0.03 0.07 0.52 -0.46 -0.36 0.59
3 -0.23 -0.03 0.10 -0.33 -2.83 -0.36 1.00 -2.39
Avg. -0.05 -0.04 0.01 -0.05 -1.53 -1.51 0.17 -0.93
post-formation bSMB t(bSMB)
1 1 0.91 1.14 1.37 -0.46 36.44 44.08 39.55 -10.52
2 0.40 0.64 0.91 -0.51 18.44 28.22 34.45 -15.74
3 -0.25 0.04 0.28 -0.53 -17.31 2.30 11.38 -15.93
2 1 0.68 1.00 1.38 -0.70 32.70 53.10 51.63 -19.17
2 0.28 0.52 0.80 -0.52 12.04 24.09 33.24 -16.25
3 -0.31 0.01 0.28 -0.58 -11.96 0.48 10.19 -15.35
3 1 0.71 0.97 1.35 -0.64 31.94 51.88 53.94 -18.31
2 0.31 0.58 0.87 -0.56 12.69 24.53 31.23 -14.27
3 -0.20 -0.01 0.31 -0.51 -6.84 -0.55 9.25 -10.48
Avg. 0.28 0.54 0.84 -0.56 25.83 57.37 63.01 -27.26
Panel H: SMB (ME × OP)
Char-Portfolio pre-formation bSMB-sorted portfolios
OP ME 1 2 3 1-3 1 2 3 1-3
α t(α)
1 1 -0.07 -0.06 -0.03 -0.05 -1.19 -0.95 -0.30 -0.41
2 0.05 0.10 -0.00 0.05 0.67 1.40 -0.02 0.44
3 -0.14 0.03 0.23 -0.37 -2.07 0.38 2.50 -2.88
2 1 0.05 -0.01 -0.11 0.16 0.81 -0.22 -1.61 1.73
2 -0.06 -0.06 -0.03 -0.02 -0.95 -1.02 -0.48 -0.26
3 -0.09 0.06 -0.01 -0.08 -1.62 1.03 -0.10 -0.82
3 1 0.07 0.06 -0.15 0.22 1.03 0.87 -1.69 1.93
2 -0.09 -0.10 -0.07 -0.02 -1.41 -1.57 -0.90 -0.21
3 0.09 0.02 -0.03 0.12 2.04 0.28 -0.39 1.17
Avg. -0.02 0.00 -0.02 0.00 -0.70 0.14 -0.58 0.02
post-formation bSMB t(bSMB)
1 1 0.83 1.16 1.42 -0.59 39.16 56.16 45.04 -15.33
2 0.27 0.62 0.83 -0.57 10.44 24.82 27.10 -14.22
3 -0.34 -0.01 0.19 -0.52 -14.46 -0.63 5.69 -11.54
2 1 0.63 0.94 1.25 -0.62 28.71 45.45 50.49 -18.49
2 0.30 0.57 0.84 -0.54 13.70 28.85 33.40 -16.78
3 -0.31 -0.00 0.23 -0.54 -16.23 -0.03 9.44 -15.52
3 1 0.81 1.03 1.24 -0.43 34.79 45.60 40.33 -10.93
2 0.41 0.62 0.91 -0.50 19.15 27.18 34.89 -16.06
3 -0.24 0.03 0.35 -0.59 -15.84 1.32 13.14 -16.62
Avg. 0.26 0.55 0.81 -0.55 25.26 59.68 61.37 -27.85
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Panel I: SMB (ME × INV)
Char-Portfolio pre-formation bSMB-sorted portfolios
INV ME 1 2 3 1-3 1 2 3 1-3
α t(α)
1 1 0.08 0.03 0.08 0.00 1.32 0.60 0.80 0.01
2 -0.10 -0.06 0.01 -0.11 -1.42 -0.96 0.18 -1.02
3 -0.12 -0.06 -0.03 -0.09 -1.96 -0.91 -0.45 -0.78
2 1 0.13 0.07 0.07 0.06 2.00 1.15 0.95 0.58
2 0.07 -0.01 0.12 -0.05 0.96 -0.15 1.86 -0.57
3 -0.10 0.01 0.07 -0.17 -2.01 0.21 1.01 -1.75
3 1 -0.14 -0.15 -0.21 0.07 -2.18 -2.58 -2.90 0.68
2 -0.04 -0.05 -0.04 0.00 -0.62 -0.74 -0.49 0.00
3 0.10 0.17 0.09 0.01 2.10 2.78 1.10 0.11
Avg. -0.01 -0.01 0.02 -0.03 -0.43 -0.21 0.50 -0.55
post-formation bSMB t(bSMB)
1 1 0.79 1.17 1.46 -0.67 36.11 59.36 41.59 -15.99
2 0.29 0.58 0.92 -0.64 11.74 25.18 32.60 -16.22
3 -0.26 -0.01 0.20 -0.46 -11.57 -0.33 7.38 -11.50
2 1 0.65 0.91 1.32 -0.67 28.13 44.90 49.78 -18.20
2 0.26 0.52 0.77 -0.51 10.93 25.60 33.92 -15.39
3 -0.28 0.00 0.26 -0.54 -16.71 0.20 10.35 -15.94
3 1 0.84 1.04 1.31 -0.46 36.75 50.52 51.44 -13.14
2 0.43 0.63 0.95 -0.52 20.29 28.37 34.83 -16.07
3 -0.28 0.09 0.35 -0.64 -16.25 4.25 12.18 -16.29
Avg. 0.27 0.55 0.84 -0.57 25.95 62.36 65.07 -27.97
The table shows alphas and loadings from time-series regressions of monthly excess returns of the loading-sortedportfolios on the five Fama and French characteristic portfolios from 1963/07 - 2019/12. The column labeled ‘1-3’shows the alphas/loadings of long low-loading short high-loading hedge-portfolios. The last row shows averages ofall 9 loading-portfolios.
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Table 2.4: Results of time-series regressions of hedge-portfolios
Hedge-Portfolio Avg. α bMkt−RF bSMB bHML bRMW bCMA R2
rh,MktRF 0.10 -0.18 0.41 0.40 0.05 -0.17 -0.06 0.66
(0.80) (-2.44) (22.39) (15.18) (1.48) (-4.68) (-1.15)
rh,SMB 0.17 0.03 0.17 0.56 -0.01 -0.15 -0.16 0.72
(1.74) (0.50) (12.27) (28.28) (-0.33) (-5.57) (-3.95)
rh,HML 0.07 -0.11 0.03 -0.05 0.80 0.20 -0.54 0.61
(0.74) (-1.86) (1.80) (-2.34) (28.21) (6.68) (-12.03)
rh,RMW 0.08 -0.21 -0.05 0.04 0.31 0.69 0.11 0.65
(0.86) (-3.66) (-3.27) (1.96) (11.69) (24.80) (2.51)
rh,CMA -0.04 -0.20 0.04 0.02 -0.31 0.09 0.96 0.43
(-0.52) (-3.39) (2.60) (1.10) (-10.95) (2.90) (21.13)
EW3 0.04 -0.17 0.01 0.00 0.27 0.32 0.17 0.70
HML,RMW,CMA (0.64) (-5.45) (0.83) (0.39) (17.52) (20.56) (7.30)
EW4 0.05 -0.18 0.11 0.10 0.21 0.20 0.12 0.58
EW3+MktRF (1.17) (-5.92) (14.60) (9.75) (15.08) (13.71) (5.18)
EW5 0.07 -0.15 0.10 0.15 0.19 0.17 0.08 0.57
EW4+SMB (1.57) (-5.01) (14.08) (14.86) (13.60) (11.65) (3.83)
Stocks are first sorted based on size and one of book-to-market, profitability or investment into 3x3 portfolios. Con-ditional on those sorts, they are subsequently sorted into 3 portfolios based on the respective loading, i.e., on HML,RMW or CMA. For MktRF and SMB we use the average of three hedge portfolios, which are based on a 3x3 sort onsize and book-to-market, profitability or investment. The hedge portfolio then goes long the high loading and short thelow loading portfolios. On the bottom, we form combination-portfolios that put equal weight on three (HML, RMW,CMA), four (HML, RMW, CMA, MktRF) or five (HML, RMW, CMA, MktRF, SMB) hedge portfolios. Monthlyreturns of these portfolios are then regressed on the 5 Fama and French (2015) characteristic portfolios in the sampleperiod from 1963/07 - 2019/12.
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Table 2.5: Sharpe Ratio improvement.
p-values
rc r∗c rc−ind (rc to r∗c ) (rc to rc−ind) (r∗c to rc−ind)
HML
Mean 3.64 2.51 2.59 0.21 0.30 0.91
Vol 9.64 5.87 5.18 <0.01 <0.01 <0.01
SR2 0.14 0.18 0.25 0.09 0.01 -
RMW
Mean 3.22 2.56 2.33 0.38 0.25 0.67
Vol 7.76 5.05 5.79 <0.01 <0.01 0.91
SR2 0.17 0.26 0.16 0.02 - 0.02
CMA
Mean 2.64 2.37 2.13 0.67 0.49 0.60
Vol 6.50 4.30 3.97 <0.01 <0.01 0.02
SR2 0.16 0.30 0.29 0.01 <0.01 0.06
SMB
Mean 2.81 1.92 2.84 0.29 0.97 0.22
Vol 10.24 6.48 8.26 <0.01 <0.01 <0.01
SR2 0.08 0.09 0.12 0.34 0.12 -
MktRF
Mean 6.62 6.14 - 0.77 - -
Vol 15.09 10.45 - <0.01 - -
SR2 0.19 0.35 - <0.01 - -
In-sample optimal combination
Mean 3.50 2.83 2.59 0.05 0.01 0.27
Vol 3.24 1.94 2.21 <0.01 <0.01 0.01
SR2 1.17 2.13 1.37 <0.01 <0.01 <0.01
In-sample optimal combination (without MktRF)
Mean 2.91 2.42 2.35 0.21 0.18 0.76
Vol 3.67 2.06 2.19 <0.01 <0.01 0.10
SR2 0.63 1.37 1.15 <0.01 <0.01 <0.01
We report the average return and return volatility (annualized, and in percent) and the corresponding annualizedsquared Sharpe-ratio for different versions of each of the five characteristic and characteristic efficient portfolios.rc are the returns of the characteristic portfolios. r∗c are the returns of the characteristic efficient portfolios calculatedas in equation (2.33). rindc are the returns of the industry-neutral characteristic portfolios, where, for the first fourcharacteristic portfolios, we ex-ante hedge out 12 FF industries exposure. As the industry portfolios explain almost100% of the market portfolio, we do not calculate an industry-neutral version of the market. The last three columnsdepict tests of differences between two portfolios, i.e., CPs to CEPs, CPs to industry-neutral CPs, and industry-neutralCPs to CEPs. For the mean, we report the p-value from a t-test of equal means. For the volatility, we report thep-value from Levene’s test of equal variances. In the Sharpe ratio row, we report the p-value of the α from regressingthe second on the first portfolio. If the α is negative, we report a “-” for the p-value. The second to last panel reportsthe statistics for the in-sample Markowitz optimal combination of the five original CPs, the CEPs, and the industry-neutral portfolios. The last panel repeats the exercise, excluding the MktRF portfolio. The sample period is 1963/07- 2019/12. 113
Table 2.6: Ex-post optimal Markowitz weights
rc r∗c
CMA 0.40 0.34
HML -0.02 0.08
MktRF 0.17 0.12
RMW 0.34 0.33
SMB 0.12 0.13
We report the weights on each of the five characteristic portfolios from a full-sample ex-post Markowitz optimization.The first column reports results for the original five characteristic portfolios, and the second column for the fivecharacteristic efficient portfolios. The sample period is 1963/07 - 2019/12.
Table 2.7: Spanning tests for HML
Portfolio HML HML HML∗ HML∗
α -0.02 (-0.28) 0.00 (0.03) 0.15 (2.61) 0.09 (1.78)
bMktRF 0.03 (1.56) -0.01 (-0.70)
bSMB 0.04 (1.37) 0.03 (1.52)
bRMW 0.26 (6.68) -0.14 (-5.21)
bCMA 1.05 (22.93) 0.44 (14.06)
bMktRF ∗ 0.10 (2.96) 0.02 (1.37)
bSMB∗ 0.10 (1.88) 0.05 (1.83)
bRMW ∗ 0.12 (1.51) -0.25 (-6.72)
bCMA∗ 1.04 (11.30) 0.79 (17.86)
R2 0.47 0.19 0.32 0.50
We regress the returns of the original HML characteristic portfolio, rc,HML, (first 2 columns) as well the returns on theHML characteristic efficient portfolio, r∗c,HML, (columns 3 and 4) on the returns of the remaining four characteristicand characteristic efficient portfolios. The sample period is 1963/07 - 2019/12.
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Table 2.8: Correlations
Panel A: CPs
MktRF SMB HML RMW CMA
MktRF 1.00 0.26 -0.24 -0.24 -0.35
SMB 0.26 1.00 -0.04 -0.35 -0.04
HML -0.24 -0.04 1.00 0.09 0.66
RMW -0.24 -0.35 0.09 1.00 -0.13
CMA -0.35 -0.04 0.66 -0.13 1.00
Panel B: CEPs
MktRF ∗ SMB∗ HML∗ RMW ∗ CMA∗
MktRF ∗ 1.00 -0.27 -0.17 0.15 -0.28
SMB∗ -0.27 1.00 0.18 -0.26 0.15
HML∗ -0.17 0.18 1.00 -0.51 0.68
RMW ∗ 0.15 -0.26 -0.51 1.00 -0.49
CMA∗ -0.28 0.15 0.68 -0.49 1.00
The table shows the correlations of monthly excess returns among the CPs (Panel A) and CEPs (Panel B). The sampleperiod is 1963/07 - 2019/12.
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Chapter 3
Should Information be Sold Separately? Evidence from MiFID II 1
3.1 Introduction
A key to efficient outcomes in financial markets is efficient information production. The pro-
duction of information, both in terms of quantity and quality, depends on how it is compensated.
We study how changes in the compensation schedules for information affect its production through
the lens of sell-side research.
The compensation schedule for sell-side research has recently changed dramatically. Sell-
side research has traditionally been bundled with transactions: rather than being sold separately,
it was cross-subsidized by trading commissions. However, a new regulation in Europe (MiFID
II, the second Markets in Financial Instrument Directive) unbundles research from transactions.
Implemented on January 3rd, 2018, MiFID II forces asset managers to separate payments for sell-
side research from trading commissions. This change allows us to study how the compensation
schedules for sell-side research affect its production, a question difficult for previous empirical
research to address due to the lack of economically significant variation in the business model of
the sell-side research industry.
Specifically, we ask: What happens to firms’ analyst research quantity and quality? What are
1This chapter is based on Guo and Mota (2020). We thank Charles Angelucci, Simona Abis, Olivier Darmouni,Xavier Giroud, Larry Glosten, Juan-Pedro Gómez (the discussant), Harrison Hong, Shiyang Huang (the discussant),Wei Jiang, Luca Mertens, Sophie Moinas, Tano Santos, Paul Tetlock, Tuomas Tomunen, Laura Veldkamp, KairongXiao, conference participants at EFA 2019, SFS Cavalcade Asia-Pacific 2019 and seminar participants at AQR CapitalManagement, City University of Hong Kong, Columbia Business School, Shanghai Advanced Institute of Finance,and Singapore Management University for their insightful and helpful suggestions. We acknowledge support by theChazen Institute for Global Business at Columbia Business School and Deming Center Doctoral Fellowship.
116
the underlying mechanisms driving the changes? Answers to these questions are crucial for deter-
mining the optimal regulation of financial analysts, and more broadly, for designing the optimal
way to pay for information.
The main goal of MiFID II is to protect end investors by improving market transparency. Before
MiFID II, trading commissions were opaque and it was difficult for end clients to fully assess the
services they were paying for. This generates incentives to assets manager to over charge clients for
transaction fees, potentially under-reporting their own management fees (Di Maggio et al. (2019)).
Therefore, one provision of MiFID II is to require asset managers to bill research services clearly,
which requires unbundling the payments for research from trading.2
As a result, unbundling fundamentally changes how research is compensated and, a priori, its
consequences are unclear. On the one hand, unbundling potentially results in less analyst research
covering fewer companies.3 This is due to the nonrival nature of information. In general, produc-
ing research is costly, but once it is produced and revealed to one party, it is difficult to exclude
others from using the same information. Therefore, directly selling research could result in market
failures (see e.g. Grossman and Stiglitz (1980), Admati and Pfleiderer (1986) and Romer (1990)).
Traditionally, brokerage houses overcome this issue by cross-subsidizing the high fixed cost of
research with transactions fee and marketing to investor that research was given for “free". Un-
bundling prevents cross-subsidizing, potentially causes a marked decrease in research production.
Furthermore, a reduction in the coverage quantity could then cause a decrease in the analyst peer
pressure, which impairs coverage quality (e.g., Hong and Kacperczyk (2010)).
On the other hand, unbundling could improve analyst incentives to produce better research.
Previous studies have shown that when research is bundled with transactions, research analysts
may strategically devote more effort to researching firms that generate more trading commissions
(Harford et al. (2018)). Analysts may even have incentives to produce inaccurate and biased fore-
casts to lure trading business in house (e.g., Hong and Kubik (2003), Fang and Yasuda (2009),
Hong and Kacperczyk (2010) and Karmaziene (2019)). By making research a standalone product,
2We discuss in detail why EU regulators enforce MiFID II in the next section.3See “Mifid II leads to exodus of sellside analysts" Financial Times, June 23rd, 2018.
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unbundling could restore analyst incentives and improve research quality.
We find that the number of unique sell-side analysts covering a firm decreases after unbundling.
We perform our analyses in a difference-in-difference setting, exploring the different exposures to
unbundling between EU public firms and US public firms. We define EU public firms as the treat-
ment group and US public firms as the control group. In our main specification, analyst coverage
of EU firms changes by −0.651 analysts, which translates into a decrease of 7.45% relative to
the average coverage of these firms prior to the regulation. Contrary to the media and industry
concerns, this average drop does not come from small- or mid-cap firms but is concentrated in
large firms.4 Small firms’ coverage remains almost unchanged and large firms’ coverage drops by
10.53% on average.
Strikingly, we find that the unbundling causes coverage quality to improve. For example, mea-
sured by forecast error, coverage quality of affected firms on average increases by 19.19% relative
to the average coverage quality of these firms prior to the regulation. This result differs from
previous literature (e.g., Hong and Kacperczyk (2010) and Merkley et al. (2017)), which shows
a decrease in the coverage quantity implies a reduction in the coverage quality.5 One plausible
explanation for the difference is that unbundling strengthens analyst competition. Analysts who
sell research as a stand-alone product are likely to compete more directly in the quality domain.
Inferior analysts being competed out of business could account for the simultaneous decrease in
the coverage quantity and increase in the coverage quality.
To be more specific, at least two economic forces foster competition. First, unbundling forbids
asset managers to pass research costs to end investors through trading commissions. Most asset
managers have decided to charge research costs against their own profit and loss. Internalizing
research cost makes asset managers be much more selective and opt for better research. Sec-
ond, unbundling puts an explicit price on research. The evaluation scheme prior to the regulation
4See “French watchdogs calls for rethink of research rules". Financial Times, November 27th, 2018.5In their setting (i.e., under bundling), many analysts have other objectives (e.g., generating trading commissions)
in addition to quality. The quality of research relies on a few independent and impartial analysts who put quality inthe first place. The decrease in the quantity implies both a reduction in the peer pressure and a high propensity to losethese impartial analysts. As a result, research quality worsens.
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presents a problem similar to moral hazard in teams. An individual’s evaluation is not directly tied
to an individual’s output, but to a bundled output consisting of research and transactions. How-
ever, under unbundling, analysts are evaluated directly by the services they provide. They have
stronger incentives to provide better research. As a result of those two forces, analysts compete in
the quality domain to attract and maintain clients.
We find evidence of two specific predictions of the competition channel: 1) analysts who pro-
duce worse research are more likely to be forced out of the analyst market (extensive margin) and
2) analysts who stay produce better research (intensive margin). For example, using ranks gener-
ated by analyst average forecast error (Hong and Kubik (2003)), we show that analysts who provide
worse forecasts (low-ranked analysts) are more likely to stop working. Conditional on staying, af-
fected analysts’ average forecast error also decreases. Although in a different setting, the beneficial
effects of unbundling in our paper could be related to Edelen et al. (2012). They study the effects
of unbundling distribution fees from commissions and find that unbundling imposes transparency,
mitigates agency conflicts and improves fund performance.
As extensions, we show that individual analyst forecast revision generates a more substan-
tial absolute market-adjusted abnormal return. This evidence suggests that individual forecasts
become more informative, which echos our findings on the coverage quality improvement. Inter-
estingly, when we turn to the sum of abnormal returns over all the individual forecast revisions,
we find that aggregate abnormal returns decrease after unbundling. This result suggests that the
total amount of new information in all the analyst forecast revisions decreases. We interpret these
results via the trade-off between forecast quantity and quality. While individual forecasts become
more informative, the total amount of valuable forecasts decreases.
We also find that the effects of unbundling may not be homogeneous across brokerage houses.
We document that large brokerage houses are likely to be more affected and lay off more analysts.
To the extent that brokerage houses affiliated with large banks are larger in size, the result implies
that these types of houses, whose research featured substantial bundling before the regulation, are
more likely to be affected. This evidence suggests that certain types of brokerage houses could find
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it more difficult to survive under unbundling and that the market structure of the sell-side industry
may begin to change.
On the aggregate level, we find no evidence that firms’ earnings announcements convey more
information, nor do we find evidence on the widening of firms’ bid-ask spread. Although these
results do not contradict our findings on coverage quality improving, the aggregate market effect
of MiFID II does not seem to manifest itself immediately. Since the reform is relatively recent, we
expect that more time is needed to assess its overall impact on the capital markets. As a final note,
due to data availability, systematic analyses on the welfare impact of unbundling falls out of the
scope of our paper and is left for future studies.6
Our paper makes three contributions. To begin with, we are the first to investigate both the
impact and the underlying mechanism of unbundling on analyst research production. The output
of this project is crucial to resolve the vivid debate among academics, policymakers and practi-
tioners about the consequences of unbundling imposed by MiFID II. Furthermore, investigating
unbundling provides valuable information to policy makers and helps to shape future policy design
in other jurisdictions in addition to Europe. As US Security Exchange Commission chairman Jay
Clayton pointed out:7
“It is important to have data and other information about how MiFID II’s research
provisions are affecting broker-dealers, investors and small, medium, and large issuers,
including whether research availability has been adversely affected.”
Second, our paper contributes to the literature on analyst behavior. It has been long established
that analyst forecasts are on average optimistically biased due to incentive problems (e.g., Dre-
man and Berry (1995), McNichols and O’Brien (1997), and Chopra (1998) and Hong and Kubik
(2003)). Fang and Yasuda (2009), Hong and Kacperczyk (2010) and Kempf (2019) convincingly
show that implicit mechanisms such as career concerns and peer competition discipline analyst be-6As an example, unbundling may also change the pricing of transactions, which plays an important role in analyz-
ing investors’ welfare. However, systematic information on commission fees is hard to obtain, especially in Europe.Though some surveys suggest commission fees are dropping, a comprehensive analysis of commissions and investor’swelfare falls out of the scope of our paper.
7See SEC Press Release: https://www.sec.gov/news/press-release/2018-301.
120
havior. Our analyses depart from, but also complement, these prior studies by showing that direct
market competition helps to discipline analysts even further. A unique finding in our paper is that
a decrease in the coverage quantity can be accompanied by an increase in the coverage quality due
to the strengthening of analyst competition.
Third, unbundling offers a unique setting through which we can study the optimal way to pay
for information (e.g., Veldkamp (2006b), [2006a], Van Nieuwerburgh and Veldkamp (2010)). In-
formation generally has positive externalities, and its production features high fixed costs. Bundling,
though creating incentive problems, covers the high fixed cost and allows for more information
production. It potentially enables easier and wider access to information. Unbundling, on the
other hand, restores the incentive problems but may result in the market unraveling and the under-
provision of certain information. Our results suggest that the improvement in the information
quality by selling information separately could come at a cost of reducing information quantity.
In the accounting literature, more recent works study MiFID II, mainly focusing on its effects
at the analyst level or the firm level (Fang et al. (2019), Lang et al. (2019)). What differs in our
work is that we construct a sample based on analyst-firm pairs, which allows us to identify the
mechanism for the drop in coverage quantity and the improvement in coverage quality. Our unique
contribution is to show that after the regulation, analyst competition is enhanced. We present clear
evidence that inaccurate analysts drop out, and that the ones who stay produce better research.8
Di Maggio et al. (2019) also studies unbundling using detailed transaction-level data in the US.
They emphasize the conflicts of interests between asset managers and end clients. They show that
bundling allows asset managers to under-report management fees. Our paper has a different focus.
We study how unbundling affects sell-side research provisions. Via investigating unbundling, we
aim to understand the effects of changing compensation schedule on information provision.
The remaining of the paper proceeds as follows. In Section 3.2, we provide regulation back-
ground. In Section 3.3, we develop our testable hypotheses. In Section 3.4, we describe our
8Another difference from Lang et al. (2019) is that we use annual data instead of quarterly data. Since we empha-size causality and mechanism, annual data allows us to mitigate concerns specific to the use of quarterly data that mayconfound our identification. These include: forecast seasonality, poor data coverage, selection bias, and staleness. De-tailed explanation can be found in Appendix C.1.2.
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empirical design and the data we use. We present the firm level analyses in Section 3.5, analyst
analyses in Section 3.6, conduct complementary analyses Section 3.7 and conclude in Section 3.8.
3.2 Regulation background
MiFID II attempts to ensure a high degree of harmonized protection for investors in financial
instruments by improving market transparency and competitiveness. It is considered as one of the
most influential regulatory changes in the EU in response to 2008 financial crisis.
The unbundling provision in MiFID II prohibits asset managers from accepting “fees, com-
missions or any monetary or non-monetary benefits paid or provided by a third party”.9 However,
it provides an exception for research services provided by third parties as long as the asset man-
agement firm pays for it directly. Asset managers can either pay for research directly (against the
firm’s profit and loss) or pass costs onto clients by setting up a research payment account (“RPA”)
under the consent of clients.10 Whichever method asset managers choose, payments for research
needs to be separated, or unbundled, from payments for transactions (Figure 3.1b). According to
a survey by CFA Institute, the majority of asset managers pay for research directly, mainly due to
competition pressure from the whole asset management industry.11 With management fees declin-
ing and asset managers absorbing research costs internally, CFA institute expects a greater focus
on profitability and efficiency concerning research procurement.
Before MiFID II, analyst research was provided “for free" in exchange for trading or investment
banking business. The cost of research was cross-subsidized by trading commissions. Trading
commissions were usually passed onto asset managers’ clients who were unaware of the embedded
research cost (Figure 3.1a). This practice is known as bundling or payment via “soft dollars",
Bundling traces its origin to 1950’s. At that time, commission fees used to be fixed at a high
level (around 1% per share in the US before the May Day 1975) and brokerage houses compete
9Article 24(7) of MiFID II Directive and Article 11 of Commission Delegated Directive (EU) 2017/59310Even with RPA, clients are fully aware of the research cost. They are able to opt out purchasing research if they
choose to.11“MiFID II, One Year On" CAF Institute, 2019.
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for clients by providing “free" research services (Jones (2002)). Gradually, bundling also becomes
demand-driven (Blume (1993) and Egan (2018)): Asset managers benefit from bundling.12 “Soft
dollars" are borne ultimately by end-investors. Payments for research in the form of trading com-
missions are not reported in the expense ratio and are not disclosed in the management fees. Hence,
“soft dollars" are hidden cost for end clients. On top of that, the provision of “free" supplementary
research services by the executing brokers – such as analyst research reports, corporate access,
or other non-monetary benefits – creates incentives for asset managers to route the trades to that
broker and the potential to trade more often than is appropriate for the clients. It may also preclude
the use of other brokers who may provide better execution services.
Although the practice could hurt end investors, in 1975, the soft-dollar industry lobbied the
US Congress to amend the 1934 Securities Exchange Act by adding Section 28 (e). This section
allows asset managers in the US to pay for research with soft dollars from client commissions
without breaking their fiduciary duty. Member states of the EU essentially followed the same
practice before the onslaught of MiFID II.
EU regulators are increasingly concerned that bundling practice hurts end investors and overly
favors asset managers. To protect end investors and promote transparency in the fee structure, they
mandate unbundling as part of MiFID II. A subsequent effect of unbundling becomes manifested
in the sell-side research industry. Unbundling completely changed the way sell-side research is
compensated. It provides us a valid and timely setting where we can study how the compensation
schedules for sell-side research affect its production.
The MiFID II regime, on its face, applies only to asset managers with a physical presence or
domicile in the European Economic Area (EEA). This includes US asset managers with an au-
thorized European subsidiary providing investment services to clients in the EEA. But given the
regime’s complexity and wide-ranging reach, the key provision extends its influences globally. For
example, US broker-dealers are indirectly affected by MiFID II if they provide investment research
12This is different from bundling in the traditional Industrial Organization literature. In many IO studies, bundlingis a way for the supply side to price-discriminate consumers and extract consumer surplus. See a summary in Tirole(1988).
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services to EEA firms or EEA clients, or to US asset managers that provide services to EEA clients.
Receiving payments for research directly forces them to be registered as investment advisers sub-
ject to more strict regulation. Foreseeing the important consequences to US asset management
business, in October 2017, the SEC issued a temporary no-action relief to “reduce confusion and
operational difficulties that might arise in the transition to MiFID II’s research provisions" valid
until 2020.13 The relief allows US broker-dealers to receive direct payments from EEA clients
without being registered as financial advisers.
European Parliament began to discuss MiFID II in May 2014 and plan to apply it on January
3rd, 2017. Due to widespread concerns that the infrastructure would not be ready, the EU parlia-
ment decided to allow for a one-year delay for the launch of the regulation. On June 30, 2016, the
Official Journal of EU announced that MiFID II was supposed to be translated into national law by
July 3rd, 2017 and become fully applicable as from January 3rd, 2018.
It is worth noting that unbundling is only one of many important provisions of MiFID II.
For example, under MiFID II, post-trade transparency is extended to non-equity instruments and
post-trade information needs to be made public close to real time. High frequency trading firms
are required to set order limits and use circuit breakers to limit or temporarily halt trading to avoid
erroneous orders.14 However, unbundling is the most relevant and direct provision affecting analyst
research. It is possible that other provisions in MiFID II also affect some part of analyst research,
but as will be clear in the latter part of the paper, it would very difficult for other provisions to
account for all the findings in our paper both at the firm level and at the analyst level. The impact
of MiFID II on analyst research production arguably comes first and mostly from unbundling.
13See SEC no-action relief, October 26th, 2017.14See a summary by Bank of America Merrill Lynch: https://www.bofaml.com/en-us/content/mifid-ii-regulation-
summary-requirements.html
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3.3 Hypotheses development
We begin by examining the effects of unbundling on research quantity. Research is a cost center
and is difficult to price (e.g., Romer (1990)). Being unable to cross-subsidize the cost of research
from transactions could force brokerage houses to scale back the amount of analyst research they
produce. More importantly, if investors, who attach little value to research (e.g., passive investors),
opt out from purchasing it, the total amount of wealth that can be allocated to research payments
will further decrease. Consequently, using analyst coverage as a measure for research quantity, we
anticipate that:
H1: Sell-side analyst coverage of firms in affected regions will decrease compared with the
coverage of firms in unaffected regions.
We further test whether the coverage of small firms and large firms are differentially affected,
which is the main concern of unbundling raised by market participants. We argue that large firms
are more likely to be affected:
H2: In affected regions, coverage of large firms will decrease MORE than of that of small
firms.
To understand the logic, notice that large firms usually have a larger amount of coverage to
begin with. The large number of research analysts covering a certain firm probably implies that
a lot of work was of low quality. Under unbundling, asset managers, who internalize research
costs in most cases, will have to be much more selective to purchase research. Under such cir-
cumstances, we expect that asset managers opt for better research and discard low quality services.
This indicates that large firms will lose more coverage.
The above hypothesis goes directly against a widespread concern in the market. Practition-
ers believe that small- and medium-sized firms will suffer more because they benefit the most
from cross-subsidization. Trading commissions collected from trading firms with larger demand
(large firms) are used to cover the research cost of small firms. This is no longer allowed under
15See “The EU’s Unbundling Directive is Reinforcing the Power of Scale". The Economist, January 5th, 2019.
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unbundling.15 Robert Ophèle, chairman of the Autorité des Marchés Financiers of France, com-
mented that MiFID II has very detrimental effects on research, especially for mid-caps and that
Europe was engaged in a “dangerous game" as research capacity was being pared back for many
smaller companies.16 The answer to this apparent conflict in the priors should be an empirical one
and is worth investigating.
We then move to study the impact of unbundling on research quality. We argue that one of
the main drivers for the change in the quality is analyst competition. Unbundling makes analyst
compete more directly in the quality domain, and the overall research quality will improve:
H3: Coverage quality for firms in affected regions will increase compared with unaffected
regions.
There are at least two economic forces fostering competition. To begin with, asset managers
can no longer blindly pass research costs to end clients. Paying for research out of their own pock-
ets in most cases, they will be selective and opt for the best research.17 On top of that, unbundling
changes the evaluation schemes for research analysts. Before the regulation, research was bun-
dled with transactions. Research analysts used to have other incentives in addition to accuracy and
quality (e.g., generating fees). Under unbundling, analysts are evaluated and compensated directly
by the services they provide. Their incentives to provide high-quality research are strengthened.
The two forces imply that analysts will compete more directly in the quality domain as they try
to attract and maintain clients. It is then natural to anticipate that the overall research quality will
improve.
It is worth noting that H1 and H3 altogether deviate from previous literature. It has been shown
that coverage quality decreases together with coverage quantity (e.g., Hong and Kacperczyk (2010)
and Merkley et al. (2017)). According to this view, the potential drop in the analyst coverage after
MiFID II will imply the deterioration of the analyst coverage quality. We believe that the difference
lies precisely in whether research is bundled or not. Under bundling, analysts are disciplined by
16“French watchdog calls for rethink of research rules" Financial Times, November 27th, 2018.17Even with RPA, asset managers will still be careful about quality because end clients can veto the purchase of
unnecessary research.
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their independent and impartial peers. A decrease in the coverage quantity implies not only a
reduction in the peer competition but also an increase in the propensity to lose these impartial
analysts. Consequently, coverage quality deteriorates. The unbundling requirement of MiFID II
fundamentally changes how sell-side research is evaluated. For the first time, research analysts
have to work out the value of their research, which ties closely to the quality. Fighting for the
limited resources from the buy-side, they compete more directly in the quality domain and their
incentives to provide better research are enhanced, regardless of the total number of analysts. The
urge for independent and impartial peers as a discipline device is weakened.
If analysts compete more directly in the quality domain, we expect that the improvement in
the coverage quality comes from two margins: 1) conditional on not exiting the analyst market,
analysts produce better research (intensive margin); 2) everything else being equal, inaccurate
analysts are more likely to exist the analyst market (extensive margin). “The analyst community
will [split] into those really good analysts — who will be able to earn more than they currently do
— and the average ones who will lose out.”18 These arguments lead to our fourth hypothesis:
H4: Everything else being equal, analysts who stay provide better research than before and
analysts who produce worse research are more likely to drop out.
Importantly, we are not trying to argue that the competition among research analysts was non-
existent before the regulation. In fact, competition has always existed. For example, the ranking
provided by Institutional Investors on an annual poll is a critical metric to access analysts’ prestige.
Career concerns and peer pressure have also served to discipline analysts (Hong and Kubik (2003),
Hong and Kacperczyk (2010)). But compared with unbundling, these are all indirect mechanisms
disciplining analysts. A direct mechanism such as unbundling, which puts an explicit price on the
research services, strengthens the competition and enhances analyst incentives to produce better
research.
18Laurence Hollingworth, former vice-chairman of EMEA investment banking at JPMorgan. “Mifid II and thereturn of the ‘star’ analysts" Financial Times, February 26th, 2018,.
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3.4 Empirical design and data
3.4.1 Empirical design
We employ a difference-in-difference strategy. The strategy calls for proper treatment and
control groups, which is not straightforward in the case of MiFID II. Unbundling in MiFID II
puts constraints on asset managers, not on analysts nor publicly traded firms. It affects the trading
relationship between asset managers and brokerage houses. However, systematic information on
the trading relationship between the two parties is not available to researchers, especially in Europe.
We have instead systematic information on analysts and publicly traded firms they cover.
To investigate the impact of unbundling on analyst research and test the hypotheses with the
data we have, we leverage a well-established fact: local investors portfolios mostly consist of local
securities (Home Bias).19 This implies that analysts covering EU firms are more likely to serve EU
clients who are subject to MiFID II. In other words, these analysts are more likely to be affected.
This further implies that coverage outcomes of EU firms domiciled and listed in the EU, the main
targets of these analysts, are more likely to be affected as well.
We define the treatment group to be analysts covering mostly EU firms and firms domiciled and
listed in Europe, and the control group to be analysts covering mostly US firms and firms domiciled
and listed in the US. In our sample, analysts’ portfolios are extremely concentrated: in most cases,
they focus either exclusively on EU firms or US firms (See Figure C.1 in C.2). We then define EU
analysts to be the analysts whose portfolios consist of at least 70% of EU firms and US analysts to
be analysts whose portfolios consist of at most 30% of EU firms. The heterogeneous impact of the
regulation on analysts and firms between the two regions is the main variation through which we
identify the impact of unbundling.20
19See French and Poterba (1991), Coval and Moskowitz (2001), Ahearne et al. (2004) and Van Nieuwerburgh andVeldkamp (2009).
20In theory, if an EU fund manager trades a US stock through a brokerage house, the US stock would be indirectlyaffected by the MiFID II. This leads to the absence of a perfect control group. What we explore here is the difference inthe exposure of the treatment: EU analysts and EU firms are more exposed to the treatment than their US counterparts.
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The identifying assumption is that, in the absence of MiFID II, coverage outcomes of the
treatment group and the control group would have maintained parallel trend. The good news is that
unbundling aims to impose transparency and protect investors. It is not a response to prior events
regarding analyst research. This lends us plausible exogenous variations. Nevertheless, a cross-
country comparison still calls for careful examinations of endogeneity issues that may violate the
identification assumption. We consider a myriad of robustness checks to allow for the possibility
of time-varying heterogeneity across differentially treated groups, including splitting post dummy
into year dummies, adding timing-varying fixed effects and conducting several placebo tests. All
the evidence suggests that the parallel-trend assumption holds and our empirical results are causal.
3.4.2 Data
Our data on analyst forecasts comes from I/B/E/S detail files. We focus on forecasts of annual
earnings per share (EPS) in the current fiscal year since it is the most commonly issued forecasts
in the I/B/E/S dataset and has the widest coverage. For each firm, we take the most recent forecast
by each analyst to account for staleness issues. As a result, we have one forecast issued by one
analyst for one firm in a given fiscal year. The sample selection is consistent with a large number
of papers in the literature (e.g., Hong and Kacperczyk (2010) and Giroud and Mueller (2011)).
Annual balance sheet information comes from Worldscope. Stock exchange and price infor-
mation come from Datastream. Since all three datasets are provided by Thomson Reuters, we are
able to merge them using the unique I/B/E/S identifier. MiFID II went into formal discussion in
the European Parliament in May 2014. To assess its impact, we choose our sample period from
fiscal year 2014 to fiscal year 2018.21 Details of the construction of firm level observations can be
found in Appendix C.1.1.
To account for IPOs and delistings which mechanically affect analyst coverage, we construct a
sample in which all firms have valid accounting and price information from 2014 to 2018. In other
21Firms with fiscal-year end in December 2018 usually have valid financial information in early 2019. Our dataruns until the calendar year May 2019.
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words, all firms in our sample survived during the entire period. Moreover, we only consider firms
that appeared at least once in the I/B/E/S dataset during the relevant time period. We put zero’s
for analyst coverage when a firm is not covered by any analysts in a given year, hence not present
in the I/B/E/S data set. Our final sample has 21, 960 firm × year observations with 4, 392 firms
in each year. Out of all the firm × year observations, 486 of them do not have return on assets
(ROA). Since all the missing values spread out evenly across the years and most of them appear
only once for one firm, we fill in these missing ROAs using the industry level (Worldscope Item
06010) cross-sectional median in a given year.22
We construct three measures for firm level analyses: analyst coverage (Coveragejt), forecast
error (ForecastErrorjt) and forecast dispersion (ForecastDispersionjt). Coveragejt is defined
as the number of unique analysts covering firm j in fiscal year t. ForecastErrorjt is defined
as the absolute difference between the firm’s actual EPS and the mean of the analyst forecasts.
ForecastDispersionjt is defined as the standard deviation of all the forecasts across all the ana-
lysts following the same firm in a given fiscal year. Following previous literature, we scale forecast
error and forecast dispersion by the firm’s previous year-end stock price to mitigate heteroskedas-
ticity concerns.23 To ensure the reliability of these two measures, we require at least 2 different
analysts providing forecasts for the firm during the fiscal year.24
Since forecast error and dispersion are not defined for firms with coverage less than 2, we
construct two samples for firm level analyses. The first one is the sample for coverage quantity,
which contains all the firms satisfying our selection criterion (21, 960 firm × year observations).
This sample captures the change in the analyst coverage quantity even when firms have coverage
less than 2, possibly zero (not being covered at all). The second one is the sample for coverage
quality in which forecast error and forecast dispersion are properly defined. To limit the effects
of outliers on our results, we remove observations in the sample for coverage quality for which
22We obtain very similar results if we simply delete these observations. We also construct a balanced sample bydeleting all the firm-year observations if one ROAs in one year is missing. We lose about 9% of the total sample butthe results go through.
23See Gu and Hackbarth (2013), Zhang (2006b), Thomas (2002), Zhang (2006b) 2006a.24See Gu and Hackbarth (2013) and Giroud and Mueller (2011).
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forecast error and forecast dispersion are larger than 10% of the firm’s previous year-end price
(around 2% of the sample).25 Finally, to alleviate the concerns for the composition effect, we
remove all observations of a firm from this sample if that firm’s forecast error or dispersion is not
defined in any given year.26
We present summary statistics for both samples in Table 3.1 and Table 3.2. In general, US
firms are larger, have lower book-to-market ratios and lower ROAs.27 Looking at the sample for
coverage quantity, we observe that on average US firms have more coverage than EU firms. While
US firms have on average 11.145 analysts producing earning forecasts each year, EU firms have
on average 8.558. Looking at the sample for coverage quality, we observe that both forecast error
and dispersion are larger in the EU. The average forecast error is 0.724% for EU firms and 0.442%
for US firms. Similarly, the average forecast dispersion is 0.848% for EU firms and 0.539% for
US firms. The distribution of analyst coverage is quite left skewed in both regions, and more so in
the EU (see Figure C.2 in Appendix C.2). Notice that for coverage less than 2, quality measures
are not defined and those firms are excluded from the sample for quality. Even after the sample
selection, we remain with a large number of unique firms in both regions, 1, 111 for the EU and
1, 693 to the US.
For analyst level analyses in the latter part of the paper, we focus on analyst-firm pairs. For
each pair, we can calculate the forecast error by taking the absolute distance between the actual
annual earnings and the analyst forecast, scaled by the firm’s previous year-end price. Similar to
firm level data, we remove analyst-firm pairs for which the forecast error is larger than 10% of
the firm’s previous year-end price (around 3% of the sample). Details of the construction of other
important variables can be found in the Appendix C.1.3.
25See Gu and Hackbarth (2013) and Giroud and Mueller (2011).26For example, if firm A does not have a valid forecast error in one year, we remove all the observations of firm A
from the sample. Our results hold if we only remove observations of A in that specific year.27In Appendix C.5, we check that all our results are robust to a propensity score matching procedure in which we
discard observations that are too different.
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3.5 Investigating the impact of unbundling: firm level analyses
We first conduct firm level analyses and examine the impact of unbundling on firms’ coverage
outcomes. We investigate the following empirical model:
Yjt = β1Treatj × Postt + β2Xjt + αj + αt + εjt (3.1)
Yjt measures either analyst coverage Coveragejt, defined as the number of unique analysts
covering firm j in fiscal year t or coverage quality ForecastErrorjt, defined as the absolute dis-
tance between the firm’s actual EPS and the mean of the analyst forecasts, scaled by the firm’s
previous year-end price.28 Treatj is a dummy equal to 1 if a firm is domiciled and listed in Eu-
rope. Postt is a dummy equal to 1 if the fiscal year is equal to 2018. Xjt is a set of control variables
including: log of market capitalization (LN SIZE), log of book to market ratio (LN BM), return
on equity (ROA), total investment return in the current year (RET), return volatility (RETVOL),
GDP growth rate (GDP GROWTH) and unemployment rate (UNEMPLOYMENT RATE) in the
country where the firm is domiciled. When using ForecastErrorjt as the dependent variable, we
also control for the log of the average of the days between the analyst forecast date and the actual
earnings report date (LN DISTANCE). This control is constructed from the analyst forecasts by
taking the average over all the analysts following the same firm. It is likely to be an outcome of un-
bundling and suffers from the bad control problems (Angrist and Pischke (2009b)) if we measure
it year by year. Hence, we measure this variable in 2014 and interact it with Post (see for example
Barrot (2016)).29 Since unbundling does not affect public firms directly, other firm level controls
are not likely to be bad controls. Hence, we measure them year by year. We obtain very similar
results if we measure them in 2014 and interact them with Post. Finally, we also include firm and
time fixed effects. H1 and H3 both imply that β1 < 0.
To explore the heterogeneous response, we split firms into small firms and large firms. We
28In the paper, analyst coverage will sometimes be referred as coverage quantity.29We obtain very similar results if we exclude this control.
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first calculate the average market capitalization in the pre-regulation years for each firm. Small
firms are defined as firms whose average market capitalization falls below the median. To maintain
the proportion of EU and US firms fixed, we calculate the median cut-offs separately in both
regions.30 We first run a difference-in-difference regression within the EU between small firms
and large firms:
Yjt = β3Smallj × Postt + β4Xjt + αj + αt + εjt (3.2)
We then perform the following triple-difference regression:
Yjt = β5Treatj × Postt + β6Treatj × Postt × Smallj +
+β7Smallj × Postt + β8Xjt + αj + αt + εjt (3.3)
When Yjt measures Coveragejt, H2 implies both that β3 > 0 and β6 > 0.
To assess the validity of the parallel trends assumption and provide evidence on the dynamic
impact of unbundling, we set up a Granger causality test, as suggested in Angrist and Pischke
(2009b). The goal is to see whether causes happen before consequences and not the other way
around. To do this, we split the Postt dummy into Dt year dummies, where t ∈ {2015, ..., 2018}
and run the following specification:
Yjt =∑t
ηt(Dt × Treatj) + β9Xjt + αt + αj + εjt (3.4)
We choose 2014, the year in which MiFID II went into discussion as our reference year. Standard
errors in all the analyzes are clustered at the country level. Although we already control for the
firm level characteristics, we repeat the analyses using a propensity score matching procedure to
mitigate the concerns that our results may be driven by the observable differences at the firm level.
All the results are robust to the matching procedure and details can be found in Appendix C.5.
30To account for the possibility that firm size changes over the years and large firms may become small firms afterthe regulation, we also define the Small dummy using the market capitalization in each year. This way, the variableSmall varies over the years. We obtain virtually the same results.
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3.5.1 The impact of unbundling on analyst coverage
We first look at the overall effect of unbundling on analyst coverage. Figure 3.2 shows the time
series trends in the average analyst coverage of EU and US firms. A sharp decrease in the analyst
coverage of EU firms can be observed after unbundling. In fact, Panel A of Table 3.5 shows that
the average analyst coverage of EU firms changes from 8.74 in the pre-period to 7.831 in the post-
period. Even if there seems to be a small decrease in the average coverage of US firms as well, the
magnitude is much smaller and is not statistically significant.
We formally test H1 by estimating Model (3.1). Column (1) of Table 3.6 reports the result.
After unbundling, analyst coverage of EU firms changes by−0.651. This translates into a decrease
of 7.45% relative to the average analyst coverage of these firms prior to the regulation.31
Model (3.1) is suitable to recover the parameter of interest β1 only if the parallel trend assump-
tion holds. We test this assumption by estimating the dynamic coefficients described in Model
(3.4). Figure 3.5a shows the plot of dynamic coefficients with a 95% confidence interval.32 The
dynamic coefficients are significant only for 2018. This is strong support for the parallel trend
assumption. We further conduct a placebo test in which we focus on the pre-regulation years and
define the Post dummies as if the regulation occurred in one of these pre-regulation years. If the
parallel trend assumption holds, the coefficient in front of the interaction term Treatj × Postt
should not be statistically significant and if it is, the magnitude should be much smaller. Column
(1) to (3) in Panel A of Table 3.10 shows the results. None of the coefficients are statistically
significant. We take these results as evidence that parallel trend assumption is very likely to hold
in our setting. It is reasonable to believe that our control group establishes a valid counterfactual
of what would have happened to the treatment group in the absence of the reform.
We conclude that unbundling has had a negative effect on analyst coverage. Analyst coverage
has been widely used as a measure of research production quantity. We interpret the decrease
31We perform the same analyzes in the sample for coverage quality. Results are qualitatively the same and can befound in Table C.6 of Appendix C.4.2.
32Point estimates are reported in Table C.4 in the Appendix C.4.1. In the Appendix the readers can find pointestimates for all other dynamic coefficient plots presented in the following sections.
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in coverage as evidence that there is a causal impact of unbundling on the quantity of research
produced by analysts.
We now turn to explore the heterogeneous effects of the regulation on analyst coverage (H2).
Both Figure 3.3 and Panel A of Table 3.5 show clear evidence that the analyst coverage of small
firms remains relatively unchanged and the analyst coverage of large firms decreases significantly.
These results are also confirmed in the formal difference-in-difference estimation. Column (2) of
Table 3.6 shows that the analyst coverage of small firms in the EU decreases much less than that of
large firms in the EU. The result is further strengthened by the triple-difference analyses in column
(3). The coefficient in front of the triple-difference term is 1.891 and statically significant. For
large firms, the analyst coverage change by −1.594, which translates in to a 10.53% decrease in
the average analyst coverage of large firms prior to the regulation. In Table C.7 of Appendix C.4.2,
we present the regression results in logs. All the results are qualitatively the same. These results
support H2: analyst coverage of large firms decreases more than that of small firms.33
In summary, we have shown that unbundling causes an aggregate decrease in the analyst cov-
erage of EU firms compared with US ones and that this decrease is more pronounced for large
firms. These are evidences in support for H1 and H2. The results are surprising: it contradicts
the common view in the media that small firms would be most affected. We interpret these results
through lenses of competition in the market for analyst research. When it becomes mandatory for
investors to pay separately for research, they are likely to stop buying low-quality research. Large
firms on average have more coverage than small firms and the probability that low-quality research
is produced is higher. If investors opt out of inferior research, large firms are more affected.
3.5.2 The impact of unbundling on analysts forecast quality
After establishing the negative effect of unbundling on analyst coverage (coverage quantity),
we turn to explore the impact on coverage quality. Panel B of Table 3.5 presents the results of a
33In Table C.8 of Appendix C.4.2, we also perform difference-in-difference analyses between EU firms and USfirms but separately for small and large firms (e.g., small EU firms vs. small US firms; large EU firms vs. large USfirms). We obtain very similar results: the decrease in the coverage is concentrated in large firms.
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simple one-difference analysis. It shows that the forecast error decreases for EU firms. In Figure
3.4, we plot the empirical cumulative distribution of the forecast errors. We can see that for EU
firms, the distribution of the post-year is “smaller than" the distribution of the pre-years since the
post-year distribution lies mostly above that of the pre-years. We do not observe a similar trend
among US firms. We also plot the histogram of the forecast errors in the pre- and post-regulation
years in Figure C.3 of Appendix C.2 and observe a similar pattern: the histogram in the post-year
shifts towards 0 for EU firms, indicating an overall decrease in the forecast error. Again, we do not
observe a clear similar pattern for US firms. All the evidence suggests that the forecast error of EU
firms decreases after unbundling.
Table 3.6 reports the formal difference-in-difference results. Notice that the number of obser-
vations changed from the previous analyses on coverage quantity, because we now focus on the
sample for coverage quality. Column (4) of Table 3.6 shows that overall, the change in the forecast
error of EU firms is −0.142%. This translates into a decrease of 19.19% relative to the average
forecast errors of EU firms prior to the regulation. The statistically and economically significant
decrease shows that unbundling has caused analyst research to be more precise, an indication of
quality improvement. Column (2) shows that the change in the forecast errors is comparable among
both small and large firms. In fact, by checking the triple interaction term in column (3) of the same
table, we find no evidence that the coverage quality of small and large firms are affected differen-
tially. Finally, we perform the dynamic coefficient test described in Model (3.4). The results can be
found in Figure 3.5b. We do not find evident violations of the parallel trend assumption. Placebo
tests in column (4) to (6) of Table (3.10) show reassuring evidence. Hence, we are confident in
claiming that unbundling causes an increase in analyst research quality in the EU.
The results presented in this subsection are in line with hypothesis H3. Even though we doc-
ument a decrease in the coverage quantity due to unbundling, we find that the coverage quality
improves. This provides supportive evidence that unbundling disciplines analyst forecast behavior.
Being evaluated directly and fighting for limited resources from the buy-side, analysts compete
more intensively among the quality domain and produce better forecasts.
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3.6 Investigating the channel: analyst level analyses
To reconcile the simultaneous decrease in the coverage quantity and the increase in the coverage
quality, we argue that analyst competition is enhanced. Quality becomes the main concern of
analysts due to unbundling. The enhancement of competition 1) motivates existing analysts to
produce better forecasts (intensive margin) and 2) makes analysts who produce worse forecasts
more likely to drop out of the analyst market (extensive margin). To find evidence of the two
margins, we now zoom in to the analyst level and test (H4).
3.6.1 Intensive margin
We begin with the first part of H4. To compare forecast accuracy measured by forecast error
within the same analyst over different years, we focus on analyst-firm pairs that exist throughout
the whole sample period (from 2014 to 2018). We conduct analyses similar to the ones done at the
firm level:
Yijbt = γ1Treati × Postt + γ2Xi × Postt + γ3Zijt + αi + αj + αb + αt + εijbt (3.5)
Yijbt is the forecast error analyst i working in brokerage house b incurs on firm j in fiscal year
t (the absolute difference between firm j’s actual earnings and the analyst i’s forecast, scaled by
firm j’s previous year-end price). Treati is a dummy equal to 1 if the analyst is an EU analyst.
Postt is a dummy equal to 1 if the fiscal year equal to 2018. Analyst fixed effect αi ensures that we
compare forecast error within the same analyst across different years. Ideally, we should include
firm × year fixed effect (αjt) to subsume any firm-level, time-varying heterogeneity that may
confound our causal interpretation. However, the geographic concentration of analyst portfolios as
shown in Figure C.1 implies that αjt will almost subsume Treati × Postt. Instead, we can only
include firm fixed effect and year fixed effect. We also include brokerage fixed effect αb to control
for brokerage firms the analysts work for.
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To control for time-varying heterogeneity, we include both analyst-level controls and firm-level
controls. Xi is a vector of standard analyst-level controls that are shown to affect analyst forecast
errors, including the log of the number of firms the analyst follows (LN FIRMS COVERED),
the log of the average coverage of the portfolio firms that the analyst follows (LN AVERAGE
COVERAGE), the log of the number of years one analyst worked (LN TENURE) and the log of
the days between the forecast date and the earnings report date (LN DISTANCE). These variables
are likely to be the outcomes of unbundling and serve as bad controls if we measure them year by
year. Hence, we measure them in 2014 and interact them with Post. We obtain similar results if
we simply exclude these variables. Zijt include firm level controls as defined in Section 3.5. Since
unbundling does not affect public firms directly, these controls are not likely to be bad controls and
we measure them year by year. We obtain similar results if we measure them in 2014 and interact
them with Post. Standard errors are clustered at the firm level.34 H4 implies that γ1 < 0.
To mitigate the concern for idiosyncratic noise in analyst-firm level analyses, we aggregate our
measures at the analyst level. To be more specific, we estimate the following model:
Yibt = γ4Treati × Postt + γ5Xi × Postt + γ6Zit + αi + αb + αt + εibt (3.6)
Yibt is the average of all the forecast errors analyst iworking in brokerage house b incurs in year
t. Treati and Postt are defined as before. In the baseline regression, we include brokerage house
+ year fixed effect (αb + αt). We also investigate the specification where we include brokerage
house× year fixed effect (αbt), which kills all the time-varying brokerage house level variation that
may confound our causal interpretation. This strong fixed effect may also kill some meaningful
variation. For example, if unbundling disciplines analysts through the brokerage house they work
for (e.g., brokerage houses decide to put more pressure on analysts to produce better research after
MiFID II), αbt will prevent us from capturing this channel. Hence, we take this specification as a
robustness check.
Similar to firm level analyses, we estimate a triple-difference model with respect to analysts
34This is a conservative way of clustering. Clustering at analyst level leads to smaller standard errors.
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mostly covering relatively small firms (small analysts) and analysts mostly covering relatively
large firms (large analysts). To achieve this, we first calculate the average market capitalization
of all the firms within an analyst portfolio in a given year. We then average the average market
capitalization across all the pre-regulation years. Small analysts are defined as analysts whose
average of the portfolio average market capitalization falls below the median.35 As before, we
calculate the median cutoff separately in both regions. To aggregate firm level controls to the
analyst level, we simply average the firm level variables within an analyst’s portfolio. Standard
errors are clustered at the analyst level. H4 implies that γ4 < 0. Table 3.3 reports some summary
statistics of the sample we use. EU analysts, in general, follow fewer firms and have larger forecast
errors.
Table 3.7 reports the regression results. Column (1) and Column (2) present results at the
analyst-firm pair level. Column (3) and (4) present the results at the analyst level with brokerage
house + year fixed effects. Column (5) and (6) present the results at the analyst level with broker-
age house× year fixed effect. The results are consistent over all these specifications: analysts who
stay after the regulation produce lower forecast errors. Using column (2) as the main specification,
the average forecast error of EU analysts changes by −0.131%, which translate into a 16.01% de-
crease in the average forecast errors of EU analysts prior to the regulation. The triple interaction
term further shows that the magnitude in the decrease is comparable among analysts who focus on
small firms and analysts who focus on large firms. Notice that the total number of observations
drops a lot in the brokerage house × year fixed effect specification. If we allow for brokerage
house × year fixed effect, all the meaningful variations come from brokerage houses that covering
both EU firms and US firms. Hence we focus on analysts who work for multi-continent brokerage
houses in this specification. Contrary to the analyst level, we do have a sufficient number of bro-
kerage houses that cover firms in both continents. Even with a smaller number of observations, we
still observe a statistically significant decrease in the average forecasting error.
35In principle, one can define small analysts to be analysts focusing on small firms. But analyst portfolio is a mixof both small and large firms. In most cases, large firms are the majority. Focusing on analysts covering only smallfirms leads to limited observations.
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Figure 3.6 presents the dynamic coefficients plots for all three specifications with a 95% confi-
dence interval. Unbundling takes effect only after the implementation date. Placebo tests in Panel
B of Table 3.10 show similar evidence: none of the coefficients are statistically significant in the
pre-regulation years. The results all suggest that the parallel trend assumption is very likely to hold
in our setting.
The results presented in this subsection are in line with the first part of hypothesis H4: affected
analysts who continue to work after the regulation produces better forecasts.
3.6.2 Extensive margin
Baseline comparison
We now turn to the second part of H4. We want to compare forecast quality between analysts
who drop out due to unbundling and analysts who do not. To achieve this, we need a quality
measure that is comparable across different analysts. The simplest measure is the average forecast
errors incurred by the analyst as defined above. However, different analysts tend to cover different
firms. Some firms are more difficult to forecast than others. An analyst with a high average forecast
error may either be 1) analyst who does not perform well or 2) analyst who follows firms more
difficult to analyze. Therefore, the average forecast error is problematic when we want to compare
across different analysts.
To account for all these issues, we follow Hong and Kubik (2003) to construct a relative accu-
racy measure comparable across different analysts. First, we sort the analysts covering a specific
firm in a year based on their forecast errors. Then, we assign a rank based on the sorting: the best
analyst receives the first rank. In case of a tie, we assign all those analysts the midpoint value of the
ranks they take up. Notice that the maximum rank an analyst can get depends on the total number
of analysts covering the firm. Analysts covering thinly followed firms will on average have lower
ranks and are deemed to be better. To take this into account, we scale an analyst’s rank for a firm
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by the number of analysts that cover that firm. Formally, we use the following score measure:
Scoreijt = 100− Rankijt − 1
Number of Analystsjt − 1× 100 (3.7)
where Number of Analystsjt is the number of analysts who cover firm j in year t. The more
accurate the forecast is, the lower the rank and the higher the score. We compute the scores for
every firm j in year t. To reduce idiosyncratic noise in the specific analyst-firm pairs and get the
analyst level score in the pre-regulation years, we follow Hong and Kubik (2003) and define the
relative accuracy measure (RelativeAccuracyi) to be:
RelativeAccuracyi =1
T
T∑t
(1
J
J∑j
Scoreijt)
where J is the set of firms analyst i covers in year t and T includes all the years prior to 2018. To
increase the likelihood that the analyst is affected by MiFID II, we focus on analyst-firm pairs that
exist consecutively in 2015, 2016, 2017. If the analyst covers the stock for three consecutive years
and suddenly stops covering it after the regulation, it is more likely that the stop is due to MiFID
II.
Table 3.4 presents summary statistics for the sample we use for the extensive margin analyses in
this subsection. By construction, the mean and median of the relative accuracy measure is around
50. The analysts we study covers on average 10 firms and have worked for about 10 years.
We focus on EU analyst and run the following regression at the analyst-firm level:36
Stopij = π1RelativeAccuracyi + π2Xij + αj + εij (3.8)
36We also use RelativeAccuracyij , relatively accuracy defined on analyst-firm pair by averaging across the years,for robustness checks and results are qualitatively the same.
141
and the following regression at the analyst level:37
DropOuti = π3RelativeAccuracyi + π4Xi + εi (3.9)
On the analyst-firm level, we define a dummy variable (Stopij) equal to 1 if the analyst i stops cov-
ering the firm j after the regulation. At the analyst level, we define a dummy variable (DropOuti)
equal to 1 if the analyst stops covering all the firms he/she used to cover before the regulation. The
firm fixed effect αj ensures that we compare different analysts within the same firm. Controls Xij
in Model (3.8) include the log of the number of unique firms the analyst follows prior to 2018 (LN
FIRMS COVERED), the log of the average of the average coverage of the portfolio firms that the
analyst follows across all the years prior to 2018 (LN AVERAGE COVERAGE) and the log of the
number of years one analyst has worked prior to 2018 (LN TENURE).38 We do not have firm level
controls due to the fixed effect αj . In addition to these variables, controls Xi in Model (3.9) fur-
ther include standard firm level controls aggregated at the analyst level as defined in the previous
sections. Standard errors are clustered at the analyst level for Model (3.8) and the brokerage house
level for Model (3.9). H4 implies that π1 < 0 and π3 < 0.
Column (1) in Table 3.8 shows the result of Model (3.8) at the analyst-firm level with firm fixed
effect. The result confirms our hypothesis: higher relative accuracy (better forecast quality) makes
it less likely for an analyst to stop covering a firm. Within the same firm, if the analyst’s relative
accuracy improves by 1 point, he/she is 83.9 basis points less likely to stop covering a firm. This
translates into a 3.93% drop in the unconditional probability of stopping covering a firm after the
regulation.
Column (3) shows the result of Model (3.9) at the analyst level with the brokerage house fixed
effect. The dependent variable is a dummy equal to 1 if the analyst stops covering all firms he/she
used to cover prior to the regulation. As we can see, a one-point increase in the relative accuracy
37We also conduct logit regression and results are very close. It is more econometrically appealing to clusterstandard errors and to include fixed effects in the linear model.
38For LN AVERAGE COVERAGE, we first take the average over the firms the analyst covers and then take theaverage over all the years prior to 2018. All the variables are measured prior to 2018 and are not likely to be affected bythe regulation. Our results are robust when we measure them in 2015 or just simply exclude them from the regression.
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results in a 62.2 basis decrease in the probability of dropping out of the sample. This translates
into a 2.58% decrease in the unconditional probability of dropping out. Suppose that there are
8 analysts (the average number of analysts covering an EU firm prior to the regulation) covering
a firm. If one of them improves his/her ranking from 4th to 3rd, his/her relative accuracy will
improve by 14.3 points. This makes him/her 8.89% less likely to drop out and potentially be laid
off (14.3× 0.00622). Moreover, the coefficients in front of analyst experience (LNTENURE) is
positive and highly significant. This shows that experienced analysts are less likely to drop out. To
the extent that analysts with longer experiences tend to produce better forecasts, this result conveys
further supportive evidence that more accurate analysts are more likely to stay.
Pre and post comparison
To sharpen our analyses, we perform similar regressions year by year and investigate whether
analyst accuracy matters more after unbundling. To achieve this, we define a dummy variable
Stopijt+1 equal to 1 if analyst i covering firm j at year t stops covering the same firm at year
t+1. At the analyst level, we define a dummy variable DropOutit+1 equal to 1 if the analyst stops
covering all the firms he/she used to cover at year t. We then turn (3.8) and (3.9) into:
Stopijt+1 = π5RelativeAccuracyit ∗ Postt + π6RelativeAccuracyit
+ π7Xijt + αj + αb + αt + εijt (3.10)
DropOutit+1 = π8RelativeAccuracyit ∗ Postt + π9RelativeAccuracyit
+ π10Xit + αb + αt + εit (3.11)
RelativeAccuracyit is the average of Scoreijt over all firm j analyst i covers at year t. Postt
is a dummy equal to 1 for year equal to 2017.39 Controls Xijt and Xit are defined in a similar
fashion. Standard errors are clustered at the firm level for (3.10) and at the brokerage house level
for (3.11).39Following Hong and Kubik (2003), we assume that the employment decision depends on the analyst performance
in the previous year.
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The question we seek to answer here is that among the analyst population, whether more in-
accurate analysts are on average more likely to stop/drop out after unbundling. If the answer is
yes, we anticipate π5 < 0 and π8 < 0 in the EU analyst sample but not in the US analyst sample.
Notice that (3.10) and (3.11) are not standard panel regressions. They are different cross-section
regressions stacked over time. The way we define Stopijt+1 and DropOutit+1 conditions on an-
alyst covering the firm at t. If analyst i stops or drops out at t + 1, he/she will not be included
when we define dummies for year t + 2. In fact, it is common that analysts who drop out in one
year never reappear in the later years, i.e., many analysts appear only once in the analyses. For this
reason, we do not include the analyst fixed effect. We include other important controls as defined
in the above subsection. Instead of taking the average over all the pre-regulation years, we need
to measure them year by year. Since the latest control variables are measured in 2017, they are
determined before the regulation and are not likely to be the outcomes of the regulation.
Table 3.9 present the results. Column (1) shows the result of the analyst-firm level focusing
on EU analysts. As predicted, the coefficient in front of RelativeAccuracyit ∗ Postt is negative
and statistically significant, which implies that analysts producing better forecasts are more likely
to keep covering the same firm after the regulation. Column (2) presents the same analysis on US
analysts and we do not observe a similar pattern. This provides further evidence that analysts with
worse forecast records are more likely to stop covering a firm after unbundling only when they are
affected. We perform a triple-difference-type analysis in column (3), and the coefficient in front
of the triple interaction terms again confirms our hypothesis: forecast accuracy matters more after
unbundling for affected analysts. The results using DropOutit+1 as the dependent variable can
be found in column (4) to (6). The magnitude of all the coefficients is comparable with the ones
obtained at the analyst-firm level. Notice that when an analyst drops out, he/she stops covering
all the firms. This is a strong requirement because many analysts stop covering a set of firms
without completely dropping out. Thus, the variation at the analyst level may not be enough to
allow for a triple-difference-type analysis. This could explain why the coefficient in front of the
triple interaction term is not statistically significant.
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In summary, the results presented in Table (3.8) and (3.9) are all in line with the second part
of H4. In other words, analysts who have lower relatively accuracy (analysts who produce worse
forecasts) are more likely to stop covering a firm and even drop out. Forecast accuracy matters
more after unbundling only among affected analysts. This section provides additional evidence on
the competition channel: analysts compete for research quality due to unbundling. The ones with
worse forecast records are more likely to be cast out.
3.7 Robustness check and extensions
Previous sections focus on analyzing the impact of unbundling on sell-side research production
and the underlying channel driving the results. We now conduct a few additional analyses to show
that our findings are robust. We also study how unbundling affects brokerage house employment
and what the capital market effects of MiFID II are.
3.7.1 Firm’s brokerage house coverage
In the previous analyses, we show that firms’ analyst coverage drops. One concern is that
this drop comes from brokerage houses laying off analysts providing duplicated research services.
For example, if two analysts cover the same firm in the same brokerage house, the one providing
duplicated or worse research may be laid off. If this is the case, a drop in the analyst coverage does
not imply a drop in the brokerage house coverage. Investors are still able to get access to the same
amount research from these brokerage houses and potentially from better analysts. In other words,
the quantity of research does not decline.
Although one brokerage house rarely hires two analysts covering the same public firm due
to redundancy, we check firms’ brokerage house overage directly.40 We perform difference-in-
difference analyses similar to Model (3.1) but replace the dependent variable with the number of
unique brokerage houses covering the firm. Under the condition that the relationship between
40This is a well-established empirical fact (e.g., Hong and Kacperczyk (2010)). In our sample, among all thebrokerage house-firm pairs, 86% of them has only one analyst coverage.
145
investors and brokerage houses are sticky (as shown, for example, in Di Maggio et al. (2019)), a
reduction in firms’ brokerage house coverage implies that investors lose access to research on these
firms from these brokerage houses, which further suggest a decrease in the quantity of research
supplied to these investors.
Table 3.11 shows the results. As we can see, firms’ brokerage house coverage drops after
unbundling. Similar to previous analyses, this decrease is driven by large firms. Large firms lose
more than 1 brokerage house after this regulation. The results here suggest that investors’ access
to firms’ research through brokerage houses may reduce. From these investors’ point of view, the
quantity of research decreases.41
3.7.2 Other quality measures
Analyst forecast quality is hard to measure. To show that our results are robust, we repeat our
analyzes using other commonly used measures of forecast quality.
Non-market-response based measures
First, we follow previous research and use forecast dispersion, defined as the standard deviation
of all the forecasts across all the analysts following the same firm in a given fiscal year, as a proxy
for firm level forecast quality (e.g., Gu and Hackbarth (2013), Behn et al. (2008)). One intuition
behind this measure is the following: if accuracy becomes analysts’ main concern, dispersion will
decrease when all of their forecast quality improves and the forecast values converge to the true
value.
One-difference analyses in Panel C of Table 3.5 reveal that the dispersion of EU firms decreases
after the regulation. Difference-in-difference analyses in Panel A of Table 3.12 further confirm the
result: unbundling causes a decrease in the forecast dispersion of the EU firms compared with
the US firms. The magnitude is comparable between small firms and large firms. These results
are consistent with the analyses using forecast error. Dynamic coefficient plot in Figure 3.5c and
41In untabulated test, we also find that the number of unique firms EU brokerage houses cover decreases.
146
placebo tests in column (7) to (9) of Table 3.10 both show no evident violations of the parallel trend
assumption. We conclude that the coverage quality of EU firms, measured by forecast dispersion,
indeed improves after the regulation. The analyses also show that the beliefs of different analysts
are converging after this regulation.
Another measure for quality is the number of firms each analyst covers. It is reasonable to
believe that if one analyst covers fewer firms, due to specialization, he/she will devote more time
to each firm and provide better forecasts. Panel B of Table 3.12 shows the results of the difference-
in-difference analyses similar to Model (3.6). The dependent variable is the number of firms each
analyst covers. We focus on analysts who cover at least one firm throughout the sample in Column
(1). As we can see, EU analysts cover less firms after the regulation and the decrease is statically
significant. We find similar evidence in column (2) in which we focus on all the analysts in our
sample. These results further support that the quality of analysts research in EU improves after
unbundling.
Market-response based measures
We can also assess analyst forecast quality using market responses to analyst forecasts. In-
tuitively, if analyst forecast quality improves and contains more information, stock prices should
move more substantially on the analyst forecast revision dates. Hence, we focus on the absolute
market-adjusted abnormal returns on the analyst forecast revision dates. Improvement in the fore-
cast quality suggests more significant absolute market-adjusted abnormal returns on the revision
dates.
We define three measures to capture this effect. At the analyst-firm level, we calculate the
absolute market-adjusted abnormal return on the forecast revision date:
ABRetj,i,d = |Retj,i,d −Retm,d| (3.12)
42In this section, we focus on the revision dates, i.e., dates on which analysts revise his/her forecasts. Our results,both at the analyst-firm level and at the firm level, are robust if we focus on all dates on which analysts issue forecasts.
147
Retj,i,d denotes the daily return of firm j when analyst i revises forecast for firm j at date d.42
To mitigate data errors in Datastream, we winsorize Retj,i,d at the 1% level. Retm,d denotes the
daily return of the stock market. Here, we define the market return for EU and US separately by
calculating the value-weighted stock returns of all the firms in each continent. If multiple revisions
occur on the same day for the same firm, we assign each analyst covering that firm the same
abnormal return. In an extreme case, we could attribute the abnormal returns generated by more
informative analysts to analysts who simply herds with the others. To mitigate this concern, we
keep only the first three analyst revisions by the exact revision time. ABRetj,i,d then helps us to
capture the new information in the forecast revisions at the analyst-firm level.
At the firm level, we aggregate analyst revisions. We first compute a yearly measure of aggre-
gate analyst informativeness (AGAI). Following previous literature (e.g., Frankel et al. (2006) and
Lehavy et al. (2011)), we define AGAI as follows: For a given firm in a given fiscal year, we first
sum the absolute market-adjusted abnormal returns on all the forecast revisions dates across all the
analysts. We then divide it by the sum of absolute market-adjusted abnormal returns of all trading
days for the firm in the given fiscal period. Specifically,
AGAIjt =
∑NREV Sd=1 |Retj,d −Retm,d|∑TDAY Sd=1 |Retj,d −Retm,d|
(3.13)
where Retj,d denotes the daily return of firm j and Retm,d denotes the daily return of the stock
market. NREV S is the set of unique forecast revision dates over all the analysts for the given firm
in the given fiscal year. We exclude forecast revision dates that coincide with earnings announce-
ments. This mitigates the concern that analyst forecast revisions respond to publicly available
earnings information. Intuitively, AGAI measures the aggregate abnormal returns on all forecast
revision dates. It allows us to capture the total amount of new information in the analyst forecast
revisions.43 Furthermore, AGAI incorporates changes in the total number of forecasts (the quantity
of information) caused by both changes in the number of analysts covering a firm and the number
43AGAI treats multiple revisions by different analysts on the same firm as one aggregate revision. It measures theaggregate information generated by all analysts on a given revision date.
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of forecasts issued by one analyst. All else being equal, a decrease in the total number of forecast
revisions causes a decrease in AGAI.
To account for the changes in the total number of forecast revisions, we normalize AGAI by
the number of forecast revision dates of a given firm in the given fiscal year. Formally, we define
the average analyst informativeness as:
AV GAIjt =
∑NREV Sd=1 |Retj,d −Retm,d|∑TDAY Sd=1 |Retj,d −Retm,d|
× 1
NREV Sj(3.14)
where NREV Sj is the number of unique forecast revision dates. AVGAI then measures the aver-
age informativeness of one analyst forecast revision date.
We perform similar difference-in-difference analyses (Model 3.1) using the three new mea-
sures. Standard firm level controls are included. At the analyst-firm level, we include the log of the
number of days between two revision dates as an additional control. Standard errors are clustered
at the firm level.
We report the results in Table 3.13. Column (1) shows the results at the analyst-firm level.
We include analyst × firm fixed effect to capture changes in the abnormal return within the same
analyst-firm pair across different times. As we can see, analyst forecasts generate larger abnormal
returns after unbundling. This is evidence that individual analyst forecasts become more informa-
tive. Column (2) aggregates different analyst revisions at the firm level. It shows that the average
informativeness of one revision date improves after the regulation. These results provide further
evidence that individual analyst quality increases. In column (3), we show the results of aggregate
informativeness without normalizing the number of forecast revision dates. Interestingly, the coef-
ficient in front of TREAT × POST becomes statistically negative, suggesting a likely decrease
in the aggregate informativeness of analyst forecasts.
We interpret the results as a trade-off between quantity and quality. While individual forecasts
become more informative, the total number of valuable forecasts decreases after the regulation.
Hence, even though average analyst informativeness increases, the aggregate informativeness of
44Results of small firms and large firms can be found in the Appendix C.4.3.
149
analyst forecasts decreases.44
As a final note, we are aware of potential concerns with abnormal returns on the revision dates.
For example, analysts could respond to prior public disclosure events. In this case, their revisions
could appear to provide more information than they actually do. We try to address these concerns
by focusing on a short window (1-day) and by excluding revision dates coinciding with earnings
announcement dates. But still, abnormal returns on the forecast revision dates are not the cleanest
measure. Hence, we view our results here suggestive rather than conclusive.
3.7.3 Alternatives
In our paper, we argue that the enhancement of competition among analysts in the quality do-
main is one driver of our results. One assumption we rely on is that asset managers internalize
research costs and put more emphasis on research quality. What if these asset managers just claim
to internalize the cost but in effect still make hidden research payments through inflated commis-
sions? If that is the case, they probably would not focus a lot on research quality because end
investors bear the costs. Although it is hard to preclude this possibility based on the data we cur-
rently observe, for this argument to hold, commissions fees should at least stay more or less the
same, if not increase. However, recent surveys suggest that commissions fees drop by around 30%
due to unbundling.45 A study by Financial Conduct Authority (FCA) also finds no evidence of
asset managers passing research cost through trading commissions and break the new rule. Ac-
cording to this study, expensing research costs out of asset managers’ own profits already saved
end investors in the UK around £180 million in 2018. The FCA expects that the overall savings
from MiFID II rules could reach £1 billion over the next five years.46
Moreover, unbundling makes many end investors become aware of the hidden cost. End in-
vestors such as pensions, insurance companies, and sovereign funds have always been proponents
of unbundling due to opaque fee structures and inflated trading costs. As a result, asset managers
45"Bank and brokers suffer ‘dramatic’ fall in commissions" Financial Times, June 2nd, 2018.46Andrew Bailey, Chief Executive of the FCA, keynote speech on MiFID II at the European Independent Research
Providers Association.
150
face greater pressure to reduce commission fees after unbundling. Hiding research cost by inflating
fees not only exposes asset managers to severe legal risks but put them at a disadvantage amid the
increased market competition in the asset management industry. All these arguments suggest that
it is unlikely for asset managers to hide research costs and continue the “soft dollar" practice as
under bundling.
Another common worry is that other provisions in MiFID II may also affect sell-side research.
For example, post-trading transparency may make more information available to the general pub-
lic and less analysts research is needed. That is why we observe a drop in the analyst coverage.
However, post-trading transparency reveals mainly order flow information. Translating order flow
information into firms’ fundamental information which analysts specialize in is difficult. In this
case, analyst research should still be needed. Even if we assume that post-trading transparency
reveals fundamental information, the transparency story implies that small firms will be more af-
fected: the trading process of thinly traded stocks, which in most cases are small stocks, is more
likely to feature opaqueness. The improvement in transparency should benefit small firms more
than large firms. This further implies that fewer analysts on small firms are needed because more
information on small firms is now available. But we observe the opposite: small firms’ analyst
coverage remains unchanged and large firms’ coverage drops. To sum up, it could be the case that
other provisions may confound our results but it is unlikely for a provision other than unbundling
to explain all our findings.
An alternative story that can explain our findings is learning. Maybe EU analysts are be-
coming better at learning over the years and begin to produce better forecast results regardless of
unbundling.47 While this alternative is plausible and harder to preclude entirely, it does not fully
justify the sudden improvement in the overall forecast quality right after unbundling. First, if it
were not for unbundling, the learning process is likely to take more time and the effect should
manifest itself gradually over the years. If that were the case, our placebo test should have picked
up the learning effect, but we do not observe changes in the forecast quality in our placebo test.
47If analysts become better at learning due to unbundling, the story does not contradict our argument: unbundlingincentivizes analysts to produce better forecasts. One way to improve their forecasts is to become better at learning.
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Second, the change in the cumulative distributions of forecast errors (i.e., Figure 3.4) shows that
quality improvement is a general phenomenon. It could be the case that a few analysts are better
at learning right after the regulation for reasons unrelated to unbundling, but it is be difficult to
argue that most of the analysts happen to become better at learning at the same time, right after the
regulation, and for reasons unrelated to unbundling.
We further investigate the learning story in Table 3.14. We introduce the lagged forecast error
in our regressions (similar to Model (3.5) and Model (3.6)). The intuition behind is the following:
analysts producing larger forecast errors in the previous period could face greater career pressure
and become better at learning to improve their performance in the current period, regardless of
unbundling. Thus, controlling for lagged forecast error help us to capture the change in the analyst
learning process unrelated to unbundling. We then check whether our results are robust to the
inclusion of the new control. Column (1) presents the results at the analyst-firm pair level. Column
(2) presents the results at the analyst level with brokerage house + year fixed effects. Column (3)
presents the results at the analyst level with brokerage house × year fixed effects. After adding the
new control, our results still hold and the coefficient of interest remains statistically significant and
economically meaningful.48 The results also show that larger previous forecast errors do predict
smaller current forecast errors, which explains why the magnitudes of the coefficients of EU ×
POST generally become slightly smaller. We conclude that learning may contribute but does not
explain the whole story: on top of learning, the competition introduced by unbundling still plays
an important role in driving the results.
3.7.4 Brokerage house level employment
In addition to research quantity and quality, unbundling may also affect different types of bro-
kerage houses differentially. The differential impact has important implications for the market
structure of the sell-side research industry (e.g., maybe the industry will begin to consolidate be-
48For example, in column (2), 0.122% translates into a 14.91% decrease in the average forecast error of EU analystsprior to the regulation.
152
cause certain types of brokerage houses are more affected and could not survive). To explore this
heterogeneity, we attempt to compare the employment results of independent research firms (we
will call them boutique houses) with the results of brokerage houses affiliated with large invest-
ment banks. Boutique houses normally do not provide trading services, while the business model
of research in brokerage houses affiliated with large banks features heavy bundling. It is likely
that the latter will be more affected by the regulation. However, our data only provides us with an
anonymous ID for the brokerage house analysts work for. We are unable to recover the real name
of these brokerage houses. To overcome this data limitation, we focus on the size of the brokerage
houses, i.e., the number of analysts each brokerage house employs. It is reasonable to assume that
boutique houses are smaller in size than houses affiliated with large banks.
To understand which type of houses are more affected by the regulation, we then perform the
following analysis within EU brokerage houses:
Ybt = φ1Smallb × Postt + φ2Xbt + αb + αt + εbt (3.15)
Ybt is the number of unique analysts working in brokerage house b in year t. EU brokerage
houses are defined to be the brokerage houses that only hire EU analysts. Smallb is a dummy
equal to 1 if the average number of analysts a brokerage house hires in the pre-regulation years falls
below the median. Postt is a dummy equal to 1 if the fiscal year t is equal to 2018. The control
Xbt includes standard firm level controls as defined previously. We average the firm level variables
within the brokerage house portfolio to get the brokerage house level firm controls. Standard errors
are clustered at the brokerage house level.
The results are presented in Table 3.15. Column (1) shows the results within EU brokerage
houses: after the regulation, large brokerage houses on average lose around 3 more analysts than
small houses. This can also be seen from the plot in Figure C.4 of Appendix C.2. Column (2)
shows the results of a triple-difference specification similar to Model (3.3). The coefficient in
front of the triple interaction term is not significantly different from 0: it seems that US large
brokerage houses also lose more analyst during this period.
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The results in this section seem to be inconclusive. It is true that within the EU, large brokerage
houses are more affected. However, within the US, a region unaffected by the regulation directly,
large brokerage houses are also more affected. It is possible that small brokerage houses may not be
a good proxy for independent research firms and for this reason, brokerage houses in the US are not
valid counterfactuals in the triple-difference analyses. In addition, the number of observations at
the brokerage house level is small and the results thus may suffer from a low-power issue. With all
these limitations in mind, we leave careful analyses on how MiFID II have changed the landscape
of brokerage houses for future research.
3.7.5 Capital market effects
So far, our analyses focus on sell-side research. We now explore the capital market effects
of unbundling, or more generally, the capital market effects of MiFID II. Since capital market
outcomes are potentially affected by many other factors, the goal in this section is to show what
has happened, rather than to apply tight identification strategies and claim causality. To be coherent
with our previous analyses, we only focus on firms with valid I/B/E/S coverage in our sample.
Following the previous literature, we focus on two important variables at the firm level: earn-
ings announcement information content (EAinfojd) and bid-ask spread (Bid Ask Spreadjt)
(e.g., Cumming et al. (2011), Christensen et al. (2016) and Merkley et al. (2017) ). We per-
form exercises similar to Model (3.1) but replace the dependent variables to be either EAinfojt
or Bid Ask Spreadjt.
EAinfojt is defined as:
EAinfojt =1∑
d=−1
|Retj,d −Retm,d| (3.16)
where d denotes days around a firm’s earnings announcement date t, j denotes the firm, Retj,d49Here, we define the market return for EU and US separately by calculating the value-weighted returns of all the
firms in a given continent. Our results are qualitatively the same if we use all stocks in each country to calculate thestock market return.
154
denotes the daily return of firm j and Retm,d denotes the daily return of the stock market.49 To
mitigate data errors in Datastream, we winsorize Retj,d at the 1% level. EAinfo captures the
informativeness earnings announcements: its value should be close to 0 if analyst forecasts are
informative enough and no additional information is conveyed at the actual earnings report date.
The daily bid-ask spread is computed as the difference between the two prices divided by the
midpoint. We winsorize the spread at the 1% level. We then take the mean of the daily spread over
the year for a given firm and obtain Bid Ask Spreadjt. Bid-ask spread is a common measure of
market liquidity. If the overall informativeness of analyst forecast and market liquidity situation
do not deteriorate, we anticipate β ≤ 0. Results are shown in Table 3.16.
Column (1) and (2) are results for earnings announcement information content. Column (1)
shows the standard difference-in-difference result, while column (2) presents the dynamic coeffi-
cient estimates. Although the coefficient of interest is positive in column (1), it is not statistically
significant. In fact, column (2) reveals that all the coefficients are negative, and the parallel trend
assumption may not hold in this regression. The evidence suggests that firms’ earnings announce-
ments do not convey more information after unbundling. Similarly, for bid-ask spread, the overall
impact is not statistically different from zero. It seems that bid-ask spread decreased in 2017, one
year prior to the regulation. Overall, the results in this table imply that capital market situations do
not deteriorate after MiFID II.
These findings do not contradict with the previous studies by Christensen et al. (2016) and
Cumming et al. (2011) who show that capital market regulation aiming to improve transparency
and competition has overall positive effects on capital market outcomes. The findings are also con-
sistent with our story. Competition among analysts is strengthened after the regulation, resulting
in the improvement of forecast quality. This further improves the informativeness of analyst re-
ports and has non-negative effects on the liquidity of the market. However, we are aware that both
EAinfojd andBid Ask Spreadjt are noisy aggregate outcomes that can be affected by many other
factors in addition to analyst forecasts. Moreover, the reform is fairly recent, and its aggregate im-
pact may take some more time to manifest. The aggregate impact of MiFID II on capital markets
155
is an important question and is worth investigating more carefully in future research projects.
3.8 Conclusion
In this paper, we investigate the impact of unbundling on analyst research production. Firms
affected by unbundling experienced a more substantial drop in analyst coverage. Such a drop
does not come from small- or mid-cap firms but is concentrated in large firms. Furthermore,
firms’ coverage quality improves. We argue that the enhancement of analyst competition could
explain the results. Unbundling puts an explicit price on analyst research. On the one hand, asset
managers become more selective in purchasing research because they need to internalize research
costs. On the other hand, analysts are evaluated directly by the services they provide and have
stronger incentives to produce better research. As a result, analysts compete more directly in the
quality domain to maintain and attract clients. We find evidence of the two specific predictions
of the competition channel: 1) analysts who stay produce better research (intensive margin); 2)
analysts who produce worse research are more likely to stop working (extensive margin). Our
results highlight a potential trade-off between quantity and quality: improvement in the quality of
research by unbundling comes at a cost of reducing the quantity of research. Overall, our paper
provides a timely investigation of an important and controversial regulation. It helps to shed light
on key questions and debates, including how research should be paid for and how the market for
analysts should be regulated.
Our paper focuses on one important aspect of information production – the sell-side research
production but is silent on other dimensions of information production. For example, the rising
cost of sell-side research may encourage more buy-side players to establish their in-house research
team. A larger proportion of information production may then migrate from the sell-side to the
buy-side. Instead of offering conclusive answers, we view our paper as an important starting
point to understand how the compensation schedule for information affects the overall information
production. There are many interesting follow-up questions worth exploring: Will the sell-side
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research markets begin to consolidate? Will research migrate from the sell-side to the buy-side?
What are the welfare implications for investors? We leave these questions for future research.
3.9 Figures
Figure 3.1: Illustration of Bundling and Unbundling
(a) Bundling
(b) Unbundling
This figure illustrates heuristically the two regimes in which sell-side research is compensated. Under bundling,research is paid through trading commissions and the commissions are passed on to end clients. Under unbundling,research is required to be paid separately. Asset managers can either pay for research directly (against the firm’s profitand loss) or pass the costs to clients by setting up a research payment account (“RPA”) under the consent of clients.Most asset managers opt for purchasing researching directly. The figure also shows that data we use for this projectcomes from the sell-side and the public firms it covers.
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Figure 3.2: Average Analyst Coverage Over Time (EU vs. US)
●●
●
●●
−1
0
1
2014 2015 2016 2017 2018
Adj
uste
d A
vera
ge N
umbe
r of
Ana
lyst
s pe
r F
irm
● US EU
This figure shows the average analyst coverage of EU firms and US firms over time. Analyst coverage is the numberof unique analysts covering a specific firm in fiscal year t. We report the averages of the period from 2014 to 2018 andadjust the coverage value so that both lines start at 0 in 2014.
Figure 3.3: Average Analyst Coverage Over Time between Small Firms and Large Firms in the EU
● ● ● ● ●
−5.0
−2.5
0.0
2.5
5.0
2014 2015 2016 2017 2018
Adj
uste
d A
vera
ge N
umbe
r of
Ana
lyst
s pe
r F
irm
● Small Large
This figure shows the average analyst coverage of small firms and large firms in the EU. Analyst coverage is thenumber of unique analysts covering a specific firm in fiscal year t. Small firms are firms whose average fiscal year-endmarket capitalization before 2018 falls below the median. We report the averages of the period during 2014 to 2018and adjust the coverage value so that both lines start at 0 in 2014.
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Figure 3.4: Empirical Cumulative Distribution of Forecast Error at the Firm Level
0.00
0.25
0.50
0.75
1.00
0.0 2.5 5.0 7.5 10.0Forecast Error (%) of EU Firms
Fra
ctio
n of
the
Tota
l Num
ber
of F
irms
Pre Post
(a)
0.00
0.25
0.50
0.75
1.00
0.0 2.5 5.0 7.5 10.0Forecast Error (%) of US Firms
Fra
ctio
n of
the
Tota
l Num
ber
of F
irms
Pre Post
(b)
This figure plots the empirical cumulative distribution of the forecast errors in the pre- and post-regulation years. Toget the forecast errors in the pre-regulation years, we simply average firms’ forecast errors overall all the pre-years.
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Figure 3.5: Firm Level Outcomes (Dynamic Coefficients)
●●
●●
●
−3
−2
−1
0
1
2
2014 2015 2016 2017 2018
Dyn
amic
Coe
ffici
ents
with
95%
Con
fiden
ce In
terv
al
(a) Coverage
●● ●
●
●
−1.0
−0.5
0.0
0.5
1.0
2014 2015 2016 2017 2018
Dyn
amic
Coe
ffici
ents
with
95%
Con
fiden
ce In
terv
al
(b) Forecast Error
●●
●
●
●
−1.0
−0.5
0.0
0.5
1.0
2014 2015 2016 2017 2018
Dyn
amic
Coe
ffici
ents
with
95%
Con
fiden
ce In
terv
al
(c) Forecast Dispersion
This figure shows the dynamic effect of unbundling. We split the post dummies into year dummies (Model (3.4)) andplot the coefficient estimates along with a 95% confidence interval. We choose 2014, the year in which MiFID II wentinto discussion, as our reference year. Standard errors are clustered at the country level.
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Figure 3.6: Analyst Level Forecast Error (Dynamic Coefficients)
●●
●
●
●
−1.0
−0.5
0.0
0.5
1.0
2014 2015 2016 2017 2018
Dyn
amic
Coe
ffici
ents
with
95%
Con
fiden
ce In
terv
al
(a) Analyst Firm Pair Level
● ●
●
●
●
−1.0
−0.5
0.0
0.5
1.0
2014 2015 2016 2017 2018
Dyn
amic
Coe
ffici
ents
with
95%
Con
fiden
ce In
terv
al
(b) Analyst Level (B House + Year Fixed Effects)
●●
●●
●
−1.0
−0.5
0.0
0.5
1.0
2014 2015 2016 2017 2018
Dyn
amic
Coe
ffici
ents
with
95%
Con
fiden
ce In
terv
al
(c) Analyst Level (B House × Year Fixed Effects)
This figure shows the dynamic effect of unbundling in the intensive margin analyses at the analyst level. We splitthe post dummies into year dummies and plot coefficient estimates along with a 95% confidence interval. We choose2014, the year in which MiFID II went into discussion, as our reference year. Standard errors are clustered at theanalyst level.
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3.10 Tables
Table 3.1: Firm Level Summary Statistics (Sample for Coverage Quantity)
EU Firms: 2133 firms in total
Statistic Mean Median Pctl(25) Pctl(75) St. Dev.
Coverage 8.558 4 1 13 9.761Book to Market 2.448 1.046 0.595 1.855 5.799Investment Return (%) 11.597 7.429 −13.127 28.959 43.462Market Capitalization (Bil $) 5.324 0.547 0.114 2.751 17.385Return on Assets (%) 2.919 4.574 0.992 8.020 17.484Return Volatility (%) 33.330 28.996 22.628 38.431 17.041
US Firms: 2259 firms in total
Statistic Mean Median Pctl(25) Pctl(75) St. Dev.
Coverage 11.145 8 4 16 10.162Book to Market 1.792 0.814 0.450 1.556 3.228Investment Return (%) 5.851 3.560 −16.456 24.010 39.807Market Capitalization (Bil $) 10.235 1.531 0.388 5.608 38.128Return on Assets (%) 1.082 3.954 0.934 7.698 23.676Return Volatility (%) 35.025 29.326 22.355 41.698 19.025
This table provides the summary statistics of important firm level variables in the sample for coverage quantity. Cov-erage is the number of unique analysts covering a certain firm. Book to Market is defined as total asset (Worldscopeitem 02999) minus long-term debt (Worldscope item 03251) over market value (Worldscope item 08002). Investmentreturn is Worldscope item 08801, measured as (market price at year t+ dividends−market price at year t− 1)/marketprice at year t− 1). Market capitalization is Worldscope Item 08002 measured in billion dollars. Return on Assets isWorldscope Item 08326. Return volatility is the annualized standard deviation of daily returns over a year for a givenfirm.
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Table 3.2: Firm Level Summary Statistics (Sample for Coverage Quality)
EU Firms: 1111 firms in total
Statistic Mean Median Pctl(25) Pctl(75) St. Dev.
Coverage 13.887 11 5 21 10.163Forecast Error (%) 0.724 0.340 0.126 0.848 1.085Dispersion (%) 0.848 0.456 0.224 0.960 1.163Book to Market 2.415 0.922 0.537 1.564 5.701Distance 120.245 115.029 94.026 141.500 43.478Investment Return (%) 11.775 9.067 −8.107 27.482 33.974Market Capitalization (Bil $) 9.595 2.174 0.692 7.529 23.104Return on Assets (%) 6.046 5.374 2.661 8.866 12.240Return Volatility (%) 27.868 26.029 21.319 32.267 10.164
US Firms: 1693 firms in total
Statistic Mean Median Pctl(25) Pctl(75) St. Dev.
Coverage 13.679 11 6 19 10.071Forecast Error (%) 0.442 0.176 0.064 0.458 0.801Dispersion (%) 0.539 0.218 0.091 0.558 0.930Book to Market 1.575 0.732 0.416 1.362 2.398Distance 114.431 111.444 90.545 134.000 35.818Investment Return (%) 7.821 5.300 −12.515 24.561 35.532Market Capitalization (Bil $) 13.356 2.598 0.892 8.674 43.561Return on Assets (%) 3.818 4.605 1.289 8.276 12.466Return Volatility (%) 31.033 27.152 21.528 36.711 14.279
This table provides the summary statistics of important firm level variables in the sample for coverage quality. Tobe included in this sample, firms need to be covered by at least 2 analysts each year. Coverage is the number ofunique analysts covering a certain firm. Forecast error is defined as the absolute distance between the firm’s actualannual earnings per share and the mean of the analyst forecasts, scaled by the firm’s previous year-end price. Forecastdispersion is defined as the standard deviation of all the forecasts across all the analysts following the same firm inthe same year, scaled by the firm’s previous year-end price. Book to Market is defined as total asset (Worldscopeitem 02999) minus long-term debt (Worldscope item 03251) over market value (Worldscope item 08002). Distance isthe average of the days between the analyst forecast date and the firm’s actual EPS report date. We take the averageover all the analysts following the same firm and measure this variable in 2014. Investment return is Worldscopeitem 08801, measured as (market price at year t+ dividends−market price at year t − 1)/market price at year t − 1).Market capitalization is Worldscope Item 08002 measured in billion dollars. Return on Assets is Worldscope Item08326. Return volatility is the annualized standard deviation of daily returns over a year for a given firm. We removeobservations for which forecast error and forecast dispersion is larger than 10% of the firm’s share price at the end ofthe previous year.
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Table 3.3: Analyst Level Summary Statistics (Sample for Intensive Margin)
EU Analysts: 1211 in total
Statistic Mean Median Pctl(25) Pctl(75) St. Dev.
Average Forecast Error (%) 0.812 0.656 0.376 1.091 0.623Average Distance 78.751 70.500 41.000 105.000 52.712Average Coverage of Portfolio Firms 21.658 22.286 14.167 28.750 9.587Number of Firms Follows 7.557 7 5 10 3.817Tenure (years) 8.915 8 4 14 5.797
US Analysts: 1387 in total
Statistic Mean Median Pctl(25) Pctl(75) St. Dev.
Average Forecast Error (%) 0.403 0.272 0.156 0.504 0.396Average Distance 81.877 84.235 56.845 101.500 38.765Average Coverage of Portfolio Firms 21.367 20.250 14.229 27.279 10.047Number of Firms Follows 10.547 10 7 14 5.972Tenure (years) 8.740 8 4 13 5.432
This table provides the summary statistics of important variables used in the intensive margin analyses at the analystlevel. Average Forecast Error is the average of forecast errors (scaled by the firm’s previous year price) across all thefirms the analyst covers in a given year. Average Distance is the average of the days between the analyst forecast dateand the firm’s actual EPS report date. We take the average across all the firms within an analyst portfolio and measurethis variable in 2014. Average Coverage of Portfolio Firms is the average of the analyst coverage of all the firms theanalyst follows in 2014. We take the average across all the firms within an analyst portfolio. N of Firms Follows isthe number of firms the analyst follows in 2014. Tenure is the total number of years the analyst appeared in I/B/E/S,from 1995 to 2014. EU analysts are the analysts whose portfolios consist of at least 70% of EU stock and US analystsare the analysts whose portfolios consist of at most 30% of EU stocks. We remove analyst-firm pairs for which theforecast error incurred by the analyst are larger than 10% of the firm’s previous year-end price.
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Table 3.4: Analyst Level Summary Statistics (Sample for Extensive Margin)
EU Analysts: 1841 in total
Statistic Mean Median Pctl(25) Pctl(75) St. Dev.
Average Coverage of Portfolio Firms 20.069 21.000 13.562 26.781 8.509Number of Firms Follows 9.402 9 6 12 4.799Relative Accuracy 51.141 51.619 45.160 57.690 10.616Tenure (years) 10.299 9 5 14 5.938
Unconditional Probability
Stop Covering a Firm Drop Out
Unconditional Probability (%) 24.156 21.347
This table shows the summary statistics of important variables in the extensive margin analyses at the analyst level.Relative accuracy is a measure capturing the analyst forecast quality and is comparable across different analysts. Thehigher the number, the more accurate the analyst forecast is. N of Firms Follows is the number of unique firms theanalyst follows prior to 2018. Average Coverage of Portfolio Firms is the average of the analyst coverage of all theportfolio firms which the analyst follows. We take the average across all the years prior to 2018. Stop is a dummyvariable equal to 1 if the analyst stops covering a firm after the regulation. Drop Out is a dummy equal to 1 if theanalyst stops covering all the firms he/she used to cover prior the regulation. Unconditional probability is the simpleaverage of the two dummy variables.
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Table 3.5: One Difference (Pre and Post)
Panel A: Coverage (Sample for Quantity)
Pre Post Diff P-value
EU Full 8.740 7.831 -0.909 0
EU Small 2.350 2.292 -0.058 0.436
EU Large 15.136 13.375 -1.761 0
US Full 11.219 10.846 -0.373 0.117
US Small 5.003 4.447 -0.556 0
US Large 17.441 17.252 -0.189 0.588
Panel B: Forecast Error (%)
Pre Post Diff P-value
EU Full 0.742 0.652 -0.090 0.010
EU Small 0.880 0.800 -0.079 0.157
EU Large 0.604 0.502 -0.102 0.013
US Full 0.432 0.482 0.050 0.034
US Small 0.578 0.656 0.078 0.052
US Large 0.285 0.307 0.022 0.335
Panel C: Forecast Dispersion (%)
Pre Post Diff P-value
EU Full 0.870 0.762 -0.108 0.003
EU Small 0.920 0.831 -0.089 0.121
EU Large 0.819 0.693 -0.126 0.004
US Full 0.527 0.585 0.057 0.034
US Small 0.677 0.740 0.063 0.157
US Large 0.378 0.429 0.052 0.084
Panel D: Analyst Forecast Error (%)
Pre Post Diff P-value
EU Full 0.818 0.790 -0.028 0.320
EU Small 0.869 0.878 0.009 0.848
EU Large 0.767 0.701 -0.065 0.028
US Full 0.383 0.485 0.102 0
US Small 0.477 0.627 0.149 0
US Large 0.288 0.343 0.055 0.001
This table provides the average values of Coverage, Forecast Error and Forecast Dispersion and Average Forecast Error(Analyst Level) in the pre- and post-years (one difference). Pre-years include year 2014, 2015, 2016, 2017 while post-year is 2018. Panel (a) to (c) show the firm level outcomes. “Full" denotes the results for all the firms. “Small" denotesthe results for small firms. “Large" denotes the results for large firms. Small firms are firms whose average fiscalyear-end market capitalization over the pre-regulation years falls below the median. To maintain the proportion of EUand US firms fixed, we calculate the cutoff separately in both regions. Panel (d) shows the analyst level outcomes inthe sample for intensive margin analyses. “Full" denotes the results for all the analysts. “Small" denotes the results forsmall analysts. “Large" denotes the results for large analysts. To define small analysts, we first calculate the averagemarket capitalization of all the firms within an analyst portfolio in a given year. We then average the average marketcapitalization across all the pre-regulation years. Small analysts are defined as analysts whose average of the portfolioaverage market capitalization over the pre-regulation years falls below the median. To maintain the proposition ofanalysts fixed, we calculate the median cutoff separately for EU analysts and US analysts.
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Table 3.6: Firm Level Outcomes
Dependent variable:
Coverage Forecast Error (%)
Full Small vs Large Triple Diff Full Small vs Large Triple Diff
(1) (2) (3) (4) (5) (6)
EU × POST −0.651∗∗∗ −1.594∗∗∗ −0.142∗∗∗ −0.143∗∗∗
(0.196) (0.268) (0.035) (0.048)
EU × POST × SMALL 1.891∗∗∗ 0.002(0.200) (0.074)
SMALL × POST 1.678∗∗∗ −0.228∗∗∗ 0.043 0.029∗
(0.204) (0.018) (0.064) (0.016)
LN SIZE 1.797∗∗∗ 1.542∗∗∗ 1.796∗∗∗ −0.287∗∗∗ −0.288∗∗∗ −0.288∗∗∗
(0.212) (0.228) (0.204) (0.030) (0.097) (0.031)
LN BM 0.781∗∗∗ 0.841∗∗∗ 0.812∗∗∗ 0.279∗∗∗ 0.470∗∗∗ 0.278∗∗∗
(0.072) (0.146) (0.071) (0.073) (0.109) (0.073)
ROA −0.003∗∗∗ −0.004∗ −0.003∗∗∗ −0.003∗∗ −0.004 −0.003∗∗
(0.001) (0.002) (0.001) (0.001) (0.004) (0.001)
RET −0.007∗∗∗ −0.006∗∗∗ −0.007∗∗∗ 0.004∗∗∗ 0.005∗∗∗ 0.004∗∗∗
(0.001) (0.001) (0.001) (0.001) (0.001) (0.001)
RETVOL 0.531∗∗∗ 0.594∗∗ 0.529∗∗∗ 0.751∗∗ 0.111 0.750∗∗
(0.169) (0.300) (0.165) (0.317) (0.458) (0.323)
LN DISTANCE × POST 0.039 0.116 0.034(0.072) (0.082) (0.074)
GDP GROWTH −0.062∗ −0.049∗ −0.061∗∗ −0.003 −0.002 −0.003(0.033) (0.027) (0.030) (0.009) (0.009) (0.009)
UNEMPLOYMENT RATE 0.142 0.124 0.118 0.008 0.016 0.008(0.108) (0.092) (0.097) (0.013) (0.012) (0.013)
Firm FE Yes Yes Yes Yes Yes YesYear FE Yes Yes Yes Yes Yes Yes
Observations 21,960 10,665 21,960 14,020 5,555 14,020R2 0.967 0.971 0.967 0.489 0.497 0.489Adjusted R2 0.958 0.964 0.959 0.361 0.369 0.361
Note: ∗p<0.1; ∗∗p<0.05; ∗∗∗p<0.01
This table shows the results of the panel regressions specified in Model (3.1) and Model (3.3). The dependent variablein column (1) to (3) is Coverage, the number of unique analysts covering a specific firm j in fiscal year t. Thedependent variable in column (4) to (6) is Forecast Error, defined as the absolute distance between the firm’s actualEPS and the mean of the analyst forecasts, scaled by the firm’s previous year-end price. EU is a dummy variable equalto one if the firm is domiciled and listed in Europe. POST is a dummy variable equal to one if the fiscal year t isequal to 2018. SMALL is a dummy variable equal to one if firms’ average fiscal year-end market capitalization overthe pre-regulation years falls below the median. To maintain the proportion of EU and US firms fixed, we calculate thecutoff separately in both regions. Column (1) and column (4) are the results for the difference-in-difference regressionbetween EU firms and US firms. Column (2) and column (5) are the results for the difference-in-difference regressionbetween small firms and larger firms within the EU. Column (3) and Column (6) are the results for the triple-differenceregression. Standard errors are clustered at the country level.
167
Table 3.7: Analyst Level Outcomes (Intensive Margin)
Dependent variable:
Forecast Error (Analyst) (%) Average Forecast Error (%)
Full Triple Diff Full Triple Diff Full Triple Diff
(1) (2) (3) (4) (5) (6)
EU × POST −0.129∗∗∗ −0.122∗∗∗ −0.131∗∗∗ −0.113∗∗∗ −0.149∗∗ −0.132∗∗
(0.032) (0.040) (0.033) (0.037) (0.058) (0.057)
EU × POST × SMALL −0.017 −0.035 −0.067(0.049) (0.062) (0.118)
SMALL × POST 0.031 0.048 0.118(0.025) (0.055) (0.091)
LN FIRMS COVERED × POST −0.014 −0.013 −0.030 −0.028 0.045 0.052(0.020) (0.020) (0.029) (0.030) (0.042) (0.044)
LN COVERAGE × POST −0.023 −0.015 −0.093∗ −0.078 −0.019 0.039(0.019) (0.021) (0.051) (0.069) (0.078) (0.106)
LN TENURE × POST −0.005 −0.004 0.005 0.006 −0.035 −0.032(0.012) (0.012) (0.019) (0.019) (0.034) (0.034)
LN DISTANCE × POST −0.018∗∗ −0.019∗∗ −0.043 −0.043 0.019 0.016(0.008) (0.008) (0.029) (0.029) (0.036) (0.037)
Firm Level Controls Yes Yes Yes Yes Yes YesAnalyst FE Yes Yes Yes Yes Yes YesFirm FE Yes Yes No No No NoB House FE Yes Yes Yes Yes No NoYear FE Yes Yes Yes Yes No NoB House FE × Year FE No No No No Yes Yes
Observations 81,445 81,445 12,990 12,990 4,111 4,111R2 0.422 0.422 0.559 0.559 0.597 0.598Adjusted R2 0.377 0.377 0.431 0.431 0.480 0.480
Note: ∗p<0.1; ∗∗p<0.05; ∗∗∗p<0.01
This table shows the results of the panel regressions specified in Model (3.5) and Model (3.6). We focus on analyst-firm pairs that survive throughout the sample period (2014 to 2018). The dependent variable in column (1) and (2) isForecast Error, defined as the absolute distance between the firm’s actual EPS and the analyst’s forecast, scaled bythe firm’s previous year-end price. The dependent variable in column (3) to (6) is Average Forecast Error, definedas the average of forecast errors across all the firms the analyst covers in a given year. EU is a dummy variable equalto one if the analyst’s portfolio consists of at least 70% of EU stock and zero if the analyst’s portfolio consists of atmost 30% of EU stocks. POST is a dummy variable equal to one if the fiscal year t is equal to 2018. SMALL isa dummy variable equal to one for the analyst whose average of the portfolio average market capitalization over thepre-regulation years falls below the median. We take the average first over all the firms the analyst covers each yearand then over all the pre-regulation years. To maintain the proposition of analysts fixed, we calculate the median cutoffseparately for EU analysts and US analysts. Column (1) and column (2) are the results at the analyst-firm pair level.Column (3) to column (6) are the results at the analyst level. Standard errors are clustered at the firm level in column(1) and column (2), and at the analyst level column (3) to column (6).
168
Table 3.8: Analyst Level Outcomes (Extensive Margin). Probability of Stop or Dropping Out after Unbundling
Dependent variable:
Stop Covering a Firm Drop Out
(1) (2) (3) (4)
RELATIVE ACCURACY −0.008∗∗∗ −0.007∗∗∗ −0.006∗∗∗ −0.006∗∗∗
(0.001) (0.002) (0.001) (0.001)
LN TENURE −0.068∗∗∗ −0.078∗∗∗ −0.081∗∗∗ −0.100∗∗∗
(0.009) (0.014) (0.018) (0.017)
INTERCEPT 1.150∗∗∗ 0.854∗∗∗
(0.169) (0.311)
Controls Yes Yes Yes YesFirm FE Yes No No NoB House FE No No Yes No
Observations 9,595 9,595 1,841 1,841R2 0.216 0.039 0.285 0.088Adjusted R2 0.064 0.038 0.217 0.084
Note: ∗p<0.1; ∗∗p<0.05; ∗∗∗p<0.01
This table shows the results of the regressions specified in Model (3.8) and Model (3.9). The dependent variable incolumn (1) and (2) is Stop, a dummy variable equal to 1 if the analyst stops covering a firm after the regulation. Thedependent variable in column (3) and (4) is DropOut, a dummy variable equal to 1 if the analyst stops covering allthe firms he used to cover prior to the regulation. RELATIV E ACCURACY = 1
T
∑Tt ( 1
J
∑Jj Scoreijt), where
J is the set of firms analyst i covers in year t and T includes all the years prior to 2018. It is a measure capturingthe analyst forecast quality and is comparable across different analysts. The higher the number, the more accurate theanalyst forecast is. Column (1) and (2) shows the results for the analyst-firm level analyses and column (3) and (4)the analyst level analyses. Standard errors are clustered at the firm level in column (1) and (2) , and at the brokeragehouse level in column (3) and (4).
169
Table 3.9: Analyst Level Outcomes (Extensive Margin). Probability of Stop or Dropping Out Before and AfterUnbundling
Dependent variable:
Stop Covering a Firm Drop Out
EU US Pooled EU US Pooled
(1) (2) (3) (4) (5) (6)
RELATIVE ACCURACY × POST −0.001∗∗∗ 0.0001 0.0001 −0.001∗∗ −0.0005 −0.0005(0.0003) (0.0002) (0.0002) (0.0005) (0.001) (0.001)
RELATIVE ACCURACY × POST × EU −0.001∗∗∗ −0.001(0.0004) (0.001)
POST × EU 0.058∗∗∗ 0.021(0.020) (0.046)
EU × RELATIVE ACCURACY 0.006∗∗∗ 0.004∗∗∗
(0.0002) (0.0005)
RELATIVE ACCURACY −0.005∗∗∗ −0.011∗∗∗ −0.011∗∗∗ −0.003∗∗∗ −0.007∗∗∗ −0.007∗∗∗
(0.0002) (0.0001) (0.0001) (0.0003) (0.0004) (0.0003)
EU −0.293∗∗∗ −0.198∗∗∗
(0.016) (0.037)
LN TENURE −0.023∗∗∗ 0.001 −0.011∗∗∗ 0.018∗∗∗ 0.007 0.013∗∗∗
(0.002) (0.002) (0.001) (0.005) (0.005) (0.004)
Controls Yes Yes Yes Yes Yes YesFirm FE Yes Yes Yes No No NoB House FE No No No Yes Yes YesYear FE Yes Yes Yes Yes Yes Yes
Observations 68,373 96,974 165,347 11,498 10,800 22,298R2 0.112 0.230 0.174 0.237 0.333 0.274Adjusted R2 0.083 0.211 0.152 0.221 0.311 0.256
Note: ∗p<0.1; ∗∗p<0.05; ∗∗∗p<0.01
This table shows the results of the regressions specified in Model (3.10) and Model (3.11). The dependent variable incolumn (1) to (3) is Stopijt+1, a dummy variable equal to 1 if the analyst i covering firm j in year t stops coveringthe same firm in year t+ 1. The dependent variable in column (3) to (6) is DropOutit+1, a dummy variable equal to1 if the analyst stops covering all the firms in year t + 1. RELATIV E ACCURACY = 1
J
∑Jj Scoreijt, where J
is the set of firms analyst i covers in year t. It is a measure capturing the analyst forecast quality and is comparableacross different analysts. The higher the number, the more accurate the analyst forecast is. POST is a dummy equalto 1 for the year 2017. Column (1) to (3) show the results for the analyst-firm level analyses. Column (1) presents theresults for EU analysts; column (2) for US analysts and column (3) for a triple-difference analysis. Column (4) to (6)show similar results for the analyst level analyses. Column (4) presents the results for EU analysts; column (5) for theUS analysts and column (6) for a triple-difference analysis. Standard errors are clustered at the firm level in column(1) to (3) , and at the brokerage house level in column (4) to (6).
170
Table 3.10: Placebo Test
Panel A: Firm Level
Dependent variable:
Coverage Forecast Error (%) Dispersion (%)
2015 2016 2017 2015 2016 2017 2015 2016 2017
(1) (2) (3) (4) (5) (6) (7) (8) (9)
EU × POST −0.071 −0.177 −0.160 −0.006 0.013 0.043 −0.050 −0.046 −0.003(0.113) (0.138) (0.152) (0.044) (0.027) (0.049) (0.031) (0.045) (0.071)
Controls Yes Yes Yes Yes Yes Yes Yes Yes YesFirm FE Yes Yes Yes Yes Yes Yes Yes Yes YesYear FE Yes Yes Yes Yes Yes Yes Yes Yes Yes
Observations 17,568 17,568 17,568 11,216 11,216 11,216 11,216 11,216 11,216R2 0.974 0.974 0.974 0.534 0.533 0.533 0.597 0.597 0.597Adjusted R2 0.965 0.965 0.965 0.377 0.377 0.377 0.463 0.462 0.462
Note: ∗p<0.1; ∗∗p<0.05; ∗∗∗p<0.01
Panel B: Analyst Level
Dependent variable:
Average Forecast Error (%)
2015 2016 2017
(1) (2) (3)
EU × POST −0.029 −0.056∗ 0.021(0.032) (0.034) (0.035)
Firm Level Controls Yes Yes YesAnalyst Level Controls × Post Yes Yes YesAnalyst FE Yes Yes YesB House FE Yes Yes YesYear FE Yes Yes Yes
Observations 10,392 10,392 10,392R2 0.601 0.601 0.601Adjusted R2 0.446 0.446 0.446
Note: ∗p<0.1; ∗∗p<0.05; ∗∗∗p<0.01
Panel A of this table shows the results of the panel regressions similar to Model (3.1) but only covers the pre-regulationyears. The dependent variable in column (1) to (3) is Coverage, the number of unique analysts covering a specificfirm j in fiscal year t. The dependent variable in column (4) to (6) is Forecast Error, defined as the absolute distancebetween the firm’s actual EPS and the mean of the analyst forecasts, scaled by the firm’s previous year-end price. Thedependent variable in column (4) to (6) is Forecast Dispersion, defined as the standard deviation of all the forecastsacross all the analysts following the same firm in the same year, scaled by the firm’s previous year-end price. EU isa dummy variable equal to one if the firm is domiciled and listed in Europe. From column (1) to column (3), POSTis a dummy variable defined as if the regulation occurred in 2015, 2016, 2017, respectively. Similar definition appliesto column (4) to (6) and column (7) to (9) . Column (1) to (3) are the results for Coverage. Column (4) to (6) arethe results for Forecast Error. Column (7) to (9) are the results for Forecast Dispersion. Standard errors areclustered at the country level. Panel B of this table shows the results of the panel regressions similar to Model (3.6).The dependent variable in column (3) to (6) is Average Forecast Error, defined as the average of forecast errorsover all the firms the analyst covers in a given year. EU is a dummy variable equal to one if the analyst’s portfolioconsists of at least 70% of EU stock and zero if the analyst’s portfolio consists of at most 30% of EU stocks. Fromcolumn (1) to column (3), POST is a dummy variable defined as if the regulation occurred in 2015, 2016, 2017,respectively. Standard errors are clustered at the analyst level.
171
Table 3.11: Firms’ Brokerage House Coverage
Dependent variable:
Brokerage Houses per Firm
Full Small vs Large Triple Diff
(1) (2) (3)
EU × POST −0.403∗∗∗ −1.081∗∗∗
(0.151) (0.207)
EU × POST × SMALL 1.359∗∗∗
(0.154)
SMALL × POST 1.275∗∗∗ −0.099∗∗∗
(0.157) (0.019)
Firm FE Yes Yes YesYear FE Yes Yes Yes
Observations 21,960 10,665 21,960R2 0.972 0.978 0.972Adjusted R2 0.965 0.972 0.965
Note: ∗p<0.1; ∗∗p<0.05; ∗∗∗p<0.01
This table shows the results of the panel regressions similar Model (3.1) on the sample for coverage quality. Thedependent variable is Brokerage Houses per F irm, the number of unique brokerage houses covering a specificfirm in fiscal year t. EU is a dummy variable equal to one if the firm is domiciled and listed in Europe. POST isa dummy variable equal to one if the fiscal year t is equal to 2018. SMALL is a dummy variable equal to one iffirms’ average fiscal year-end market capitalization over the pre-regulation years falls below the median. To maintainthe proportion of EU and Column (1) is the result of the difference-in-difference regression between EU firms and USfirms. Column (2)is the result of the difference-in-difference regression between small firms and larger firms withinthe EU. Column (3) is the result of the triple-difference regression. Standard errors are clustered at the country level.
172
Table 3.12: Other Measures of Quality
Panel A: Firm Level Dispersion
Dependent variable:
Dispersion (%)
Full Small vs Large Triple Diff
(1) (2) (3)
EU × POST −0.166∗∗∗ −0.195∗∗∗
(0.024) (0.042)
EU × POST × SMALL 0.058(0.063)
SMALL × POST 0.048 −0.015∗∗
(0.066) (0.007)
Controls Yes Yes YesFirm FE Yes Yes YesYear FE Yes Yes Yes
Observations 14,020 5,555 14,020R2 0.561 0.550 0.561Adjusted R2 0.451 0.436 0.451
Note: ∗p<0.1; ∗∗p<0.05; ∗∗∗p<0.01
Panel B: Number of Firms per Analyst
Dependent variable:
Firms Covered
(1) (2)
EU × POST −0.791∗∗∗ −0.705∗∗∗
(0.130) (0.110)
Firm Level Controls Yes YesAnalyst Level Controls × Post Yes YesAnalyst FE Yes YesBrokerage House FE Yes YesYear FE Yes Yes
Observations 14,435 26,555R2 0.875 0.865Adjusted R2 0.839 0.805
Note: ∗p<0.1; ∗∗p<0.05; ∗∗∗p<0.01
Panel A of this table shows the results of the panel regressions specified in Model (3.1) and Model (3.3). The dependentvariable is Forecast Dispersion, defined as the standard deviation of all the forecasts across all the analysts followingthe same firm in the same year, scaled by the firm’s previous year-end price. EU is a dummy variable equal to oneif the firm is domiciled and listed in Europe. POST is a dummy variable equal to one if the fiscal year t is equalto 2018. SMALL is a dummy variable equal to one if firms’ average fiscal year-end market capitalization over thepre-regulation years falls below the median. To maintain the proportion of EU and US firms fixed, we calculate thecutoff separately in both regions. Column (1) is the result for the difference-in-difference regression between EU firmsand US firms. Column (2) is the result for the difference-in-difference regression between small firms and larger firmswithin the EU. Column (3) is the result for the triple-difference regression. Standard errors are clustered at the countrylevel. Panel B of this table shows the results of the panel regressions specified in Model (3.6). The dependent variableis Firms Covered, the number of firms one analyst covers in fiscal year t. EU is a dummy variable equal to one ifthe analyst’s portfolio consists of at least 70% of EU stock and zero if the analyst’s portfolio consists of at most 30%of EU stocks. POST is a dummy variable equal to one if the fiscal year t is equal to 2018. Column (1) is results foranalysts who cover at least one firm throughout the sample period. Column (2) is the result of all the analysts in oursample. Standard errors are clustered at the analyst level.
173
Table 3.13: Abnormal Return and Analyst Informativeness
Dependent variable:
Absolute Abnormal Return Average Analyst Informativeness Aggregate Analyst Informativeness
(1) (2) (3)
I(EU *post) 0.001∗∗∗ 0.0003∗∗∗ −0.009∗∗∗
(0.0002) (0.0001) (0.001)
Controls Yes Yes YesFirm FE No Yes YesAnalyst × Firm FE Yes No NoYear FE Yes Yes Yes
Observations 550,693 19,391 19,391R2 0.319 0.496 0.917Adjusted R2 0.231 0.353 0.894
Note: ∗p<0.1; ∗∗p<0.05; ∗∗∗p<0.01
This table shows the results of the panel regressions similar to Model (3.1). The dependent variable in column (1)is ABRet ( Absolute Abnormal Return), the absolute market-adjusted abnormal return on the forecast revision datefor each analyst-firm pair. The dependent variable in column (2) is AV GAI (Average Analyst Informativeness). Itcaptures the average informativeness of one forecast revision date. The dependent variable in column (3) is AGAI(Aggregate Analyst Informativeness). It captures the aggregate informativeness of all revision dates. EU is a dummyvariable equal to one if the firm is domiciled and listed in Europe. POST is a dummy variable equal to one if thefiscal year t is equal to 2018. Standard errors are clustered at the firm level.
174
Table 3.14: Learning Effect (Lagged Forecast Error as Control)
Dependent variable:
Forecast Error (Analyst) (%) Average Forecast Error (%)
(1) (2) (3)
EU × POST −0.134∗∗∗ −0.122∗∗∗ −0.158∗∗∗
(0.033) (0.035) (0.059)
LAGGED ERROR (PAIR) −0.071∗∗∗
(0.013)
LAGGED ERROR −0.142∗∗∗ −0.085(0.039) (0.097)
Firm Level Controls Yes Yes YesAnalyst Level Controls × Post Yes Yes YesFirm FE Yes No NoAnalyst FE Yes Yes YesB House FE Yes Yes NoYear FE Yes Yes NoB House FE × Year FE No No Yes
Observations 65,156 10,392 3,276R2 0.447 0.600 0.623Adjusted R2 0.393 0.446 0.479
Note: ∗p<0.1; ∗∗p<0.05; ∗∗∗p<0.01
This table shows the results of the panel regressions specified in Model (3.5) and Model (3.6). The dependent vari-able in column (1) is Forecast Error, defined as the absolute distance between the firm’s actual EPS and theanalyst’s forecast, scaled by the firm’s previous year-end price. The dependent variable in column (2) to (3) isAverage Forecast Error, defined as the average of forecast errors across all the firms the analyst covers in agiven year. EU is a dummy variable equal to one if the analyst’s portfolio consists of at least 70% of EU stockand zero if the analyst’s portfolio consists of at most 30% of EU stocks. POST is a dummy variable equal to oneif the fiscal year t is equal to 2018. We include lagged forecast error as a control for the analyst learning ability.LAGGED ERROR (PAIR) is the lagged forecast error at the analyst-firm pair level. LAGGED ERROR is theaverage lagged forecast error at the analyst level. We take the average over all the firms the analyst covers. Column (1)presents the results on the analyst-firm pair level. Column (2) presents the results on the analyst level with brokeragehouse plus year fixed effects. Column (3) presents the results on the analyst level with brokerage house times yearfixed effects. Standard errors are clustered at the firm level in column (1) and at the analyst level in column (2) and(3).
175
Table 3.15: Brokerage House Employment
Dependent variable:
Number of Analysts
Small vs Large Triple Diff
(1) (2)
SMALL × POST 3.490∗∗ 3.943∗∗∗
(1.467) (0.863)
EU × POST × SMALL −0.543(1.587)
EU × POST −0.135(1.529)
Controls Yes YesB House FE Yes YesYear FE Yes Yes
Observations 545 1,185R2 0.953 0.953Adjusted R2 0.940 0.941
Note: ∗p<0.1; ∗∗p<0.05; ∗∗∗p<0.01
This table shows the results of the panel regressions specified in Model (3.15). The dependent variable isNumber of Analysts Hired, defined as the number of unique analysts each brokerage house hires in each year.EU is a dummy variable equal to one if the brokerage house only hires EU analysts in the years prior to the regulation.POST is a dummy variable equal to one if the fiscal year t is equal to 2018. SMALL is a dummy variable equalto one if the average of the number of analysts a brokerage house hires over the pre-regulation years falls below themedian. To maintain the proportion of EU and US brokerage houses fixed, we calculate the cutoff separately in bothregions. Column (1) is the results for a difference-in-difference regression within the EU between small brokeragehouses and large brokerage houses. Column (2) is the result of the triple-difference regression. Standard errors areclustered at the brokerage house level.
176
Table 3.16: Capital Market Effects
Dependent variable:
EAinfo Bid Ask Spread
(1) (2) (3) (4)
EU × POST 0.002 0.0001(0.001) (0.001)
EU × Y15 −0.005∗∗∗ 0.0005(0.001) (0.001)
EU × Y16 −0.004∗∗ 0.0002(0.002) (0.0003)
EU × Y17 −0.004∗∗ −0.001∗∗
(0.002) (0.0005)
EU × Y18 −0.001 −0.00005(0.001) (0.001)
Controls Yes Yes Yes YesFirm FE Yes Yes Yes YesYear FE Yes Yes Yes Yes
Observations 20,322 20,322 20,322 20,322R2 0.453 0.454 0.925 0.925Adjusted R2 0.304 0.305 0.904 0.904
Note: ∗p<0.1; ∗∗p<0.05; ∗∗∗p<0.01
This table shows the results of the panel regressions specified in Model (3.1). The dependent variable in column (1)and column (2) is EAinfojt. EAinfojt is defined as EAinfojt =
∑1d=−1 |Retj,d − Retm,d|, where d denotes
days around a firm’s earnings announcement date t, j denotes the firm, Retj,d denotes the daily return of firm j andRetm,d denotes the daily return of the stock market. To mitigate data errors in Datastream, we winsorize Retj,d at the1% level. The dependent variable in column (3) and column (4) is Bid Ask Spreadjt. The daily bid-ask spread iscomputed as the difference between the two prices divided by the midpoint. We winsorize the spread at the 1% level.We then take the mean of the daily spread over the year for a given firm and obtain Bid Ask Spreadjt. EU is adummy variable equal to one if the firm is domiciled and listed in Europe. POST is a dummy variable equal to one ifthe calendar year t is equal to 2018. Y 15, Y 16, Y 17, Y 18 are year dummy variables that are ones if the calendar yeart is equal to 2015, 2016, 2017, 2018. Column (1) to column (2) are results for EAinfojt. Column (3) to column (4)are results for Bid Ask Spreadjt. Standard errors are clustered at the country level.
177
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Appendix A: Chapter 1
A.1 Data Appendix
A.1.1 Variable definitions
For corporate bond pricing data, I use WRDS bond returns which is based on TRACE and
FISD. For CDS-spreads data, I use Markit single name CDS-spread composites. All data is down-
loaded directly from the WRDS data service. The data set is bond returns centered. Details on the
merging algorithm can be found in A.1.4.
A.1.2 Measuring SG&A
I follow Peters and Taylor (2017) in measuring SG&A. Specifically, SG&A is the Compustat
variable XSGA minus XRD minus RDIP. There are two exceptions to this rule: (1) When XRD
exceeds XSGA but is less than cogs, SG&A is measured as XSGA with no further adjustments or
(2) When XSGA is missing, SG&A is set to zero. I also set XRD and RDIP to zero when missing.
As explained by Peters and Taylor (2017), the logic behind this formula is as follows:
According to the Compustat manual, XSGA includes R&D expense unless the
company allocates R&D expense to cost of goods sold (COGS). For example, XSGA
often equals the sum of Selling, General and Administrative and Research and De-
velopment on the Statement of Operations from firms’ 10-K filings. To isolate (non-
R&D) SG&A, we must subtract R&D from XSGA when Compustat adds R&D to
XSGA. There is a catch: When a firm externally purchases R&D on products not yet
being sold, this R&D is expensed as In-Process R&D and does not appear on the bal-
ance sheet. Compustat adds to XSGA only the part of R&D not representing acquired
In-Process R&D, so our formula subtracts RDIP (In-Process R&D Expense), which
188
Compustat codes as negative. We find that Compustat almost always adds R&D to
XSGA, which motivates our formula above. Standard & Poor’s explained in private
communication that, “in most cases, when there is a separately reported XRD, this is
included in XSGA.” As a further check, we compare the Compustat records and 10-K
filings for a random sample of one hundred firm-year observations with non-missing
XRD. We find that Compustat includes R&D in XSGA in 90 out of one hundred cases,
partially includes it in XSGA in one case, and includes it in COGS in seven cases. Two
cases remain unclear even after asking the Compustat support team. The screen above
lets us identify obvious cases in which xrd is part of COGS. This screen catches six of
the seven cases in which XRD is part of COGS. Unfortunately, identifying the remain-
ing cases is impossible without reading SEC filings. We thank the Compustat support
team from Standard & Poors for their help in this exercise. (Appendix B.2)
A.1.3 FISD Cleaning
FISD provides 4 databases of interest: “fisd_issue" that gives information at bond issue level,“fisd_mergedissuer"
that gives information about the bond issuer , “fisd_ratings_hist" to access the historical rating at
each moment in time, and finally “fisd_amt_out_hist" to be able to access each bonds amount
outstanding.
To calculate amount outstanding by firm, we consider the following bond types: US Corporate
Convertible (CCOV), US Corporate Inflation Indexed (CCPI), US Corporate Debentures (CDEB),
US Corporate LOC Backed (CLOC), US Corporate MTN (CMTN), US Corporate MTN Zero
(CMTZ), US Corporate Paper (CP), US Corporate Pass Thru Trust (CPAS), US Corporate PIK
Bond (CPIK), US Corporate Strip (CS), US Corporate UIT (CUIT), US Corporate Zero (CZ), US
Corporate Bank Note (USBN), US Corporate Insured Debenture (UCID).
To calculate firms bond net issuance we use variation in amount outstanding from Mergent
FIDS.
189
A.1.4 Merge FISD to Compustat
We use Merget FISD data set to retrieve bond characteristics. The bond identifier in FISD is
ISSUE ID, that maps one to one to CUSIP 9-digits. We use Compustat data set to retrieve firm-
level characteristics. Firm identifier in Compustat is GVKEY. The goal is to merge firm with the
bonds they issued.
CUSIP 6-digit is a firm identifier. The main challenge is though is that firms can issue bonds
through their subsidiaries and the CUSIP 6-digit does not reflect the parent company identity.
Our first task is to go from CUSIP 9-digit to a parent 6-digit CUSIP. I do this in two steps.
First, I merge FISD-issue data with FISD-issuer to the PARENT ID. I then get PARENT CUSIP,
the CUSIP 6-digit to the PARENT ID from FISD-issue. Second, I use SDC to get the UPARENT
CUSIP, the Ultimate Parent CUSIP 6-digit.
The figure below shows for all corporate bonds in FISD the successful merges with Compustat
(Panel a) and the successful merge with Compustat and Markit CDS data (Panel b).
Figure A.1: Successful Mergers
0
2000
4000
6000
2003 2005 2007 2009 2011 2013 2015 2017 2019 2021
Am
ount
Out
stan
ding
(Fa
ce V
alue
Bi $
)
Merged Not Merged
(a) FISD + Compustat
0
2000
4000
6000
2003 2005 2007 2009 2011 2013 2015 2017 2019 2021
Am
ount
Out
stan
ding
(Fa
ce V
alue
Bi $
)
Merged Not Merged
(b) FISD + Compustat + CDS
This figure shows the amount outstanding of all corporate bonds in FISD dataset. In green it is the amount outstandingwith successful merge with Compustat (Panel a) or Compustat and CDS data from Markit (Panel b). In red is theamount outstanding not merged.
190
A.2 Measures of Aggregate Safety Premium
AAA credit spread: It is the face-value weighted credit spread of AAA rated firms. I consider all
bonds in the sample. This measure was first introduced by Krishnamurthy and Vissing-Jørgensen
(2012a).
BBB − (AAA and AA) basis spread: It is the face-value weighted CDS-bond basis spread be-
tween “BBB” and “AAA and AA.” The difference in credit risk is controlled by the CDS correction
in the basis calculation. This measure is inspired by Krishnamurthy and Vissing-Jørgensen (2012a)
safety premium, who suggest to use the credit spread between BBB and AAA, but control for dif-
ferences in credit risk. The reason I use “AAA and AA" instead only “AAA" is because, in recent
years, there are only two US corporations that are rated AAA, Johnson & Johnson and Microsoft.
In order to minimize the influence of company-specific shocks I use the set of AAA and AA bonds.
Note that a large component of the BBB−AAA spread is due to credit risk, this is the reason I use
the basis spread instead of credit spread.
Box trade: Difference between a benchmark rates from the put-call parity relationship for European-
style options and UST yields. I used the 18-months maturity. Data is downloaded from Binsbergen’
personal website (here).
Structurally estimated: Based on the the model presented in Section 1.3, we can write the basis
as
basisi,t = (αi,t+1 − 1)ϕt (A.17)
=
[αµi,t exp
(−ψ bi,t+1
Et (Πt+1)
)− 1
]ϕt. (A.18)
Substituting all αi,t, we can re-write this relation as
basisi,t+1 =
[exp
(−ψ
∑k≥0
µkIt−k
)− 1
]ϕt where It =
bt+1
EtΠt+1
(A.19)
From this relationship we would like to estimate ψ, µ and ϕϕϕ = [ϕ1, ..., ϕT ]. I use a non-linear
191
least square estimation.
Consider the following estimation equation
basisi,t = (αi,t+1 − 1)ϕt + εi,t (A.20)
Let
{ψ, µ, ϕϕϕ} = argminψ,µ,ϕϕϕ∑t
∑i
ε2i,t (A.21)
be the unbiased estimator of interest.
Notice that given ψ and µ, each ϕt necessary is
ϕt = (xxxTt xxxt)−1xxxTt bbbt, (A.22)
where bbbt = [basis1,t, ..., basisN,t], xxxt = [x1,t, ..., xN,t] and
xi,t(ψ, µ) := (αi,t+1 − 1) (A.23)
Hence, we can replace (A.23) in (A.24) and get that
{ψ, µ} = argminψ,µ∑t
[bbbTt bbbt −
xxxTt bbbtxxxTt xxxt
]. (A.24)
Once we have {ψ, µ}, we can simply replace it in (A.22) to have an estimation of the UST
safety premium, ϕt.
A.3 Model
A.3.1 Price of the Bond
The main advantage of considering a model with liquidity default is that we can calculate the
price of the debt for each (Kt+1, Bt+1) in closed form. The price of the debt is given by
192
Pt+1 = a1 (1 + rc0p1) + a2rc1p2 + ϕ (Kt+1, Bt+1;xt, zt) (A.25)
where rc0 = (1− ξ)(1− δ)Kt+1 − fKt+1 −Bt+1
Bt+1
(A.26)
rc1 = (1− ξ)Kζt+1
Bt+1
(A.27)
mt =β
exp(xt)γ(A.28)
µ = µx + µz + σ2xγ (A.29)
σ =√σ2x + σ2
z (A.30)
a1 = mt exp
(µxγ +
1
2σ2xγ
2
)(A.31)
a2 = a1 exp
(µ+
1
2σ2
)(A.32)
p1 = Φ
(ln d− µ
σ
)(A.33)
p2 = Φ
(ln d− µ− σ2
σ
)(A.34)
Φ(·) is the normal distribution cdf. (A.35)
To see that, start with the bond price equation:
P (Kt+1, Bt+1;xt, zt) = E[Mt+1
((1− I{Vt+1<0}
)+ I{Vt+1<0}
Lt+1
Bt+1
)]+ s(Kt+1, Bt+1;xt, zt)
(A.36)
Or we can rewrite it as
P (Kt+1, Bt+1;xt, zt) =
[E[Mt+1]− E
[Mt+1I{Vt+1<0}
Bt+1 − Lt+1
Bt+1
]]+ s(Kt+1, Bt+1;xt, zt)
(A.37)
where s(Kt+1, Bt+1;xt, zt) is the safety premium for the bond.
193
But,
Bt+1 − Lt+1
Bt+1
=Bt+1 + (1− ξ) (f − (1− δ))Kt+1
Bt+1
− (1− ξ)Xt+1Zt+1Kζ
Bt+1
(A.38)
= rct − rct+1Xt+1Zt+1 (A.39)
We can find a close form solution to Pt, by solving the expectation in equation (A.37).
Lemma A.1 Let X = exp(x) and Z = exp(z), such that x ∼ N(µx, σx) and z ∼ N(µz, σz).
Then,
E[XαZβI{XZ<d}
]= exp(µxα + µyβ +
1
2
(σ2xα
2 + σ2zβ
2))Φ
(ln d− µx − µy − ασ2
x − βσ2z√
σ2x + σ2
z
)(A.40)
Hence, the price of the bond is:
Pt+1 = mtE[Xγt+1 + rctX
γt+1I{XZ<d} + rct+1X
γ+1ZI{XZ<d}]
+ s (Kt+1, Bt+1;xt, zt)(A.41)
= [at+1 (1 + rctpt+1) + a2rct+1p2] + s (Kt+1, Bt+1;xt, zt) (A.42)
(A.43)
where at+1 = exp
(µxγ +
1
2σ2xγ
2
), (A.44)
pt+1 = Φ
(ln d− µx − µz − γσ2
z√σ2x + σ2
s
)(A.45)
a2 = mt exp
(µx(γ + 1) + µz +
1
2(σ2
x(γ + 1)2 + σ2z
)(A.46)
p2 = Φ
(ln d− µx − µz − (γ + 1)σ2
z − σ2z√
σ2x + σ2
s
)(A.47)
194
A.3.2 Optimization
Figure A.2: Firm’s Total Value as Function of Capital and Debt Issuance
(a) Unconstrained optimal policy(b) Constrained optimal policy
This figure shows how, the total value of the firm varies with the amount capital invested and bond issued. The bluedot is the optimal policy {k∗t+1, b
∗t+1} that maximizes the value of the firm. In Panel (a) the firm’s investment is
unconstrained and Panel (b) firm’s investment is constrained. The parameter choices are: ϕt = 1%.
A.4 Infinite Horizon Dynamic Model
In this section, I present a numerical implementation of the infinite horizon version of the
model introduced in Section 1.3. The results are qualitatively equivalent to those obtained in the
two period model.
A.4.1 Simulation Strategy
For easiness of notation, in this section I omit the i subscript. Let
∫t = (kt, bt, αt, xt, zt, ϕt) (A.48)
be the vector state space representation of the firm at time t, where kt and bt are respectively the
level of capital and the debt issuance of the firm, i.e. the action, taken by the firm at time t− 1, αt
is the firm’s perceived safety, while xt, zt and ϕt are respectively the aggregate and idiosyncratic
195
productivity shocks and the aggregate safety premium. Note that the description of the state space
given here is slightly different than the one given in Section 1.3, as I replaced the net worth wt
with the action variables kt and bt. Recall that the net worth of the company is determined by the
formula
wt := exp(xt + zt)kζt + lv(1− δ)kt − bt, (A.49)
hence, given the action and the realization of productivity shocks, the net worth is determined. The
advantage of the parametrization proposed here is that it allows for a joint discretization of the
state space and the action space where each possible level of net worth generated by the choice of
an action and a realization of productivity shocks is faithfully represented.
As observed in Section 1.3, the value of the firm is given by the solution of the Bellman equa-
tion
V (∫t) = maxkt+1,bt+1
d(kt+1, bt+1; ∫t) + Et [Mt,t+1Vt+1(∫t+1)] . (A.50)
To find the optimal policy, first I discretize the state space, and then I apply the standard value
function iteration method (see for e.g. Stokey (1989)).
A.4.2 State Space Discretization
I discretize the state space by defining discrete spaces Sk, Sb, Sα, Sx, Sz and Sϕ for each
component of the state space vector and taking the Cartesian product of these sets. For Sk, Sb
and Sα I take a uniformly spaced grid of 41 points ranging from 1 and 1200 for Sk, 0 and 90 for
Sb, and 0 and 1 for Sα. For Sx, Sz and Sϕ, I follow a technique for approximating AR(1) models
with Markov chains originally introduced by Rouwenhorst (1995), generating three points for each
space. As noted in Kopecky and Suen (2010), when simulating highly persistent processes, this
approximation scheme is more reliable than alternative approaches commonly used in the literature
such as Tauchen (1986) or Tauchen and Hussey (1991).
196
Figure A.3: Issuance Response to Perceived Safety
This figure shows the optimal debt issuance as a share of kt as function of perceived safety, αt.
A.4.3 Main Results
This paper is mainly interested in the sensitivity of optimal bond issuance as a function of
perceived safety. In Figure A.3 I plot the numerical simulation of this function for the set of
approximation scheme described above. As one can see, the full dynamic model preserves the
qualitative behavior observed in the two period model.
197
A.5 Additional Empirical Results
Table A.1: Impact of Cross-basis on Firm’s Decisions Conditional on Positive Debt Issuance Including Ratings FE
Dependent variable:
Net PayoutCapital
InvestmentR & D SG & A
Intangible
InvestmentAcquisitions
Financial
Investment∆ Cash
(1) (2) (3) (4) (5) (6) (7) (8)
Cross-basis × DebtIssuance 0.041∗∗ 0.017 −0.002 0.003 0.001 −0.082 0.014 −0.051
(0.016) (0.016) (0.004) (0.004) (0.006) (0.056) (0.021) (0.052)
Cross-basis 0.003 0.017 0.0004 0.001 0.001 0.030 0.005 −0.019
(0.011) (0.011) (0.003) (0.002) (0.003) (0.023) (0.008) (0.023)
DebtIssuance 0.278∗∗∗ 0.183∗∗∗ 0.001 0.007 0.008 0.887∗∗∗ 0.115∗∗∗ 0.879∗∗∗
(0.028) (0.012) (0.007) (0.005) (0.008) (0.082) (0.024) (0.091)
CDS-spread −0.005 −0.050∗∗∗ −0.0002 0.006∗∗∗ 0.005∗∗ −0.024∗ −0.005 0.009
(0.012) (0.013) (0.002) (0.002) (0.002) (0.013) (0.006) (0.017)
log(Total Assets) −0.183∗∗∗ −0.099∗∗∗ −0.102∗∗∗ −0.330∗∗∗ −0.432∗∗∗ −0.272∗∗∗ −0.015 −0.604∗∗∗
(0.042) (0.026) (0.010) (0.007) (0.013) (0.075) (0.033) (0.096)
CHE (% assets) 0.023∗∗∗ −0.0001 −0.0005 −0.005∗∗∗ −0.005∗∗∗ 0.083∗∗∗ −0.004 −0.181∗∗∗
(0.003) (0.001) (0.001) (0.0005) (0.001) (0.010) (0.003) (0.009)
Tobin’s Q 0.023∗∗∗ 0.010∗∗∗ 0.001 0.003∗∗∗ 0.004∗∗∗ −0.001 −0.003∗ 0.017∗∗
(0.005) (0.002) (0.001) (0.001) (0.001) (0.004) (0.002) (0.007)
Leverage Ratio (%) −0.021∗∗∗ −0.010∗∗∗ −0.001∗∗∗ −0.005∗∗∗ −0.006∗∗∗ 0.002 0.001 −0.019∗∗∗
(0.002) (0.001) (0.0003) (0.0005) (0.001) (0.004) (0.002) (0.004)
ROA (%) 0.087∗∗∗ 0.044∗∗∗ 0.008∗∗∗ 0.008∗∗∗ 0.015∗∗∗ 0.026∗∗∗ 0.019∗∗∗ 0.013
(0.014) (0.013) (0.002) (0.002) (0.004) (0.008) (0.007) (0.020)
Firms FE Yes Yes Yes Yes Yes Yes Yes Yes
Time FE Yes Yes Yes Yes Yes Yes Yes Yes
Ratings FE Yes Yes Yes Yes Yes Yes Yes Yes
Observations 19,227 19,227 19,227 19,227 19,227 19,227 19,227 19,227
R2 0.418 0.688 0.766 0.940 0.902 0.116 0.059 0.139
Adjusted R2 0.396 0.676 0.757 0.938 0.898 0.083 0.024 0.106
Note: ∗p<0.1; ∗∗p<0.05; ∗∗∗p<0.01
This table shows regression results from estimating R3. The y-variable are (2) net payout, which is dividends plus netequity repurchase, (2) capital investment, which is CAPEX plus net PPE bought, (3) R&D expenses, (4) 30% of SG&Aexpenses, (5) intangible investment, which is R&D plus 30% of SG&A expenses, (6) acquisitions. All independentvariables are measured in time t + 1 and normalized by lag total assets. For the x-variables, cross-basis is the firm-level CDS-bond basis minus the basis index, basis index is the face-value weighted average of CDS-bond basis in thecorporate bond market and DebtIssuance is an indicator variable equal to 1 if net debt issuance is strictly positive and0 otherwise. The controls are CDS spread at the firms level, log of total assets, Tobin’s Q, CHE as percentage of totalassets, book leverage ratio and return on assets (ROA). All columns include time, firm and rating buckets fixed effects.All independent variables are measured in quarter t. Standard errors are reported in parenthesis and are clustered bytime. Data is quarterly from 2003Q1 to 2019Q3.
198
Table A.2: Impact of Cross-basis on Firm’s Decisions Conditional on Positive Debt Issuance Including Ratings FE
Dependent variable:
Net PayoutCapital
InvestmentR & D SG & A
Intangible
InvestmentAcquisitions
Financial
Investment∆ Cash
(1) (2) (3) (4) (5) (6) (7) (8)
Cross-basis 0.055∗∗∗ 0.040∗∗∗ 0.002 0.005∗∗ 0.007∗ 0.019 0.013 −0.025
(0.018) (0.013) (0.003) (0.002) (0.004) (0.016) (0.010) (0.022)
CDS-spread −0.087∗∗∗ −0.086∗∗∗ −0.005∗∗ −0.002 −0.007∗∗ −0.038∗∗ −0.010∗∗ −0.012
(0.019) (0.019) (0.002) (0.002) (0.003) (0.015) (0.005) (0.019)
log(Total Assets) −0.231∗∗∗ −0.125∗∗∗ −0.109∗∗∗ −0.341∗∗∗ −0.450∗∗∗ −0.281∗∗∗ −0.024 −0.658∗∗∗
(0.041) (0.024) (0.010) (0.008) (0.012) (0.080) (0.033) (0.097)
CHE (% assets) 0.023∗∗∗ −0.0004 −0.0004 −0.005∗∗∗ −0.005∗∗∗ 0.078∗∗∗ −0.005 −0.186∗∗∗
(0.003) (0.001) (0.001) (0.0005) (0.001) (0.009) (0.003) (0.009)
Tobin’s Q 0.018∗∗∗ 0.008∗∗∗ 0.001 0.002∗∗∗ 0.002∗∗ 0.004 −0.002 0.012
(0.005) (0.002) (0.001) (0.001) (0.001) (0.004) (0.002) (0.007)
Firms FE Yes Yes Yes Yes Yes Yes Yes Yes
Time FE Yes Yes Yes Yes Yes Yes Yes Yes
Observations 19,227 19,227 19,227 19,227 19,227 19,227 19,227 19,227
R2 0.391 0.675 0.765 0.939 0.901 0.087 0.056 0.120
Adjusted R2 0.369 0.663 0.757 0.937 0.897 0.053 0.021 0.088
Note: ∗p<0.1; ∗∗p<0.05; ∗∗∗p<0.01
This table shows regression results from estimating R3. The y-variable are (2) net payout, which is dividends plus netequity repurchase, (2) capital investment, which is CAPEX plus net PPE bought, (3) R&D expenses, (4) 30% of SG&Aexpenses, (5) intangible investment, which is R&D plus 30% of SG&A expenses, (6) acquisitions. All independentvariables are measured in time t + 1 and normalized by lag total assets. For the x-variables, cross-basis is the firm-level CDS-bond basis minus the basis index, basis index is the face-value weighted average of CDS-bond basis in thecorporate bond market and DebtIssuance is an indicator variable equal to 1 if net debt issuance is strictly positive and0 otherwise. The controls are CDS spread at the firms level, log of total assets, Tobin’s Q, CHE as percentage of totalassets, book leverage ratio and return on assets (ROA). All columns include time, firm and rating buckets fixed effects.All independent variables are measured in quarter t. Standard errors are reported in parenthesis and are clustered bytime. Data is quarterly from 2003Q1 to 2019Q3.
A.5.1 Cash Flow Identity
It is useful to do a complete study of how firms use the proceeds from debt issuance in response
to the cross-basis. We can use the cash-flow statement to do a “follow the money" approach
and how does the firm use the funds from issuance. This identity also justifies my measures of
real investment (capital, intangible and acquisitions) and financial investment. I also estimated
199
Equation (R3) for all variables in (A.51), I did not find any patterns that alters the results and
interpretation in the body of the paper.
To follow the money, for every firm and quarter, consider the augmented budget equation
F − (i+ l′ − (1 + rl)l) = (d− e)− (Pb′ − b),
the prime notation denotes one period ahead values, F as before is the net cash flow from opera-
tions, i is total investment, l − (1 + rl)l is change in cash (or liquid assets), d is total payouts to
shareholders, e is equity issuance, therefore d − e is net payout to equity holders and Pb′ − b net
debt issuance.
I map the budget equation to the cash-flow identity in Compustat data by calculating the fol-
lowing:
Total Net Debt Issuance = Net Payouts + Real Investment +
Financial Investment + ∆Cash − Net Operating Profits + Others(A.51)
I consider further breakdowns for total net debt issuance and real investments. In Compustat
one can disentangle total debt issuance in current debt (less than one year maturity), and long-term
debt(less than one year maturity). This differentiation is interesting because the basis calculations
only captures bond liabilities for time to maturity longer than one year. Therefore long-term debt
issuance is the main dependent variable of interest. Real investment can be broken down in three
categories: capital investment, intangible investment and acquisitions. This is interesting because
forms of investment that are not purely capital expenditure is becoming increasingly important
among the largest US firms.
• Net Operating Profits (F): net operating cash flow net minus intangible investment.
• Total Debt Issuance (TDI): the total net debt issuance, TDI = NDI + NCDI , where NDI is
the non-current net debt issuance and NCDI is the current debt issuance.
200
• Real investment (RINV): RINV = KINV + ACQ + IINV, where KINV = CAPX - SPPE,
AQC is acquisitions and INVV is in intangible investment, IINV = R&D + SG&A .
• ∆Cash is the cash variation, ∆ Cash = CHECH.
• Financial Investment (FINV): FINV = IVCH - SINV - IVSTCH.
• Other: the residual, Others = − IVACO − FIAO − TXBCOF
A.6 CDS-bond Basis
We follow Elizalde et al. (2009) and apply the par equivalent CDS spread methodology, or
PECS, to compute the CDS bond basis.
To fix notation, let r(s) be the instantaneous short interest rate, and λi(s) the instantaneous
hazard rate for issuer i. We define the discount curve Z(t) and the survival probability curve Si(t)
for issuer i as
Z(t) := e−∫ t0 r(s)ds, (A.52)
Si(t) := e−∫ t0 λi(s)ds. (A.53)
(A.54)
Given a bond issued by issuer iwithN interest paymentsCF1, CF2, . . . CFN at times t1, t2, . . . tN ,
principal value V and maturity tN , its dirty price50 is given by the formula
P =N∑n=1
Z(tn)Si(tn)CFn + Z(tN)Si(tN)V. (A.55)
Given a CDS contract withM remaining payments, with payment times t1, t2, . . . , tM and year
50Inclusive of accrued interest.
201
fractions ∆1,∆2, . . . ,∆M the present value of the contract for the protection buyer is given by
πpb = NCM∑m=1
∆mZ(tm)Si(tm) +NC
2
M∑m=1
∆mZ(tm) [S(tm−1)− S(tm)] (A.56)
while for the counter-party of the contract, the protection seller, the net present value is given by
πps = N(1−RR)M∑m=1
Z(tm) [S(tm−1)− S(tm)] . (A.57)
where N is the notional value, RR is the recovery rate, and C is the CDS spread. In particular, the
CDS par spread Cpar is the one for which
πpb(Cpar) = πps (A.58)
The PECS methodology consists in three steps. First, one bootstraps a survival probability
curve SCDSi (t) from CDS prices. Second, one defines the bond-implied survival probability curve
SBondi (t) = SCDSi (t) + βi by choosing the β that minimizes the difference between market prices
PMktj and prices Pj(SBondi ) implied by Formula (A.55), averaging over all issued bonds j for issuer
i
βi := argmin∑j
(PMktj − Pj(SBondi )
)2. (A.59)
In this phase, one needs to recall that bonds in the US market are quoted using the clean price,
hence one must re-add the accrued interest before taking the difference. Finally, one can define the
par equivalent CDS spread Cpecs for a given tenor tM by solving Equation (A.58) with the survival
probability given by SBondi (t). The CDS-bond basis B(t) is given by the difference Cpecs − Cpar.
202
A.7 Alternative Model with Limits to Arbitrage
A.7.1 Explicit Model of Arbitrageurs
At each time t, the arbitrageur must choose his consumption Cat , his investment in risky assets
Qai,t+1, in the uncollateralized loans Ba
u,t+1 and in the collateralized loans Bac,t+1.
Let W at be the wealth of the arbitrageur in time t.
W at = QQQa
tXXX t +Bau,t +Ba
c,t − Cat (A.60)
As in Gârleanu and Pedersen (2011), I assume that arbitrageurs must post margins to finance
their positions. Margins are paid both in long and short positions.
The arbitrageur solves the problem51
max{ct,Qt+1,Bu,t+1,Bc,t+1}∞t=0
Et
[∑t
βtU (Ct)
](A.61)
s.t. Qt+1PPP t +Bu,t+1Pu,t +Bc,t+1Pc,t ≤ Wt (A.62)∑i
mi,t|Qi,t+1|Pi,t +Bu,t+1Pu,t ≤ Wt, (A.63)
where mi,t is the margin requirement of asset i and time t. All other terms are standard.
Suppose that u(c) = c(1−γ)
1−γ and ∆ct+1 = ln(Ct+1
Ct
)= µc + ρc∆ct + σ2
cηc,t+1, where ηc,t+1 ∼
N(0, 1)
From the agent’s a first-order conditions we have:
E(ru,t+1 − rc,t+1) = ψt (A.64)
E(ri,t+1 − rc,t+1) +1
2σ2i = covt
(mat+1, ri,t+1
)− mi,t (A.65)
where ψt = ln(λt+κtλt
)and mi,t = ln
(λt+κtmi,tsign(Qi,t+1)
λt
)51We drop the subscript a to ease the notation.
203
To see this, I solve the Lagrangian,
L = Et
[∑t
βtU (Ct) + λt (Wt −Qt+1PPP t −Bu,t+1Pu,t −Bc,t+1Pc,t) +
κt
(Wt −
∑i
mi,t|Qi,t+1|Pi,t −Bu,t+1Pu,t
)] (A.66)
[∂L
∂Qi,t+1
]: Et [− (λt + κtmi,tsign(Qi,t+1))Pi,t + (λt+1 + κt+1)Xi,t+1] = 0 (A.67)
=⇒ Pi,t = Et[λt+1 + κt+1
λt + κt
λt + κtλt + κtmi,tsign(Qi,t+1)
Xi,t+1
](A.68)
[∂L
∂Bu,t+1
]: Et [− (λt + κt)Pu,t + (λt+1 + κt+1)] = 0 (A.69)
=⇒ Pu,t = Et[λt+1 + κt+1
λt + κt
](A.70)
[∂L
∂Bc,t+1
]: Et [−λtPc,t + λt+1 + κt+1] = 0 (A.71)
=⇒ Pc,t = Et[λt+1 + κt+1
λt
](A.72)
[∂L
∂ct
]: Et [u′(Ct)− λt − κt] = 0 (A.73)
=⇒ u′(Ct) = λt + κt (A.74)
Hence, the price of each asset i must be equal evolves two Lagrange multipliers from the
arbitrageur problem. The first λt is the traditional budget constraint. The second is the κt is the
204
margin constraint. In world in which there is a second set of agents that value safety services, the
arbitrageurs is short in in assets that provide safety services. In this case, the safety premium is
higher, higher the margin of requirement of the asset.
A.7.2 An Example of a Negative CDS-bond Trade
In this subsection I present an example for the negative CDS-bond basis for a Marriot (MAR 3
3/4 10/01/25, rated BBB−), 5-year maturity bought in end of September 2020. The example builds
on negative CDS-basis trade presented in Boyarchenko et al. (2018) and Bai and Collin-Dufresne
(2019). At the time, the CDS-bond basis of MAR was −1.3%. If investors were able to finance
themselves at the UST rate, this would represent an arbitrage trade with profits of 1.3% per year.
The key idea of this example is to flesh out the true funding costs a financial intermediary would
incur if she enters this trade. By looking at the net payouts, one can then calculate the implicit
funding cost that would make this trade unattractive.
Table A.3: Negative CDS-bond Basis Cash Flow Diagram
Funding Market
Bond Dealer
Repo rate
Funding Market
Debt Market Derivatives Market
OIS rate
BondCash Initial Margin+
CDS Trade Spread
Protection Premium (on credit event)
Cash: Bond MV – Haircut
OIS rate
Cash: Haircut
Repo Market
CDS Seller
CDS-Bond Basis Trader
Cash: Margin
Figure A.3 shows a cash-flow diagram for a generic negative trade transaction. In this example,
the investor is a generic intermediary that buys the bond in the bond market, buys CDS protection
in the derivatives market and funds the position in the funding market. Funding markets are of two
types: secured lending and unsecured lending. I assume the bond transacts at par and the investor
205
enters in $10 Million position. All the cash flows are summarized in Table A.4.
The first transaction is to buy the cash bond. The investor uses the bond as collateral in the repo
market and pays the repo rate. I follow Gârleanu and Pedersen (2011) and assume that haircuts for
IG bonds is 25%. She need to finance the haircut on the unsecured funding market.
The second transaction is to buy the CDS protection for the total notional value. The investor
pays the upfront payment and the CDS fixed premium of 1%. She also needs to post margin for
the CDS position. I follow the FINRA guidelines and set the margin to 12.5% of the notional.52
Both CDS payments and margins are funded in the unsecured funding market.
Finally, the investor needs to fund the total of repo haircut, and CDS upfront payment, fixed
premium and margin. The unsecured borrowing cost is investor-specific and it is not easily observ-
able. In general, the funding cost is a base rate, like OIS, plus a spread. As a benchmark, as shown
in Table A.4, I assume this spread is zero and calculate what would be net payoff of this trade.
For the notional of $10 Million, the net payoff of this trade would be $116 Thousand per year, or
1.16%. This number is smaller than the negative CDS-bond basis, but it is still large.
Finally, what would be the minimal funding cost that would make this transaction unattractive
to the investor? This rate is simply the calculation net payoff as a ratio of total unsecured funding
needed. As shown in Table A.5, this number is 3.06%, which means that an unsecured funding
cost of OIS plus a spread of 3.06% would make this trade unprofitable. When compared to the
5-year credit spread of large banks in the US, this number looks high.53 If the credit spread is
the proper cost of funding of large financial institutions, they should have been engaging in the
negative CDS-bond basis trade. Though, the credit spreads do not take into consideration the
regulation burden in taking this trade. This investment, although theoretically risk free, adds to
the risk based capital and liquidity requirements of financial institutions. 3.06% thus represent the
shadow cost of funding of the intermediary, which includes, among others, “balance sheet rental
cost" due to regulation constraints.
52For more details see FINRA website.53For comparison, 5-years yield for unsecured senior debt on September 30, 2020 for JP Morgan was 0.86%, Bank
of America was 0.9% and Citi Bank was 1.15%.
206
The balance sheet rental cost include costs related stringent regulation such as liquidity cover-
age ratios. For details on how this trade affects the balance sheet of the intermediary, the reader can
consult Boyarchenko et al. (2018). More broadly, a recent literature explores how these balance
sheet costs are linked to prices and liquidity in a variety of markets (Du et al. (2018), Duffie (2018),
Andersen et al. (2019), Fleckenstein and Longstaff (2020), Bolandnazar (2020)).
Table A.4: A Negative CDS-bond Basis Example
Variable Rate Dollar ValueCorporate Yield 3.10%Treasury Yield 0.30%CDS spread 1.50%CDS-bond basis -1.30%Cash positionBond Market Value 10,000,000.00Secured Funding 75.00% 7,500,000.00Repo Haircut 25.00% 2,500,000.00CDS positionNotional Value 10,000,000.00Upfront Payment (52,020.00)Initial margin 12.50% (1,250,000.00)Funding cost of the cash positionRepo Rate on 75% notional 0.38% (28,500.00)OIS Rate on Haircut 0.40% (10,000.00)OIS Upfront Payment 0.40% (208.08)OIS rate on CDS initial margin 0.40% (5,000.00)Trade CashflowBond Coupon 310,000.00CDS fixed premium 1.00% (100,000.00)CDS trade spread (effective) (150,000.00)Total 160,000.00TotalsTotal Payoff 160,000.00Total Funding Cost (43,708.08)Net Payoff 116,291.92
This table shows the annual cash flows for negative CDS-bond trade on bond MAR 3 3/4 10/01/25 (Marriott bond,rated BBB−) bought on Sep 2020. Bond and UST yields are from Bloomberg. Repo rate is from Bloomberg repo ratecalculation. CDS spread and OIS is from Markit. Upfront payment is from Market calculator, which can be foundhere.
207
Table A.5: Implicit Funding Cost
Variable Rate Dollar ValueNet Payoff 116,291.92Total Unsecured Funding 3,802,020.00Implicit funding rate 3.06%
This table shows the implicit funding cost that would make the negative CDS-bond trade not profitable. The exampleconsiders Marriot bond (MAR 3 3/4 10/01/25, BBB− bond) bought on Sep 2020.
208
Appendix B: Chapter 2
B.1 Notation
1. Asset specifics
N : Number of assets
M : Number of characteristics
rrr : Vector of excess returns (N × 1)
µµµ : Vector of expected excess returns (N × 1)
Σ : Variance-covariance matrix (N ×N )
X : Matrix of characteristics (N ×M)
λλλc : Vector of characteristic premia (M × 1)
2. Factor model
f : Priced factor
λ : Premium on priced factor
βββ : Vector of individual firms’ loadings (βi) on f (N × 1)
g : Vector of unpriced factors ((K − 1)× 1)
γγγi : Vector of asset i’s loadings on the unpriced factors ggg (1× (K − 1))
εi : Idiosyncratic shocks for asset i
3. Characteristic portfolios (CPs)
Wc : Matrix of CPs’ weights (N ×M)
wwwc,m : m−th column of matrix Wc (N × 1)
rrrc ≡ W>c rrr : Vector of CPs’ excess returns (M × 1)
209
µµµc ≡ Errrc : Vector of CPs’ expected excess returns (M × 1)
Σc ≡ var(W>c rrr)
: Covariance matrix of CPs’ returns (M ×M )
B : Matrix of the projection coefficients of rrr on rrrc (N ×M)
bbbm : m−th column of matrix B (N × 1)
4. Characteristic efficient portfolios (CEPs)
W ∗c : Matrix of CEPs’ weights (N ×M)
www∗c,m : m−th column of matrix W ∗c (N × 1)
rrr∗c ≡ W ∗>c rrr : Vector of CEPs’ excess returns (M × 1)
µµµ∗c ≡ Errr∗c : Vector of CEPs’ expected excess returns (M × 1)
Σ∗c ≡ var(W ∗>c r)
: Covariance matrix of CEPs’ returns (M ×M )
B∗ : Matrix of the projection coefficients of rrr on rrr∗c (N ×M)
bbb∗m : m−th column of matrix B∗ (N × 1)
5. Hedge portfolios
Wh : Matrix of hedge portfolios’ weights (N ×M)
wwwh,m : m−th column of matrix Wh (N × 1)
∆ : Matrix of hedge ratios (M ×M)
B.2 Proofs
B.2.1 The characteristic efficient portfolios
For each characteristic m, let the characteristic efficient portfolio (CEP) be the solution of the
problem:
minwwwc,m
1
2www>c,mΣwwwc,m (B.75)
s.t. www>c,mX = eee>m (B.76)
210
Where wwwc,m is an (N × 1) vector of portfolio weights, Σ is the (N ×N) covariance matrix, X an
(N ×M) characteristic matrix and eeem an (M × 1) vector with the mth entry equal to 1 and all
others equal to 0.
The Lagrangian is:
L =1
2www>c,mΣwwwc,m + κκκm
(eeem −X>wwwc,m
)(B.77)
The FOC with respect towww>c,m is given as:
Σwwwc,m −Xκκκ>m = 000 (B.78)
wwwc,m = Σ−1Xκκκ>m (B.79)
The FOC with respect to κκκm is given as:
X>wwwc,m = eeem (B.80)
κκκ>m =(X>Σ−1X
)−1eeem (B.81)
Hence,
www∗c,m = Σ−1X(X>Σ−1X
)−1eeem (B.82)
The set of CEP weights, W ∗c , an (N ×M) matrix, of which the mth column is the vector of
weights of the mth CEP, can be written as
W ∗c = Σ−1X
(X>Σ−1X
)−1(B.83)
211
B.2.2 Proof of Proposition 2.1
Part 1: Let Σ∗c be the covariance matrix of CEP returns and µµµ∗c be the expected excess returns
of the CEPs. Notice that under Assumption A1, we have that
Σ∗c =(X>Σ−1X
)−1and µµµ∗c = λλλc (B.84)
Hence, the maximum squared Sharpe ratio in the space spanned by W ∗c is:
SR∗2 = µµµ∗>c Σ∗−1c µµµ∗c = λλλ>c X
>Σ−1Xλλλc = µµµ>Σ−1µµµ (B.85)
Hence, the CEPs span the MVE portfolio.
Part 2: Let B∗ be the (N ×M) matrix of loadings from a projection of assets’ excess returns
on the the CEPs’ excess returns. Then:
B∗ = ΣW ∗c (W ∗>
c ΣW ∗c )−1 = X (B.86)
B.2.3 Proof of Proposition 2.2
Part 1: For each characteristic portfolio, the weight vector of the optimal hedge portfolio,
wwwh,m, solves
maxwwwh,m
www>h,mbbbm (B.87)
s.t. www>h,mX = 000 (B.88)
1
2www>h,mΣwwwh,m = σ2 (B.89)
Where bbbm is the mth multivariate regression coefficient of rrr on rrrc.
212
The Lagrangian is:
L = www>h,mbbbm − κκκ1,mX>wwwh,m + κ2,m
(σ2 − 1
2www>h,mΣwwwh,m
)(B.90)
The FOC with respect towww>h,m is given by:
bbbm −Xκκκ>1,m − κ2,mΣwwwh,m = 000 =⇒ (B.91)
wwwh,m =1
κ2,m
Σ−1(bbbm −Xκκκ>1,m
)(B.92)
The FOC with respect to κκκ1,m is given by:
X>wwwh,m = 0 (B.93)
Multiplying the transpose of (B.92) by X in both sides and substituting in (B.93), we have:
(bbb>m − κκκ1,mX
>)Σ−1X = 000 =⇒ (B.94)
κκκ1,m = b>mΣ−1X(X>Σ−1X
)−1(B.95)
Replacing κκκ1,m we have:
www∗h,m = Σ−1(B −X
(X>Σ−1X
)−1X>Σ−1B
)e 1κ2,m
(B.96)
where e 1κ2,m
is an (M × 1) vector with the mth entry equal to 1κ2,m
and all others equal to 0.
Substituting B we have:
www∗h,m =(WcΣ
−1c − Σ−1X
(X>Σ−1X
)−1X>WcΣ
−1c
)e 1κ2,m
(B.97)
213
By solving the problem for all characteristics m and substituting W ∗c , we have:
W ∗h =
(Wc −W ∗
cX>Wc
)Σ−1c E−1 (B.98)
where E is an (M ×M) diagonal matrix, with columns eκ2,m . �
Part 2: Rearranging Equation B.97 we have
W ∗cX
>Wc = Wc −WhEΣc (B.99)
Define ∆∗ = EΣc and A = X>Wc. Hence,
W ∗c A = Wc −W ∗
h∆∗ (B.100)
�
B.2.4 The optimal hedge ratio
The last step is to find the optimal hedge ratio ∆∗
Let
W ∗c = W ∗
cX>Wc (B.101)
And
Σ∗c = Var[W ∗>c R
]= W>
c X(X>Σ−1X)−1X>Wc (B.102)
From Equation (B.99) we have:
WhEκ2Σc = Wc − W ∗c (B.103)
214
Var[ΣcEκ2W
>h R]
= Var
[(Wc − W ∗
c
)>R
](B.104)
=⇒ ΣcEκ2ΣhEκ2Σc = Σc − Σ∗c (B.105)
But,
Σ∗c = Σc + ΣcEκ2ΣhEκ2Σc − 2W>c ΣWhEκ2Σc (B.106)
Substituting, we have:
ΣcEκ2ΣhEκ2Σc = W>c ΣWhEκ2Σc =⇒ (B.107)
∆∗ = ΣcEκ2 = W>c ΣWhΣ
−1h (B.108)
B.3 Empirical details
B.3.1 Empirical definition of main variables
We use data from Compustat and CRSP, downloaded directly from the WRDS data service.
215
Book Equity (BE) Stockholders book equity, minus the book value of preferred
stock, plus balance sheet deferred taxes (if available and fiscal
year is < 1993), minus investment tax credit (if available), mi-
nus post-retirement benefit assets (PRBA) if available. Stock-
holders book equity is shareholder equity (SEQ), common eq-
uity (CEQ) plus preferred stock (PSTK) or total assets (AT) mi-
nus liabilities (LT) plus minority interest (MIB, if available) (de-
pending on availability, in that order). Book value of preferred
stock is redemption (PSTKRV), liquidation (PSTKL), or par value
(PSTK) (depending on availability, in that order). Deferred taxes
is deferred taxes and investment tax credit (TXDITC) or deferred
taxes and investment tax credit (TXDB) plus investment tax credit
(ITCB) (depending on availability, in that order).
Market Equity (ME) Total firm market value (|PRC| ∗ SHROUT ) summed over all
securities belonging to a firm, identified by GVKEY, and if miss-
ing, by PERMCO, as of June. We give preference to GVKEY to
correctly account for tracking stocks. To be valid, ME must be
greater than zero.
Book to Market (BEME) Book equity as of December divided by market equity as of De-
cember(BEME
).
Investment (INV) Total asset (AT) growth(
ATtATt−1
− 1)
. We consider PERMCO as
the identification key. AT must be greater than zero to be consid-
ered.
Operating Profitability (OP) Operating profitability to book equity (BE) ratio. Operating prof-
itability is sales (SALE) minus cost of goods sold (COGS), minus
selling, general, and administrative expenses (XSGA), minus in-
terest expense (XINT). In order to be non-missing, SALE must be
non-missing, at least one of the other entries must be non-missing
and BE must be greater than zero.216
B.3.2 Loading estimation
We calculate ex-ante forecasts of loadings for b’s, i.e., loadings on the benchmark characteristic
portfolios; and for δ’s, i.e., the optimal hedge ratio.
To calculate ex-ante forecasts of loadings we follow Frazzini and Pedersen (2014) and use two
different data windows of individual stock returns: 12-months of daily returns for volatility and
60 months of overlapping 3-day-cumulated returns for correlation. For this estimation, we only
consider returns where Pt and Pt−1 are non-missing.
For the estimation of correlations and factor volatilities, we calculate Daniel and Titman (1997)
style pre-formation factor returns. Following their procedure, we use portfolio allocations and
weights as of June 30 (portfolio formation date), and calculate portfolio returns for the preceding
5 years, holding the allocation and weights constant for each day.
Finally, we consider the observation that returns of stocks that will be allocated to a particular
portfolio at the end of June, experience a level-shift in average returns starting already in January,
as described in Daniel and Titman (1997). To account for this, when we calculate b’s, we include a
dummy variable for the rank-year, i.e., a variable that is equal to 1 if the return observation belongs
to the year of portfolio formation.
B.3.3 Dealing with missing prices
CRSP stock files report missing values for returns (RET) if a stock does not have a valid price
for 10 periods or more. The price tolerance period represents 10 months for monthly returns
and 10 days for daily returns. For calculating traded portfolio returns, we instead follow Ken
French’s website and allow for a 200 days price tolerance period. This choice makes daily and
monthly returns comparable. For pre-formation factors as described above, where all returns can
be observed before formation, we exclude any observation with a missing price (as described
above).
217
B.4 Supplemental results
B.4.1 Portfolio bin population
Table B.1: Number of firms in each portfolio
Panel A: ME × BEME
Portfolio No. of firms
ME BEME min mean max
1 1 27 564 1040
1 2 86 552 966
1 3 189 960 1813
2 1 78 255 428
2 2 119 219 322
2 3 88 152 197
3 1 139 255 466
3 2 101 158 221
3 3 45 95 163
Panel B: ME × OP
Portfolio No. of firms
ME OP min mean max
1 1 100 1175 2137
1 2 30 497 796
1 3 24 380 776
2 1 75 189 347
2 2 68 217 317
2 3 60 207 300
3 1 52 112 199
3 2 114 174 246
3 3 121 218 308
Panel C: ME × INV
Portfolio No. of firms
ME INV min mean max
1 1 65 911 1458
1 2 29 515 967
1 3 44 699 1296
2 1 68 161 266
2 2 38 201 308
2 3 52 262 389
3 1 51 122 211
3 2 115 192 235
3 3 85 194 321
Time-series minimum/mean/maximum number of firms for which loading forecast could be calculated, within eachsize-characteristic sorted portfolio.
Table B.1 displays the minimum, mean and maximum population of the 3×3 independently
sorted ME × BEME, ME × OP, and ME × INV portfolios, counting only firms for which a
forecast loading is available. Within each of these, stocks are sorted within a characteristic bucket,
on the respective forecast loadings, i.e., when we divide the displayed numbers by three, we have
the minimum/mean/maximum number of firms of any of the 27 portfolios that the hedge portfolios
are based on.
It turns out that the resulting portfolios end up well-populated. The lowest number of firms
occurs in the small/high-OP portfolio, in 1964, when the small/high-OP portfolio contains 24
firms. In general, even portfolios of big/value stocks contain 95 stocks, on average, resulting in
loading-sorted portfolios with more than 30 stocks.
218
B.4.2 High power vs. low power
The achievable improvement on a set of CPs intimately depends on the post-formation loadings
of the hedge portfolios. Since the hedge portfolios have roughly zero expected returns, more
negative loadings means that we are capturing variation in loadings that is not related to returns,
which is translated in positive αs. Therefore, once we add these portfolios to the original CPs we
should expect large Sharpe ratio improvements.
Maximizing the variation in loadings that is not related to returns relates to the power of the
test that has as null hypothesis that the CPs form a valid asset pricing model (Daniel and Titman,
2012).
We show how the use of the methodology to forecast loadings advanced in this paper, which
we refer to as the “high power” methodology, increases the power of standard asset pricing tests.
We illustrate how a standard “low power” methodology used to estimate the loadings (see, e.g.,
Daniel and Titman, 1997; Davis et al., 2000) leads to a failure to reject asset pricing models and
thus imposes too low a bound on the volatility of the stochastic discount factor. We do so by
constructing characteristic balanced portfolios and showing that the ability of standard asset pricing
models to properly account for their average returns depends critically on whether one uses the low
or high power methodology.
The traditional low power approach uses as instruments for future loadings the result of re-
gressing monthly stock excess returns on characteristic portfolio excess returns over a moving
fixed-sized window based on, e.g., 36 or 60 monthly observations, skipping the most recent 6
months.
We first compare the low and high power methodology by looking at the post-formation load-
ings. We estimate the post-formation loadings by running a full-sample time series regression of
the monthly excess returns on the five FF CPs (see equation (2.32)). To check whether our high
power methodology results in larger dispersion of the post-formation loadings when compared
to the low power methodology, Figure B.1 shows the post-formation loadings on the x-axis and
the respective average characteristic on the y-axis for each of the 27 portfolios. Panels A and B
219
correspond to the low and high power methodology, respectively.
Consider, for example, the top panels in Figure B.1, which focus on the loadings on HML for
each of the two estimation methodologies. There are 3 × 3 groups of estimates—connected by
lines—each corresponding to a particular BEME ×ME bin. Each of those lines have three points
corresponding to the three portfolios from the conditional sort on ex-ante estimated loadings.
The ideal output would be to find variation in the loadings that is not associated with variations
in characteristics, our proxy for expected returns. Hence, the ideal equivalent of Figure B.1 would
be one in which the spread from low betas (red dots) and high betas (green dots) is maximized, but
conditional on belonging to a characteristic bucket, there is no additional correlation between the
characteristic and the forecast loading, i.e., the dashed lines are perfectly horizontal.
As it is readily apparent from Figure B.1, the high power methodology generates substantially
more cross-sectional dispersion in post-formation loadings than the low power methodology, which
is key to generating hedge portfolios that are maximally correlated with the candidate characteristic
portfolio. For example, focus on the loadings on HML for the large growth portfolios (portfolio
(1,3)). The low power methodology generates post-formation loadings on HML, bHML, for each of
the three portfolios of −0.43, −0.22 and 0.01, respectively. The high power methodology instead
generates post-formation HML loadings of−0.48,−0.18 and 0.17, respectively. For the low power
methodology, the loading of a portfolios that goes long on the low loading portfolio and short the
high loading portfolios is −0.45 with a t−statistic of −8.89. For the high power methodology the
same post-formation loading is −0.65 with a t−statistic of −12.98.
Notice that, reassuringly, both methodologies generate a positive correlation between pre- and
post-formation loadings for each of the book-to-market and size groupings. This positive correla-
tion between pre- and post extends to the case of CMA. But in the case of the loadings on RMW,
the low power methodology does not produce a consistent positive association between pre- and
post-formation loadings, whereas the high power methodology does.
The spreads in the loadings translate directly into the ability to reject the FF model. Table
B.2 Panel A shows the results of time series regressions of the low power hedge portfolios on the
220
FF CPs. First, notice that the average returns of the hedge portfolios are not statistically different
from zero, as in the high power case (Panel B). Second, notice that the loadings of each hedge
portfolio on the respective FF CP is much lower for the low power, compared to the high power
methodology. For example, the bHML for the high power methodology is 0.8 with a t-statistic of
28.21, whereas for the low power it is 0.54 with a t-statistic of 19.69. Finally, we can look at the
α’s. For the low power method we cannot reject the FF model using any of the hedge portfolios in
isolation, since all α’s are not statistically different from zero. For the equal weighted combinations
of hedge portfolios shown in the last rows of the table, we can see that the t-statistics of the αs are
significantly positive even for the low power methodology. However, the equal weight combination
αs are systematically bigger for the high power methodology.
In sum then our high power methodology forecasts future loadings better than the one used by
Daniel and Titman (1997) or Davis et al. (2000) and, as a result, they translate into more efficient
hedge portfolios as well as asset pricing tests with higher power.
221
Figure B.1: Ex-post loading vs. characteristicH
ML
Panel A: Low power
−1.5 −1.0 −0.5 0.0 0.5 1.0 1.5Post-formation bHML
0.00
0.25
0.50
0.75
1.00
1.25
1.50
1.75
2.00
BEME
Low bHMLMedium bHMLigh bHML
Panel B: High power
−1.5 −1.0 −0.5 0.0 0.5 1.0 1.5Post-formation bHML
0.00
0.25
0.50
0.75
1.00
1.25
1.50
1.75
2.00
BEME
Low bHMLMedium bHMLigh bHML
RM
W
−1.5 −1.0 −0.5 0.0 0.5 1.0 1.5Post-formation bRMW
−0.4
−0.2
0.0
0.2
0.4
0.6
0.8
1.0
OP
Low bRMWMedium bRMWigh bRMW
−1.5 −1.0 −0.5 0.0 0.5 1.0 1.5Post-formation bRMW
−0.4
−0.2
0.0
0.2
0.4
0.6
0.8
1.0
OP
Low bRMWMedium bRMWigh bRMW
CM
A
−1.5 −1.0 −0.5 0.0 0.5 1.0 1.5Post-formation bCMA
−0.2
0.0
0.2
0.4
0.6
0.8
INV
Low bCMAMedium bCMAigh bCMA
−1.5 −1.0 −0.5 0.0 0.5 1.0 1.5Post-formation bCMA
−0.2
0.0
0.2
0.4
0.6
0.8
INV
Low bCMAMedium bCMAigh bCMA
This figure shows the time-series average of post-formation characteristic portfolio loading on the x-axis and the time-series average of the respective characteristic on the y-axis of each of the 27 portfolios formed on size, characteristic(book-to-market/operating profitability/investment) and characteristic portfolio loading. Panel A uses the low powermethodology and B uses the high power methodology. The first row uses sorts on book-to-market and HML-loading,the second one operating profitability and RMW-loading and the last one investment and CMA-loading.
222
Table B.2: Results of time-series regressions on characteristic-balanced hedge-portfolios
Panel A: Low power
Hedge-Portfolio Avg. α bMkt−RF bSMB bHML bRMW bCMA R2
rh,MktRF 0.13 -0.02 0.29 0.23 -0.07 -0.16 -0.02 0.57
(1.39) (-0.33) (18.54) (10.33) (-2.26) (-5.12) (-0.46)
rh,SMB 0.11 0.02 0.14 0.39 -0.04 -0.10 -0.16 0.59
(1.38) (0.32) (10.30) (19.94) (-1.53) (-3.59) (-3.96)
rh,HML 0.03 -0.05 0.01 0.00 0.54 0.04 -0.45 0.39
(0.46) (-0.83) (0.40) (0.17) (19.69) (1.51) (-10.35)
rh,RMW 0.03 -0.09 -0.03 0.01 0.18 0.30 0.01 0.32
(0.52) (-1.64) (-2.42) (0.71) (6.98) (11.13) (0.33)
rh,CMA -0.01 -0.09 0.03 -0.01 -0.29 -0.01 0.68 0.31
(-0.21) (-1.61) (2.41) (-0.31) (-10.68) (-0.26) (16.03)
EW3 0.02 -0.08 0.00 0.00 0.15 0.11 0.08 0.40
HML,RMW,CMA (0.50) (-2.66) (0.30) (0.36) (10.62) (7.97) (3.82)
EW4 0.04 -0.06 0.07 0.06 0.09 0.05 0.06 0.28
EW3+MktRF (1.40) (-2.20) (10.40) (5.94) (6.85) (3.26) (2.66)
EW5 0.05 -0.05 0.07 0.10 0.08 0.03 0.03 0.32
EW4+SMB (1.55) (-1.89) (10.41) (9.89) (6.07) (2.52) (1.38)
Panel B: High power
Hedge-Portfolio Avg. α bMkt−RF bSMB bHML bRMW bCMA R2
rh,MktRF 0.10 -0.18 0.41 0.40 0.05 -0.17 -0.06 0.66
(0.80) (-2.44) (22.39) (15.18) (1.48) (-4.68) (-1.15)
rh,SMB 0.17 0.03 0.17 0.56 -0.01 -0.15 -0.16 0.72
(1.74) (0.50) (12.27) (28.28) (-0.33) (-5.57) (-3.95)
rh,HML 0.07 -0.11 0.03 -0.05 0.80 0.20 -0.54 0.61
(0.74) (-1.86) (1.80) (-2.34) (28.21) (6.68) (-12.03)
rh,RMW 0.08 -0.21 -0.05 0.04 0.31 0.69 0.11 0.65
(0.86) (-3.66) (-3.27) (1.96) (11.69) (24.80) (2.51)
rh,CMA -0.04 -0.20 0.04 0.02 -0.31 0.09 0.96 0.43
(-0.52) (-3.39) (2.60) (1.10) (-10.95) (2.90) (21.13)
EW3 0.04 -0.17 0.01 0.00 0.27 0.32 0.17 0.70
HML,RMW,CMA (0.64) (-5.45) (0.83) (0.39) (17.52) (20.56) (7.30)
EW4 0.05 -0.18 0.11 0.10 0.21 0.20 0.12 0.58
EW3+MktRF (1.17) (-5.92) (14.60) (9.75) (15.08) (13.71) (5.18)
EW5 0.07 -0.15 0.10 0.15 0.19 0.17 0.08 0.57
EW4+SMB (1.57) (-5.01) (14.08) (14.86) (13.60) (11.65) (3.83)
Stocks are first sorted based on size and one of book-to-market, profitability or investment into 3x3 portfolios. Con-ditional on those sorts, they are subsequently sorted into 3 portfolios based on the respective loading, i.e., on HML,RMW or CMA. For MktRF and SMB we use the average of three hedge portfolios, which are based on a 3x3 sort onsize and book-to-market, profitability or investment. The hedge portfolio then goes long the low loading and short thehigh loading portfolios. On the bottom, we form combination-portfolios that put equal weight on three (HML, RMW,CMA), four (HML, RMW, CMA, MktRF) or five (HML, RMW, CMA, MktRF, SMB) hedge portfolios. Monthlyreturns of these portfolios are then regressed on the 5 Fama and French (2015) characteristic portfolios in the sampleperiod from 1963/07 - 2019/12. In Panel A we use the low power and in Panel B we use the high power methodologyfor forecasting loadings.
223
Appendix C: Chapter 3
C.1 Data construction
C.1.1 Firm level observations
We restrict our attention to publicly traded firms in Europe and the US. To achieve this, we
require firms’ primary quotes of major shares to be listed in one of the major stock exchanges in
Belgium, Denmark, Finland, France, Germany, Iceland, Ireland, Italy, the Netherlands, Norway,
Portugal, Spain, Sweden, Switzerland, UK, and US.
To be more specific, from Datastream we select stocks with type Equity whose primary quotes
of major shares are listed in the following stock exchange markets: Euronext Brussel, OMX Nordic
Exchange Copenhagen, Helsinki, Euronext Paris, Berlin, Deutsche Boerse, Munich, NASDAQ
OMX Iceland, Dublin, Milan, Euronext Amsterdam, Oslo Bors, Lisbon, Madrid, Mercado Con-
tinuo, Stockholm, Six Swiss, London Stock Exchange, NYSE, NASDAQ (US) and Amex. We
further delete firms whose main listing place is the OTC market. The European stock exchange
markets we select consist of the 18 largest stock exchange markets in Europe. Notice that Switzer-
land is not part of EEA but given the integrity of the European financial market and the fact that
Switzerland will have to amend its current legislation to ensure that Swiss financial institutions to
have unfettered access to the EU market, we include Switzerland in our sample. Our results are
robust if we exclude Switzerland. We also require firms listed in Europe to be domiciled in one of
these European countries and firms listed in the US to be domiciled in the US. We further select
firms whose financial documents are presented in one of these countries’ local currencies: Den-
mark Krone, Euro, Great Britain Pound, Iceland Krona, Swedish Krona, Swiss Franc and USD.
To be included in our final sample, firms need to have non-empty total assets and positive
54For example, Ambac financial group went into bankruptcy in 2010 and emerged back in 2013. Its total investmentreturn in 2013 is 170455.55%. This is simply because Worldscope assigned the price of this firm from OTC the marketin 2012 to be $0.014 and the publicly traded price in 2013 is $24.56.
224
book-to-market ratio. In some cases, Worldscope records information of firms that went into re-
organization and stopped trading. In these cases, extreme values appear in total investment return
(RET, Worldscope Item 08801).54 We delete observations with total investment return above 99%
or below 1% of the total distribution of this item. Other variables used in our study are: the log
of total market capitalization at fiscal year t in dollars (LNSIZE), the log of book to market ratio
(LNBM), return on assets (ROA) and price volatility (PRICEVOL). The precise construction of all
these variables can be found in Appendix C.1.3. Table C.1 of Appendix C.3 reports the number of
firms, average coverage, average GDP growth rate and average unemployment rate in each country
in our sample.
C.1.2 Choice of data frequency
Following literature, we use annual forecast instead of quarterly forecast data for several rea-
sons (e.g., Hong and Kacperczyk (2010) and Giroud and Mueller (2011)). First, analyst forecasts
exhibit strong frequency seasonality. For example, in the US, most of the new forecasts are clus-
tered at the beginning of the year. Such seasonality varies across countries and even across firms.
It is difficult to attribute changes in quarterly forecast outcomes to MiFID II rather than to season-
ality. Second, quarterly financial reports are not mandatory. Though quarterly filing is common in
the US, it is uncommon in Europe. Data coverage and quality on a quarterly basis are poor, espe-
cially for EU firms. More importantly, since quarterly filings are not mandatory and uncommon
in Europe, focusing on firms with quarterly financial reports and earnings per share (EPS) data
suffers from severe selection bias: firms who report quarterly inherently differs from firms who do
not. Finally, since financial reports normally release with a certain lag, analyst information set will
not be updated timely when they issue quarterly forecasts, i.e., it is likely that they do not observe
firms’ last quarter true earnings when they make quarterly forecasts. Consequently, staleness is
going to be more severe in quarterly forecasts.
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C.1.3 Variable definitions
Average Coverage of Portfolio Firms The average of the analyst coverage of all the portfolio firms
that the analyst covers in a given year.
Average Forecast Error The average of forecast errors over all the firms the analyst
covers in a given year.
Book to Market (BM) Book to Market is defined as total asset (Worldscope item
02999) minus long-term debt (Worldscope item 03251) over
market value (Worldscope item 08002) (e.g., Fama and
French (1995)).
Coverage Coverage is the number of unique analysts who produce
forecasts for a certain firm during its fiscal year. Analyst
forecast information is obtained from I/B/E/S data set.
Distance (DISTANCE) Number of days between the analyst forecast date and the
firm’s actual earnings report date.
Drop Out A dummy variable equal to 1 if the analyst stops covering
all the firms he used to cover prior to the regulation.
Forecast Dispersion Forecast dispersion is defined as the standard deviation of
all the forecasts over all the analysts following the same
firm in the same year, scaled by the firm’s previous year-
end price. Analyst forecast information is obtained from
the I/B/E/S data set.
Forecast Error Forecast error is defined as the absolute distance between
the firm’s actual annual earnings per share and the mean
of the analyst forecasts, scaled by the firm’s previous year-
end price. Analyst forecast information is obtained from
I/B/E/S data set.
226
Market Capitalization (ME) Worldscope item 08002. It is firm’s market capitalization at the
fiscal year end. We convert it to USD using the exchange rate at
firm’s fiscal year end date.
N of Firms Follows The number of firms the analyst follows in a given fiscal year.
Relative Accuracy The average of all the scores across all the firms the analyst cov-
ers and across all the years prior to the regulation, as defined in
Section 3.4.
Return on Assets (ROA) Worldscope item 08326. Firms’ return on assets.
Return Volatility (RETVOL) Annualized standard deviation of daily returns over a year for a
given firm. It is constructed from Datastream item RI (Return
Index).
Stop A dummy variable equal to 1 if the analyst stops covering a firm
after the regulation.
Tenure The total number of years the analyst appeared in I/B/E/S, starting
from 1995.
Total Investment Return (RET) Worldscope item 08801. It is measured as Pt+Dividendst−Pt−1
MEt−1, P is
the firm’s year-end price.
227
C.2 Additional figures
Figure C.1: Geographic Composition of Stocks in Analyst Portfolio.
0.0
0.1
0.2
0.3
0.4
0.5
0.00 0.25 0.50 0.75 1.00Proportion of EU Firms in Analyst Portfolio Prior to 2018
Fra
ctio
n of
the
Tota
l Num
ber
of A
naly
sts
This figure shows the histogram of the geographic composition of the stocks in the analyst portfolio prior to theregulation. 1 means that all the firms the analyst covers are EU firms. 0 means that all the firms the analyst covers areUS firms.
228
Figure C.2: Average Analyst Coverage (EU vs. US)
0.0
0.1
0.2
0.3
[0,2) [2,4) [4,6) [6,8) [8,10) [10,15) [15,20) [20,20+)Average Analyst Coverage
Fra
ctio
n of
the
Toto
al N
umbe
r of
Firm
s
US EU
This figure shows the histogram of the average coverage of EU firms and US firms. Analyst coverage is the numberof unique analysts covering a specific firm in fiscal year t. We report the averages of the period from 2014 to 2018.
229
Figure C.3: Firm Level Forecast Error Distribution
Pre Post
0.0 2.5 5.0 7.5 10.0 0.0 2.5 5.0 7.5 10.0
0.00
0.05
0.10
Forecast Error (%) of EU Firms
Fra
ctio
n of
the
Tota
l Num
ber
of F
irms
(a)
Pre Post
0.0 2.5 5.0 7.5 10.0 0.0 2.5 5.0 7.5 10.0
0.00
0.05
0.10
Forecast Error (%) of US Firms
Fra
ctio
n of
the
Tota
l Num
ber
of F
irms
(b)
This figure plots the histograms of the forecast errors in the pre- and post-regulation years. To get the forecast errorsin the pre-regulation years, we simply average firms’ forecast errors overall these years.
230
Figure C.4: Average Number of Analysts per Brokerage House Over Time in the EU, Small vs. Large
● ●● ●
●
−4
0
4
2014 2015 2016 2017 2018Adj
uste
d A
vera
ge N
umbe
r of
Ana
lyst
s pe
r B
roke
rage
Hou
se
● Small House Large House
This figure shows the average number of unique analysts one brokerage house hires over the years in the EU betweensmall brokerage houses and large brokerage houses. Small brokerage houses are brokerage houses whose averagenumber of employees (analysts they hire) prior to the regulation falls below the median. We adjusted the number sothat both lines start at 0 in 2014.
231
C.3 Other summary statistics
Table C.1: Summary Statistics (Country Information)
Country N of Firms Coverage Average GDP Growth Rate Average Unemployment Rate
Belgium 70 5.851 1.490 7.648
Denmark 52 10.292 2.064 5.930
Finland 83 7.899 1.438 8.652
France 292 8.384 1.340 9.858
Germany 284 9.487 1.824 4.178
Iceland 3 1.333 3.924 3.504
Ireland 27 9.719 10.046 8.506
Italy 132 7.120 0.770 11.536
Netherlands 60 12.997 2.048 5.804
Norway 95 8.105 1.824 4.108
Portugal 19 7.526 1.828 10.626
Spain 75 15.107 2.654 19.770
Sweden 195 6.591 2.608 7.106
Switzerland 144 9.025 1.620 4.846
United Kingdom 602 8.131 2.022 4.902
United States 2, 259 11.145 2.284 4.922
This table provides information for the number of firms, the average coverage, the average GDP growth rate and theaverage unemployment rate in each country. Coverage is the number of unique analysts covering a certain firm. Wereport the averages of the period from 2014 to 2018 within each country.
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Table C.2: Summary Statistics (Small vs. Large in Sample for Quantity)
EU Firms (small): 1067 firms in total
Statistic Mean Median Pctl(25) Pctl(75) St. Dev.
Coverage 2.339 2 1 3 2.373Book to Market 2.133 1.117 0.650 1.948 4.802Investment Return (%) 11.957 4.938 −18.651 32.701 51.324Market Capitalization (Bil $) 0.175 0.114 0.044 0.257 0.176Return on Assets (%) −0.456 3.639 −1.042 7.087 21.521Return Volatility (%) 39.285 34.366 26.288 46.162 20.008
US Firms (small): 1130 firms in total
Statistic Mean Median Pctl(25) Pctl(75) St. Dev.
Coverage 4.892 4 2 7 4.092Book to Market 2.130 1.000 0.569 2.103 3.358Investment Return (%) 3.669 0.029 −23.309 23.484 46.361Market Capitalization (Bil $) 0.552 0.391 0.149 0.829 0.516Return on Assets (%) −3.578 1.762 −2.570 5.939 31.654Return Volatility (%) 42.377 36.543 26.659 51.664 21.888
This table provides the summary statistics for important variables in the sample for coverage quantity. We split thesample into small firms and large firms. Small firms are firms whose average fiscal year-end market capitalization fallsbelow the median. We define the median cutoff separately in the EU and the US. Coverage is the number of uniqueanalysts covering a certain firm. Book to Market is defined as total asset (Worldscope item 02999) minus long-termdebt (Worldscope item 03251) over market value (Worldscope item 08002). Investment return is Worldscope item08801, measured as (market price at year t+ dividends−market price at year t−1)/market price at year t−1). Marketcapitalization is Worldscope Item 08002 measured in billion dollars. Return on Assets is Worldscope Item 08326.Return volatility is the annualized daily standard deviation of returns over a year for a given firm.
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Table 1.18 Continued: Summary Statistics (Small vs. Large in Sample for Quality)
EU Firms (large): 1066 firms in total
Statistic Mean Median Pctl(25) Pctl(75) St. Dev.
Coverage 14.784 13 6 22 10.369Book to Market 2.764 0.972 0.553 1.741 6.634Investment Return (%) 11.237 8.954 −8.126 26.709 33.810Market Capitalization (Bil $) 10.477 2.753 1.211 8.424 23.488Return on Assets (%) 6.296 5.237 2.476 8.838 11.196Return Volatility (%) 27.370 25.408 20.765 31.475 10.458
US Firms (large): 1129 firms in total
Statistic Mean Median Pctl(25) Pctl(75) St. Dev.
Coverage 17.403 16 9 23 10.563Book to Market 1.453 0.658 0.375 1.240 3.057Investment Return (%) 8.035 6.647 −10.257 24.342 31.781Market Capitalization (Bil $) 19.927 5.608 2.813 15.068 52.163Return on Assets (%) 5.745 5.350 2.315 9.224 8.684Return Volatility (%) 27.667 24.843 19.983 31.756 11.686
234
Table C.3: Summary Statistics (Small vs. Large in Sample for Quality)
EU Firms (small): 556 firms in total
Statistic Mean Median Pctl(25) Pctl(75) St. Dev.
Coverage 6.819 6 4 9 4.397Forecast Error (%) 0.864 0.424 0.149 1.043 1.226Dispersion (%) 0.902 0.463 0.205 1.013 1.274Book to Market 1.799 0.921 0.547 1.494 4.330Distance 127.678 123.683 94.475 156.745 52.578Investment Return (%) 13.388 8.986 −10.783 31.634 40.040Market Capitalization (Bil $) 0.874 0.694 0.328 1.289 0.691Return on Assets (%) 4.973 5.395 2.651 8.696 11.331Return Volatility (%) 30.715 28.603 23.283 35.474 11.319
US Firms (small): 847 firms in total
Statistic Mean Median Pctl(25) Pctl(75) St. Dev.
Coverage 7.821 6 4 9 5.195Forecast Error (%) 0.594 0.266 0.099 0.656 0.974Dispersion (%) 0.690 0.290 0.117 0.767 1.105Book to Market 1.809 0.868 0.515 1.577 2.562Distance 121.377 118.4 96.3 144.6 38.789Investment Return (%) 6.578 2.473 −16.726 24.887 40.533Market Capitalization (Bil $) 1.098 0.894 0.430 1.577 0.845Return on Assets (%) 1.269 3.461 0.896 6.793 15.282Return Volatility (%) 36.119 32.136 24.824 43.103 15.930
This table provides the summary statistics for important variables in the Sample for coverage quality. To be includedin this sample, firms need to be covered by at least 2 analysts each year. We split the sample into small firms and largefirms. Small firms are firms whose average fiscal year-end market capitalization fall below the median. We define themedian cutoff separately in the EU and the US. Coverage is the number of unique analysts covering a certain firm.Forecast error is defined as the absolute distance between the firm’s actual annual earnings per share and the meanof the analyst forecasts, scaled by the firm’s previous year-end price. Forecast dispersion is defined as the standarddeviation of all the forecasts across all the analysts following the same firm in the same year, scaled by the firm’sprevious year-end price. Book to Market is defined as total asset (Worldscope item 02999) minus long-term debt(Worldscope item 03251) over market value (Worldscope item 08002). Distance is the average of the days betweenthe analyst forecast date and the firm’s actual EPS report date. We take the average over all the analysts following thesame firm and measure this variable in 2014. Investment return is Worldscope item 08801, measured as (market priceat year t+ dividends−market price at year t−1)/market price at year t−1). Market capitalization is Worldscope Item08002 measured in billion dollars. Return on Assets is Worldscope Item 08326. Return volatility is the annualizedstandard deviation of daily returns over a year for a given firm. We remove observations for which forecast error andforecast dispersion is larger than 10% of the firm’s share price at the end of the previous year.
235
Table 1.19 Continued: Summary Statistics Continued (Small vs. Large in Sample for Quality)
EU Firms (large): 555 firms in total
Statistic Mean Median Pctl(25) Pctl(75) St. Dev.
Coverage 20.967 21 14 28 9.339Forecast Error (%) 0.584 0.281 0.102 0.667 0.901Dispersion (%) 0.794 0.448 0.236 0.896 1.037Book to Market 3.032 0.925 0.526 1.662 6.748Distance 112.798 110.250 94.000 129.087 30.075Investment Return (%) 10.158 9.116 −6.239 25.065 26.450Market Capitalization (Bil $) 18.331 7.534 3.731 18.190 30.261Return on Assets (%) 7.121 5.337 2.674 8.983 13.000Return Volatility (%) 25.015 23.768 19.848 28.728 7.888
US Firms (large): 846 firms in total
Statistic Mean Median Pctl(25) Pctl(75) St. Dev.
Coverage 19.545 18 12 25 10.354Forecast Error (%) 0.289 0.121 0.045 0.298 0.537Dispersion (%) 0.388 0.174 0.075 0.405 0.681Book to Market 1.340 0.618 0.349 1.168 2.198Distance 107.477 105.570 86.808 125.500 31.060Investment Return (%) 9.065 7.647 −7.965 24.327 29.647Market Capitalization (Bil $) 25.628 8.691 4.335 21.100 59.127Return on Assets (%) 6.369 5.718 2.841 9.663 8.011Return Volatility (%) 25.941 23.731 19.377 29.930 10.107
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C.4 Additional regression results
C.4.1 Dynamic coefficients point estimates
Table C.4: Firm Level Outcomes (Dynamic Coefficients)
Dependent variable:
Coverage Forecast Error (%) Dispersion (%)
(1) (2) (3)
EU × Y15 0.050 −0.020 −0.026(0.094) (0.052) (0.045)
EU × Y16 −0.134 −0.018 −0.080∗∗∗
(0.121) (0.051) (0.029)
EU × Y17 −0.201 0.033 −0.036(0.193) (0.045) (0.073)
EU × Y18 −0.715∗∗∗ −0.143∗∗∗ −0.199∗∗∗
(0.269) (0.044) (0.038)
Controls Yes Yes YesFirm FE Yes Yes YesYear FE Yes Yes Yes
Observations 21,960 14,020 14,020R2 0.967 0.489 0.561Adjusted R2 0.958 0.361 0.451
Note: ∗p<0.1; ∗∗p<0.05; ∗∗∗p<0.01
This table shows the results of the dynamic coefficient regressions specified in Model (3.4). The dependent variable incolumn (1), is Coverage, the number of analysts covering a specific firm in fiscal year t. The dependent variable incolumn (2), is Forecast Error, defined as the absolute distance between the firm’s actual annual earnings per shareand the mean of the analyst forecasts, scaled by the firm’s previous year-end price. The dependent variable in column(3) is Forecast Dispersion, defined as the standard deviation of all the forecasts across all the analysts following thesame firm in the same year, scaled by the firm’s previous year-end price. EU is a dummy variable equal to one if thefirm is domiciled and listed in Europe. Y 15, Y 16, Y 17, Y 18 are year dummy variables equal to one if year t is equalto 2015, 2016, 2017, 2018. We include other important firm level controls whose definitions and constructions can befound in the Appendix C.1.3. Standard errors are clustered at the country level.
237
Table C.5: Intensive Margin (Dynamic Coefficients)
Dependent variable:
Forecast Error (Analyst) (%) Average Forecast Error (%)
(1) (2) (3)
EU × Y15 0.031 0.010 0.015(0.039) (0.037) (0.055)
EU × Y16 −0.044 −0.075∗ −0.034(0.036) (0.038) (0.060)
EU × Y17 0.004 −0.008 −0.017(0.037) (0.039) (0.065)
EU × Y18 −0.132∗∗∗ −0.150∗∗∗ −0.158∗∗
(0.041) (0.042) (0.077)
Frim level Controls Yes Yes YesAnalyst level Controls × Post Yes Yes YesAnalyst FE Yes Yes YesFirm FE Yes No NoYear FE Yes Yes NoB House FE No Yes NoB House FE × Year FE No No Yes
Observations 81,445 12,990 4,111R2 0.422 0.559 0.598Adjusted R2 0.378 0.431 0.480
Note: ∗p<0.1; ∗∗p<0.05; ∗∗∗p<0.01
This table shows the results of the dynamic coefficient regressions specified in Model (3.4). The dependent variablein column (1), is Forecast Error (Analyst), defined as the absolute distance between the actual annual earningsper share and the analyst’s forecast, scaled by the firm’s previous year-end price. The dependent variable in column(2) and (3) is Average Forecast Error, defined as the average of forecast errors across all the firms the analystcovers in a given year. EU is a dummy variable equal to one if the analyst’s portfolio consists of at least 70% of EUstock and zero if the analyst’s portfolio consists of at most 30% of EU stocks. Y 15, Y 16, Y 17, Y 18 are year dummyvariables equal to one if year t is equal to 2015, 2016, 2017, 2018. We include all the analysts (small and large) usedin the intensive margin analyses. Standard errors are clustered at the firms level in column (1) and at the analyst levelin column (2) and (3).
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C.4.2 Additional results for firm level coverage
Table C.6: Firm Level Coverage (Sample for Coverage Quality).
Dependent variable:
Coverage
Full Small vs Large Triple Diff
(1) (2) (3)
EU × POST −1.219∗∗∗ −2.496∗∗∗
(0.322) (0.391)
EU × POST × SMALL 2.551∗∗∗
(0.242)
SMALL × POST 1.968∗∗∗ −0.564∗∗∗
(0.229) (0.009)
Controls Yes Yes YesFirm FE Yes Yes YesYear FE Yes Yes Yes
Observations 14,020 5,555 14,020R2 0.964 0.965 0.964Adjusted R2 0.954 0.956 0.955
Note: ∗p<0.1; ∗∗p<0.05; ∗∗∗p<0.01
This table shows the results of the panel regressions specified in Model (3.1) on the sample for coverage quality. Thedependent variable is Coverage, the number of unique analysts covering a specific firm in fiscal year t. EU is adummy variable equal to one if the firm is domiciled and listed in Europe. POST is a dummy variable equal toone if the fiscal year t is equal to 2018. SMALL is a dummy variable equal to one if firms’ average fiscal year-endmarket capitalization over the pre-regulation years falls below the median. To maintain the proportion of EU and USfirms fixed, we calculate the cutoff separately in both regions. Column (1) is the result of the difference-in-differenceregression between EU firms and US firms. Column (2)is the result of the difference-in-difference regression betweensmall firms and larger firms within the EU. Column (3) is the result of the triple-difference regression. Standard errorsare clustered at the country level.
239
Table C.7: Firm Level Coverage (Results in logs).
Dependent variable:
LN (1+Coverage) LN Coverage
Full Small vs Large Triple Diff Full Small vs Large Triple Diff
(1) (2) (3) (4) (5) (6)
EU × POST −0.008 −0.076∗∗∗ −0.036 −0.116∗∗∗
(0.018) (0.024) (0.023) (0.021)
EU × POST × SMALL 0.137∗∗∗ 0.160∗∗∗
(0.031) (0.017)
SMALL × POST 0.086∗∗∗ −0.054∗∗∗ 0.079∗∗∗ −0.079∗∗∗
(0.031) (0.002) (0.018) (0.001)
Controls Yes Yes Yes Yes Yes YesFirm FE Yes Yes Yes Yes Yes YesYear FE Yes Yes Yes Yes Yes Yes
Observations 21,960 10,665 21,960 14,020 5,555 14,020R2 0.943 0.945 0.943 0.947 0.952 0.947Adjusted R2 0.928 0.931 0.928 0.933 0.939 0.934
Note: ∗p<0.1; ∗∗p<0.05; ∗∗∗p<0.01
This table shows the results of panel regressions specified in Model (3.1). The dependent variable in column (1) tocolumn (3) is Log (1 + Coverage), the log of 1 + the number of unique analysts covering a specific firm in fiscalyear t. The dependent variable in column (4) to column (6) is Log Coverage, log of the number of unique analystscovering a specific firm in fiscal year t. EU is a dummy variable equal to one if the firm is domiciled and listed inEurope. POST is a dummy variable equal to one if the fiscal year t is equal to 2018. SMALL is a dummy variableequal to one if firms’ average fiscal year-end market capitalization over the pre-regulation years falls below the median.To maintain the proportion of EU and US firms fixed, we calculate the cutoff separately in both regions.Column (1)to column (3) are results obtained in the sample for coverage quantity. Since coverage can be 0 in this sample, we put1 + Coverage inside the log function. Column (4) to (6) are the results obtained in the sample for coverage quality.Column (1) and column (4) are the results for the difference-in-difference regression between EU firms and US firms.Column (2) and column (5) are the results for the difference-in-difference regression between small firms and largerfirms within the EU. Column (3) and Column (6) are the results for the triple-difference regression. Standard errorsare clustered at the country level.
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Table C.8: Firm Level Coverage (EU Small vs. US Small and EU Large vs. US Large)
Dependent variable:
Coverage
Full Small Large Triple Diff
(1) (2) (3) (4)
EU × POST −0.651∗∗∗ 0.373∗∗∗ −1.634∗∗∗ −1.594∗∗∗
(0.196) (0.094) (0.289) (0.268)
EU × POST × SMALL 1.891∗∗∗
(0.200)
SMALL × POST −0.228∗∗∗
(0.018)
Controls Yes Yes Yes YesFirm FE Yes Yes Yes YesYear FE Yes Yes Yes Yes
Observations 21,960 10,985 10,975 21,960R2 0.967 0.874 0.955 0.967Adjusted R2 0.958 0.843 0.944 0.959
Note: ∗p<0.1; ∗∗p<0.05; ∗∗∗p<0.01
This table shows the results of panel regressions specified in Model (3.1) and Model (3.3). The dependent variable isCoverage, the number of unique analysts covering a specific firm j in fiscal year t. EU is a dummy variable equalto one if the firm is domiciled and listed in Europe. POST is a dummy variable equal to one if the fiscal year t isequal to 2018. SMALL is a dummy variable equal to one if firms’ average fiscal year-end market capitalization overthe pre-regulation years falls below the median. To maintain the proportion of EU and US firms fixed, we calculatethe cutoff separately in both regions. We split the firms into small firms and large firms and perform difference-in-difference analyses separately for them. Column (1) to column (3) are results for all the firms, small firms, and largefirms respectively. Column (4) is the result of the triple-difference regression. Standard errors are clustered at thecountry level.
241
C.4.3 Additional results for analyst informativeness
Table C.9: Analyst Informativeness (Small vs. Large).
Dependent variable:
Analyst Informativeness Aggregate Analyst Informativeness
Full Small vs Large Triple Diff Full Small vs Large Triple Diff
(1) (2) (3) (4) (5) (6)
EU × POST 0.0003∗∗∗ 0.0004∗∗∗ −0.009∗∗∗ −0.016∗∗∗
(0.0001) (0.0001) (0.001) (0.002)
EU × POST × SMALL −0.0002 0.016∗∗∗
(0.0002) (0.003)
SMALL × POST 0.0002 0.0004∗∗∗ 0.011∗∗∗ −0.006∗∗∗
(0.0002) (0.0001) (0.002) (0.002)
Controls Yes Yes Yes Yes Yes YesFirm FE Yes Yes Yes Yes Yes YesYear FE Yes Yes Yes Yes Yes Yes
Observations 19,391 8,844 19,391 19,391 8,844 19,391R2 0.496 0.398 0.496 0.917 0.924 0.917Adjusted R2 0.353 0.218 0.353 0.894 0.902 0.894
Note: ∗p<0.1; ∗∗p<0.05; ∗∗∗p<0.01
This table shows the results of panel regressions similar to Model (3.1). The dependent variable in column (1) tocolumn (3) is Analyst Informativeness. It captures the average informativeness of one forecast revision date. Thedependent variable in column (4) to column (6) is Aggregate Analyst Informativeness. It captures the aggregateinformativeness of all revision dates. EU is a dummy variable equal to one if the firm is domiciled and listed inEurope. POST is a dummy variable equal to one if the fiscal year t is equal to 2018. SMALL is a dummy variableequal to one if firms’ average fiscal year-end market capitalization over the pre-regulation years falls below the median.To maintain the proportion of EU and US firms fixed, we calculate the cutoff separately in both regions. Column (1)and column (4) are the results for the difference-in-difference regression between EU firms and US firms. Column (2)and column (5) are the results for the difference-in-difference regression between small firms and larger firms withinthe EU. Column (3) and Column (6) are the results for the triple-difference regression. Standard errors are clusteredat the firm level.
242
C.5 Propensity score matching
In our difference-in-difference analyses, we use EU firms as the treatment group and US firms
as the control group. One concern is that firms in these two continents are different. For example,
Table 3.1 shows that US firms are in general larger, have lower book-to-market ratios and lower
ROAs. Although we explicitly control for these firm level characteristics, the differences may
still confound the effects of unbundling. In this section, we conduct a standard propensity score
matching to further check whether our results are driven by the observable differences in the firm
level characteristics.
In the sample for coverage quantity, we use 2014 data and match EU firms with US firms ac-
cording to their book to market ratio, investment return, market capitalization, return on assets and
return volatility. We choose the nearest-neighbor matching method and set the caliper parameter to
be 0.25 standard deviation of the estimated propensity scores (e.g., Rosenbaum and Rubin (1985)).
With this restriction, nearest- neighbor matching will be considered only if |Pt − Pc| < 0.25σp,
where Pt and Pc are the propensity scores for the treatment and the control, and σp is the standard
deviation of the estimated propensity score of the sample.55 We repeat a similar process in the
sample for coverage quality but include distance (the average of the days between the analyst fore-
cast date and the firm’s actual EPS report date) as an additional matching covariate. Table C.10
shows the summary statistics of the covariates before and after the matching. After the propensity
score matching, in the sample for coverage quantity, the treatment group and the control group
are only different in the investment return and market capitalization. In the sample for coverage
quality, the treatment group and the control group are comparable along all the firm level char-
acteristics. Figure C.5 shows the histograms of the propensity scores after matching. We can
observe that the distributions between treatment group and control groups are comparable. In fact,
a formal Kolmogoro-Smirnov test on the two samples does not reject the null that the treatment
sample and the control sample are drawn from the same distribution. Hence, the propensity score
55We do not have a large number of control firms to select. Requiring each firm in the treatment group to bematched with a firm in the control group will again introduce dissimilarities between the two groups.
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matching effectively removes observations that are too different between the two groups based on
observables.
We then repeat the difference-in-difference analyses at the firm level. Table C.11 reports the
results. Consistent with what we find before, analyst coverage drops for EU firms and the drop is
concentrated in large firms. Similarly, forecast errors of EU firms decrease. The magnitude of these
coefficients is comparable with our baseline results without matching. Hence we conclude that
observable differences between EU firms and US firms do not drive our results and US firms could
serve as a valid counterfactual. In untabulated tests, we performance propensity score matching at
the analyst level for the intensive margin analyses and obtain similar results to the baseline model
in which we do not match the observations.
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Figure C.5: Distributions of Propensity Scores after Matching.
ControlTreated
0.25
0.50
0.75
1.00
0.3 0.2 0.1 0 0.1 0.2 0.3Fraction of the Data
Pro
pens
ity S
core
(a) Sample for Coverage Quantity
ControlTreated
0.25
0.50
0.75
1.00
0.3 0.2 0.1 0 0.1 0.2 0.3Fraction of the Data
Pro
pens
ity S
core
(b) Sample for Coverage Quality
This figure plots the histogram of the propensity scores in the matched sample between the treatment group and thecontrol group.
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Table C.10: Covariates Balance Table.
Panel A: Before Matching (Sample for Coverage Quantity)
Treated Control Diff P-value
N of Obs 2133 2259 126BM (%) 2.53 1.73 0.80 0.00Investment Return (%) 13.82 8.27 5.55 0.00Market Cap (Bil $) 5.24 9.21 −3.97 0.00ROA (%) 2.87 1.53 1.34 0.09Return Volatility 32.39 32.06 0.33 0.53
Panel B: After Matching (Sample for Coverage Quantity)
Treated Control Diff P-value
N of Obs 2074 2074 0BM (%) 1.97 1.78 0.19 0.11Investment Return (%) 11.83 9.20 2.63 0.02Market Cap (Bil $) 5.25 6.36 1.11 0.04ROA (%) 3.01 2.05 0.96 0.11Return Volatility 32.11 32.01 0.10 0.86
Panel C: Before Matching (Sample for Coverage Quality)
Treated Control Diff P-value
N of Obs 1111 1693 582BM (%) 2.44 1.53 0.91 0.00Distance 120.24 114.43 5.81 0.00Investment Return (%) 15.18 10.10 5.08 0.00Market Cap (Bil $) 9.45 11.96 2.51 0.04ROA (%) 6.08 4.26 1.82 0.00Return Volatility 26.26 28.35 −2.09 0.00
Panel D: After Matching (Sample for Coverage Quality)
Treated Control Diff P-value
N of Obs 1067 1067 0BM (%) 1.74 1.74 0.00 0.96Distance 118.86 117.37 1.49 0.38Investment Return (%) 14.75 13.35 0.408 0.31Market Cap (Bil $) 9.29 8.34 0.95 0.31ROA (%) 5.91 5.24 0.67 0.10Return Volatility 26.34 26.64 −0.30 0.52
This table shows the difference in the average values of matching covariates before and after the propensity scorematching. Book to Market is defined as total asset (Worldscope item 02999) minus long-term debt (Worldscope item03251) over market value (Worldscope item 08002). Distance is the average of the days between the analyst forecastdate and the firm’s actual EPS report date. We take the average over all the analysts following the same firm andmeasure this variable in 2014. Investment return is Worldscope item 08801, measured as (market price at year t+dividends−market price at year t − 1)/market price at year t − 1). Market capitalization is Worldscope Item 08002measured in billion dollars. Return on Assets is Worldscope Item 08326. Return volatility is the annualized standarddeviation of daily returns over a year for a given firm. Panel A and Panel show the results of sample for coveragequantity and Panel C and Panel D shows the results of the sample for coverage quality.
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Table C.11: Firm Level Outcomes (Propensity Score Matching).
Dependent variable:
Coverage Forecast Error
Full Small vs Large Triple Diff Full Small vs Large Triple Diff
(1) (2) (3) (4) (5) (6)
EU × POST −0.694∗∗∗ −1.568∗∗∗ −0.141∗∗∗ −0.120∗∗
(0.193) (0.266) (0.036) (0.048)
EU × POST × SMALL 1.753∗∗∗ −0.042(0.198) (0.065)
SMALL × POST 1.662∗∗∗ −0.102∗∗∗ 0.061 0.083∗∗∗
(0.203) (0.017) (0.059) (0.016)
Controls Yes Yes Yes Yes Yes YesFirm FE Yes Yes Yes Yes Yes YesYear FE Yes Yes Yes Yes Yes Yes
Observations 20,780 10,390 20,780 10,670 5,335 10,670R2 0.965 0.972 0.965 0.500 0.499 0.500Adjusted R2 0.956 0.964 0.957 0.374 0.372 0.374
Note: ∗p<0.1; ∗∗p<0.05; ∗∗∗p<0.01
This table shows the results of the panel regressions specified in Model (3.1) and Model (3.3). We use the propensityscore matching and match EU firms with US firms according to their book to market ratio, investment return, marketcapitalization, return on assets and return volatility. For the sample for coverage quality, we include distance as anadditional matching covariate. All variables are measured in 2014. The dependent variable in column (1) to (3) isCoverage, the number of unique analysts covering a specific firm j in fiscal year t. The dependent variable in column(4) to (6) is Forecast Error, defined as the absolute distance between the firm’s actual EPS and the mean of theanalyst forecasts, scaled by the firm’s previous year-end price. EU is a dummy variable equal to one if the firm isdomiciled and listed in Europe. POST is a dummy variable equal to one if the fiscal year t is equal to 2018. SMALLis a dummy variable equal to one if firms’ average fiscal year-end market capitalization over the pre-regulation yearsfalls below the median. To maintain the proportion of EU and US firms fixed, we calculate the cutoff separately inboth regions. Column (1) and column (4) are the results for the difference-in-difference regression between EU firmsand US firms. Column (2) and column (5) are the results for the difference-in-difference regression between smallfirms and larger firms within the EU. Column (3) and Column (6) are the results for the triple-difference regression.Standard errors are clustered at the country level.
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