Macroeconomic Uncertainty and Corporate Bond

Returns

Turan Bali Quan Wen

Summary

• We investigate the role of economic uncertainty in the cross-sectionof corporate bond returns.

• We document significant uncertainty premium for bothinvestment-grade (0.43% per month) and non-investment-grade(0.94% per month) bonds.

• Mainly driven by the outperformance of corporate bonds with highuncertainty risk.

• Uncertainty-averse institutional investors demand highercompensation to hold corporate bonds with high uncertainty risk.

• Bonds with high uncertainty risk have recently experienced anincrease in credit risk (i.e., rating downgrade) which results in animmediate negative price response, followed by higher future returns.

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Motivation

• The intertemporal capital asset pricing model (ICAPM) of Merton(1973) and Campbell (1993; 1996) indicates that in a multi-periodeconomy, investors have incentive to hedge against future stochasticshifts in consumption and investment opportunity sets.

• The ICAPM implies that state variables that are correlated withchanges in consumption and investment opportunities are priced incapital markets.

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Motivation

• Past studies provide theoretical and empirical support for the ideathat time variation in the conditional volatility of macroeconomicshocks is linked to real economic activity and asset returns (see e.g.,Gomes, Kogan and Zhang, 2003; Bloom, 2009; Allen, Bali, andTang, 2012; Drechsler, 2013; and Jurado, Ludvigson, and Ng, 2015).

• Therefore, economic uncertainty is a relevant state variable thataffects future consumption and investment decisions.

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Economic Uncertainty Index

• Bali, Brown, Caglayan (JFE, 2014)

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Economic Uncertainty Index

• Jurado, Ludvigson, and Ng (AER, 2015)

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The U.S. Corporate Bond Market

• $1.74 trillion in 1990; $11.72 trillion in 2015; annual growth rate = 8.5%• Annual issuance of $1.3 trillion ($0.3 tril. for stocks) since 2010• Daily trading volume between $12.6 and $19.7 billion since 2000• 82% of corporate bonds were held by institutional investors (insurance

companies, mutual/pension funds).

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Measuring Return and Bond Return Characteristics

• Excess return on corporate bond i at month t,

Rexcessi,t =

(Pi,t + AIi,t + Couponi,t

Pi,t−1 + AIi,t−1− 1

)− Rf ,t

- Final sample includes 61,871 bonds issued by 4,222 unique firms, fora total of 1,261,667 bond-month return observations for the periodJuly 2002 – December 2015. On average, there are 7,788 bonds permonth over the whole sample.

- About 78% are investment-grade and the remaining 22% arehigh-yield bonds.

• The uncertainty beta (βUNCi,t )

– Estimated from the monthly rolling regressions of excess bondreturns on the change in the economic uncertainty index (∆UNC)over a 36-month fied window while controlling for the bond marketportfolio (MKT):

Ri,t = αi,t + βUNCi,t · ∆UNCt + βMKT

i,t ·MKTt + εi,t ,

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Positive vs. Negative βUNC

Ri,t = αi,t + βUNCi,t · ∆UNCt + βMKT

i,t ·MKTt + εi,t ,

• Bonds with a negative uncertainty beta (βUNC < 0) can be viewedas riskier assets with high uncertainty risk because the returns ofthese bonds decrease during periods of high economic uncertainty.

• Bonds with a positive uncertainty beta (βUNC > 0) can be viewed aseffective hedging instruments providing large hedging benefitsbecause the returns of these bonds increase during periods of higheconomic uncertainty.

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Quintile Portfolios of Corporate Bonds Sorted by Uncertainty BetaQuintiles Average Average 5-factor stock 5-factor bond 10-factor

βUNC return alpha alpha alpha

Low βUNC -1.41 1.35 1.44 1.22 1.48(3.96) (4.17) (3.78) (4.19)

2 -0.40 0.57 0.57 0.48 0.58(3.46) (3.36) (3.48) (3.85)

3 -0.14 0.35 0.33 0.29 0.34(2.96) (2.63) (1.68) (1.96)

4 0.03 0.29 0.28 0.24 0.27(2.83) (2.48) (1.32) (1.59)

High βUNC 0.38 0.43 0.42 0.35 0.40(2.91) (2.68) (1.52) (1.64)

High − Low 1.79∗∗∗ -0.92∗∗∗ -1.02∗∗∗ -0.86∗∗∗ -1.08∗∗∗

t-stat (11.08) (-3.38) (-3.44) (-3.07) (-3.50)

• 10-factor: (i) MKTStock , SMB, HML, MOMStock , LIQ and (ii) MKTBond ,TERM, DEF, MOMBond , LIQBond

• Bonds in the lowest-βUNC quintile generate 11.04% per annum higher returnsthan bonds in the highest-βUNC quintile do.

• Robust controlling for five stock and five bond market factors.

• The alpha spread is due to outperformance by lowest-βUNC bonds, but not tounderperformance by high-βUNC bonds.

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Long-term Predictability

• βUNC has longer-term predictive power, lasting up to one year into the future.

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Fama-MacBeth Cross-Sectional Regressions

Model Int. βUNC βMKT βDEF βTERM βVIX ILLIQ Rating Maturity Size Lag Ret Adj. R2

(1) 0.350 -0.429 0.038(2.62) (-2.51)

(2) 0.316 -0.580 0.213 -0.023 -0.015 -0.094 0.090(2.51) (-3.31) (3.04) (-4.07) (-0.87) (-0.76)

(3) 0.231 -0.468 0.144 -0.020 -0.011 -0.095 0.057 0.117(2.11) (-2.87) (1.81) (-3.16) (-0.60) (-0.62) (6.20)

(4) -0.150 -0.448 0.173 -0.020 -0.020 0.048 0.060 0.113(-1.09) (-2.94) (3.14) (-3.68) (-1.19) (0.46) (2.81)

(5) 0.240 -0.547 0.211 -0.023 -0.014 -0.121 0.008 0.117(2.42) (-3.11) (3.02) (-3.92) (-0.80) (-0.92) (1.21)

(6) 0.318 -0.562 0.217 -0.023 -0.017 -0.104 -0.018 0.095(2.28) (-3.19) (3.03) (-3.97) (-0.96) (-0.81) (-0.36)

(7) 0.308 -0.504 0.157 -0.019 -0.009 -0.045 -0.071 0.114(2.60) (-2.80) (2.02) (-3.07) (-0.65) (-0.39) (-5.07)

(8) -0.238 -0.310 0.079 -0.013 -0.014 -0.041 0.060 0.051 0.006 0.069 -0.115 0.196(-1.99) (-2.05) (1.46) (-2.06) (-1.02) (-0.31) (8.18) (2.53) (0.87) (2.44) (-8.37)

• Bond uncertainty beta has distinct, significant information orthogonal tomarket risk, default risk, interest rate risk, market volatility risk, illiquidity,rating, maturity, and size and it is a strong and robust predictor of futurebond returns.

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Further Evidence from Credit Ratings Downgrade

∆Rating

t − 12 : t t − 24 : t t − 36 : t

Low βUNC 0.56 1.24 2.072 0.21 0.41 0.623 0.10 0.20 0.284 0.06 0.12 0.17

High βUNC 0.13 0.28 0.38

High − Low -0.43∗∗ -0.96∗∗∗ -1.69∗∗∗

t-stat (-2.39) (-3.75) (-5.26)

• Bonds with negative-βUNC , on average, have recently experienced an increase incredit risk (i.e., credit rating downgrade).

• Resulting in an immediate negative price response, followed by higher futurereturns −→ part of the driving forces for the uncertainty premium.

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Robustness Check (2): Investment-Grade Bonds Sorted by Uncertainty

Beta

Quintiles Average Average 5-factor stock 5-factor bond 10-factor

βUNC return alpha alpha alpha

Low βUNC -0.77 0.70 0.76 0.59 0.72(3.39) (3.42) (2.97) (3.25)

2 -0.24 0.37 0.37 0.32 0.37(2.86) (2.59) (2.55) (2.65)

3 -0.08 0.30 0.29 0.27 0.30(2.88) (2.62) (1.56) (2.73)

4 0.06 0.26 0.26 0.22 0.25(2.76) (2.52) (1.23) (1.46)

High βUNC 0.36 0.27 0.26 0.18 0.32(2.47) (2.33) (1.97) (1.16)

High − Low 1.13∗∗∗ -0.43∗∗ -0.50∗∗∗ -0.41∗∗ -0.40∗∗

t-stat (16.34) (-2.18) (-2.23) (-2.48) (-2.39)

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Robustness Check (3): Non-Investment-Grade Bonds Sorted by

Uncertainty Beta

Quintiles Average Average 5-factor stock 5-factor bond 10-factorβUNC return alpha alpha alpha

Low βUNC -2.21 1.63 1.72 1.47 1.78(3.95) (4.13) (3.89) (4.63)

2 -1.07 1.21 1.24 1.06 1.31(3.10) (3.19) (3.01) (3.25)

3 -0.52 0.77 0.73 0.60 0.73(3.05) (2.84) (2.95) (3.20)

4 -0.14 0.52 0.48 0.38 0.44(2.88) (2.37) (2.50) (2.69)

High βUNC 0.39 0.69 0.65 0.57 0.63(3.40) (2.97) (3.07) (3.13)

High − Low 2.59∗∗∗ -0.94∗∗∗ -1.07∗∗∗ -0.90∗∗∗ -1.15∗∗∗

t-stat (12.18) (-2.84) (-2.84) (-2.70) (-3.12)

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Summary Statistics for the Uncertainty Beta Factor

Full sample Mean t-stat

UNCF 0.54 3.01

Good states Mean t-stat Bad states Mean t-stat

CFNIA > −0.7 0.32 2.72 CFNAI ≤ −0.7 1.40 2.52

MKTStock > 0 0.50 3.24 MKTStock≤ 0 0.71 2.00

VIX ≤ VIXmedian 0.29 2.59 VIX > VIXmedian 1.38 2.79

DEF ≤ DEFmedian 0.25 2.22 DEF > DEFmedian 0.60 2.92

ILLIQ ≤ ILLIQmedian 0.17 1.08 ILLIQ > ILLIQmedian 1.06 3.43

• The uncertainty beta factor has economically and statistically significantpremium.

• Risk premia higher during financial and economic downturns.

• Consistent with the intermediate asset pricing (IAP) theory, uncertainty premiumhigher during periods of high market volatility, high default risk, and low marketliquidity.

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Testing Framework

• We examine the explanatory power of the uncertainty beta factor forthree distinct sets of test portfolios that do not necessarily relate toeconomic uncertainty (Lewellen, Nagel, and Shanken, 2010).

• We assess the the performance of the newly proposed model withthe uncertainty beta factor (Model 4):

– Model 4: 4-factor model with the uncertainty beta factor; MKTBond ,DEF, TERM, and UNCF ,

• Three test portfolios:

– 5×5 independently sorted bivariate portfolios of size and maturity.– 5×5 independently sorted bivariate portfolios of size and rating.– 12-industry portfolios of corporate bonds.

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Corporate Bond Uncertainty Beta and Firm Fundamentals3-month ahead 6-month aheadt + 1 : t + 3 t + 4 : t + 6

Operating Net Operating NetQuintiles profitability income profitability income

Low βUNC 0.74 0.68 3.39 3.442 1.59 1.41 2.06 1.893 0.44 0.30 0.66 0.374 0.42 0.21 1.04 0.57

High βUNC 1.18 1.24 0.65 0.76

High − Low 0.44 0.56 -2.74** -2.68**t-stat 0.19 0.23 -2.41 -2.31

9-month ahead 12-month aheadt + 7 : t + 9 t + 10 : t + 12

Operating Net Operating NetQuintiles profitability income profitability income

Low βUNC 1.95 1.85 4.29 4.342 2.52 2.30 2.53 2.383 0.90 0.67 1.32 1.054 0.75 0.31 1.21 0.56

High βUNC 0.21 0.18 0.53 0.43

High − Low -1.74** -1.67** -3.75*** -3.91***t-stat -2.05 -2.12 -2.99 -2.92

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Equity Uncertainty Beta and Firm Fundamentals

12-month ahead 24-month ahead 36-month aheadt + 1 : t + 12 t + 1 : t + 24 t + 1 : t + 36

Quintiles ∆MKT ∆MKT ∆MKTLeverage ∆Rating Leverage ∆Rating Leverage ∆Rating

Low βUNC 1.35 0.08 2.72 0.24 3.86 0.332 2.55 0.05 8.60 0.18 8.88 0.273 2.67 0.07 2.50 0.15 8.99 0.194 2.83 0.06 9.98 0.53 9.74 0.80

High βUNC 3.32 0.10 10.76 0.74 11.12 1.29

High − Low 1.97* 0.02 8.04*** 0.50** 7.26*** 0.96***t-stat 1.78 0.30 3.52 2.91 3.04 3.82

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Conclusion

• We document significant uncertainty premium for both investment-grade (0.43%per month) and non-investment-grade (0.94% per month) bonds.

• Mainly driven by the outperformance of corporate bonds with high uncertaintyrisk.

• Long-term predictability and credit ratings downgrade support the risk-basedexplanation of the uncertainty premium.

• Bonds with high uncertainty risk have recently experienced an increase in creditrisk (i.e., credit rating downgrade) which results in an immediate negative priceresponse, followed by higher future returns.

• Significantly large abnormal returns on bond portfolios generated by the existingfactor models are in fact compensation for macroeconomic risk.

• Therefore, institutional investors in the corporate bond market should accountfor bond exposure to economic uncertainty to accurately determine therisk-adjusted performance of their bond portfolios.

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