Structural Modeling in Practiceweb-docs.stern.nyu.edu/salomon/docs/Credit2006/Bohn.pdf · Agenda 1....

Structural Modeling in Practice

Dr. Jeffrey R. BohnHead of Research

Agenda

1. Paper Summary2. Structural Models in Practice3. Validation4. Final Thoughts5. Appendix

Paper Summary

MOODY’S KMV COMPANY. ALL RIGHTS RESERVED.4 17 May 2006COPYRIGHT ©

Test Two Hypotheses

Hypothesis 1: Black-Scholes-Merton (BSM)-based probability of default is a sufficient statistic for forecasting bankruptcy (default).

Hypothesis 2: When predicting default, the BSM model can be useful. This usefulness potentially arises from two components:

Functional form implied by the modelSolution of system of equations

“…it is entirely possible that the proprietary features of KMV’s model make its performance superior to what we document here.” p. 8


What’s in a model name?

Pseudo-“KMV-Merton” (PK): “We do not intend to imply that we are using exactly the same algorithm that Moody’s KMV uses to calculate distance to default.” footnote 2, p.1.

Naïve alternative (NA): Simple model to calculate, but retains some of the functional form of “KMV-Merton.”

Vasicek-Kealhofer (VK): Extension of BSM to barrier, perpetual option and richer capital structure framework. Note the model is not proprietary for clients.

Moody’s KMV (MKMV): Implementation of VK model to produce Expected Default Frequencies™ or EDF™ values.


Hypotheses Tested in the Following Ways on Default Data from 1980 to 2003

1. Incorporate PK into hazard model and compare PK to NA and other default forecasting variables.2. Compare short-term, out-of-sample forecasting ability of PK and NA.3. Compare several alternative approaches to calculating a PK value.4. Test the ability of PK to explain CDS-implied probabilities of default.5. Investigate via regression the relationship of corporate bond yield spreads and PK, NA, and other variables.


Stated Findings

PK values are not sufficient statistics for bankruptcy (default) prediction.

NA model performs as well as PK.

Test on 80 firms published in CFO magazine in 2003 shows NA has rank correlation of 79% with MKMV’s published EDF values.


Testing for Sufficient Statistic

Authors assume Cox-proportional hazard model for testing statistical sufficiency imposing linearity assumption on functional form.

If the model is mis-specified and certain relationships exist among the variables, this test may lead to false rejection of statistical sufficiency for the independent variable.

Better to use non-parametric tests (see Miller article.)


References

Arora, Navneet, Jeffrey Bohn, and Fanlin Zhu, 2005, Reduced Form vs. Structural Models: A Case Study of Three Models, Journal of Investment Management, Vol. 3 No. 4, pp. 43-67.

Bohn, Jeffrey, Navneet Arora, and Irina Korablev, 2005, Power and Level Validation of the Moody’s KMV EDF™ Credit Measure in the U.S. Market, MKMV White Paper.

Duffie, Darrell, Antje Berndt, Rohan Douglas, Mark Ferguson, and David Schranz, 2005, Measuring Default-Risk Premia from Default Swap Rates and EDFs, Stanford University.

Duffie, Darrell and David Lando, 2001, Term Structure of Credit Spreads with Incomplete Accounting Information, Econometrica, Vol. 69, pp. 633-664.

Duffie, Darrell, Leandro Saita, and Ke Wang, 2005, Multi-period Corporate Failure Prediction with Stochastic Covariates, CIRJE Discussion Paper.

Miller, Ross, August, 1998, Refining Ratings, Risk Magazine, Vol. 11 No. 8.Schaefer, Stephen and Strebulaev, Illya A., 2004, Structural Models of Credit Risk are

Useful: Evidence from Hedge Ratios on Corporate Bonds, Institute of Finance and Accounting Working Paper.

Stein, Roger, 2005, Evidence on the Incompleteness of Merton-type Structural Models for Default Prediction, MKMV White Paper.

Stein, Roger, Ahmet Kocagil, Jeffrey Bohn, and Jalal Akhavein, 2003, Systematic and Idosyncratic Risk in Middle-Market Default Prediction: A Study of the Performance of the RiskCalc™ and PFM™ Models, MKMV White Paper.

Structural Models in Practice


What are some other practical consideration for PD model assessment?

Diagnosability of model behavior.

Corporate transaction analysis.

Data quality and data cleaning.

Adjusting for missing or hidden defaults.

Segmenting sample by firm size.

Ability to process thousands (30,000) of firms on a daily basis.

Ability to cover newly established firms.


Vasicek-Kealhofer Model: An Extension of the BSM Framework

Black-Scholes-Merton Vasicek-Kealhofer EDF Model

Two classes of Liabilities: Short Term Liabilities and Common Stock

Five Classes of Liabilities: Short Term and Long Term Liabilities, Common Stock, Preferred Stock, and Convertible Stock

No Cash Payouts Cash Payouts: Coupons and Dividends (Common and Preferred)

Default occurs only at Horizon. Default can occur at or before Horizon.

Default barrier is total debt. Default barrier is empirically determined.

Equity is a call option on Assets, expiring at the Maturity of the debt.

Equity is a perpetual call option on Assets

Gaussian relationship between probability of default (PD) and distance to default (DD).

DD-to-EDF mapping empirically determined from calibration to historical data.


Dividend Payout Impact

MARINE PETROLEUM TRUST

EDF value considering dividend leakageEDF value ignoring dividend leakage

edf1

0.02

0.04

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YearMon

200507 200508 200509 200510 200511 200512 200601 200602 200603


Modeled Volatility for IPOs: 20% to 40% Asset Volatility

• New firms have unusually volatile equity leading to an over-estimate of asset volatility. • MKMV’s estimate of asset volatility is based on a weighted average of empirical volatility and modeled volatility.• Modeled volatility is related to the size, industry, and geography of the firm. • Modeled volatility helps alleviate difficulties with estimating asset volatility for new firms.


Modeled Volatility for IPOs: 40% to 80%

• New firms have unusually volatile equity leading to an over-estimate of asset volatility. • MKMV’s estimate of asset volatility is based on a weighted average of empirical volatility and modeled volatility.• Modeled volatility is related to the size, industry, and geography of the firm. • Modeled volatility helps alleviate difficulties with estimating asset volatility for new firms.


Impact of Modeled Volatility on Companies with Short Histories

RELIANT ENERGY INC

Empirical VolAfter combining with modeled Vol.

0.110.120.130.140.150.160.170.180.190.200.210.220.230.240.250.260.270.28

YearMon

200105

200106

200107

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200112

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Impact of Event Processing: Reducing Debt

Asset vol. went from 8% to 11% and maintained the level till next event.

Asset vol. went from 10% to 8% and maintained the level since then.


Impact of Event Processing: Changing Debt

Asset vol. went from 13% to 20% and maintained the level till next event.

Asset vol. went from 20% to 24% and maintained the level since then.


More Complexity Facilitates More Effective Handling of Actual Companies

Important to account for the total debt breakdown between short-term and long-term debt. Perpetual down-and-out option assumption consistent with firm’s treatment as an “ongoing concern”. Provides unique asset value and volatility assessment. Otherwise inferred current asset value and volatility are a function of “time-to-maturity”, making them meaningless.Low volatility firms with decent asset value paying out heavy dividends.Extensive changes in leverage over time inducing non-stationary equity volatility.Unusually large amount of convertible securities in capital structure.Empirical mapping helps capture realistic default experience.

Validation


How should PD models be evaluated?

Ranking (Sample dependencies, size of sample)

Timeliness (Aggregates vs. outliers)

Accuracy as a probability (Means vs. medians)

Explaining spreads (Disentangling loss given default, risk premia, other premia)

Corporate transaction analysis (Post transaction asset volatility impact)

Interpretation of inputs and outputs and model transparency (Model risk)

Usefulness in pricing applications (Requires term structure of EDF values)


Functional Form versus Estimation Process

Start with NA as base

Add the following replacement variables representing more sophisticated estimation:

ASG: “Raw” empirical asset volatility CSG: Blended estimation of asset volatility based on ASG and modeled volatilityXDP: MKMV’s calculated default point reflecting mostly adjustments for financial firmsVK: Implementation of just the VK model without the benefit of MKMV’s event processing system and data cleaning effortsMKMV: Full implementation of VK model with full benefit of the system

Estimation process and solving system significantly improves model performance


Comparing Models: Time Period 1996 to 2006

Sample: 3/1996 to 2/2006, U.S. companies, Book Asset > $30 million

(approximately 600,000 firm-month observations)

CAP Curve

00.10.20.30.40.50.60.70.80.9

1

0 0.2 0.4 0.6 0.8 1% Non-Default Excluded

% D

efau

lt Ex

clud

ed

1:NA2:NA+ASG3:NA+CSG4:NA+CSG+XDP5:VK w/o Cash Leak6:MKMV

Model AR

1:NA 0.747392:NA+ASG 0.758773:NA+CSG 0.76184:NA+CSG+XDP 0.764115:VK w/o Cash Leak 0.80716:MKMV 0.81349


Distance-to-Default (DD) and Credit Default Swap (CDS) Spreads

Regressing DD on log(CDS5Y)

0.00%

10.00%

20.00%

30.00%

40.00%

50.00%

60.00%

2003

07

2003

10

2004

01

2004

04

2004

07

2004

10

2005

01

2005

04

2005

07

2005

10

Date

R-S

quar

e

1:NA 2:NA+ASG3:NA+CSG 4:NA+CSG+XDP5:MKMV


Early Warning Power of EDF Measures

Months Before and After Default

ED

F, R

atin

g

MKMV EDFMoody’s Rating

Median EDF and Rating-Implied EDF for Defaulted FirmsUnited States Data: 1996-2004

• Median EDF tends to start rising 24 months before default.

• Median Rating tends to stay flat until a year before default, showing a steep rise about 4 months before default.

• EDF tends to lead the Ratings.

• EDF provides early warning power.

• EDF is dynamic and continuous, while Ratings move in discrete steps.


Does the Predicted Default Rate (EDF) match the Actual Default Rate? (Comparison to median prediction generated using a correlation model for firms in sample.)

Predicted and Actual Number of DefaultsUS Public Non-Financial Firms w/ Sales > 300 M

Years 1991-2004

EDF < 20%


Comparison of Default Predictive Power

Accuracy Ratio

Model Ratio

Merton 0.652

Reduced 0.785

MKMV 0.801


Explanation of Cross-Sectional Variation

Issuers with 4 or fewer bonds outstanding: 57%Percentage of cross-sectional variance explained for issuers of 2 to 4 bonds (median):

Basic Merton: 20%Hull-White: 37%Vasicek-Kealhofer: 46%

Issuers with 10 or more bonds outstanding: 14%Percentage of cross-sectional variance explained for issuers of 10 to 15 bonds (median):

Basic Merton: 46%Hull-White: 64%Vasicek-Kealhofer: 59%

Final Thoughts


Improving the Model Further

Enhance modeled volatility estimation

Consider liquidity-based drivers of default at shorter time horizons

Incorporate pro-forma liabilities

Incorporate macro-economic factors


Conclusion

Structural models have provided useful guidance for estimating PD values

Complexity of function and estimation process add value

Validation is both theoretically and practically difficult, but still important

Sample size is important: Small sample produces wide confidence intervals on validation work

Data quality and data cleaning critical to building useful models

Appendix


What is added to Black-Scholes-Merton in practice?

Richer characterization of capital structure

Tracking “leakage” of asset value

Barrier option modeling

Expanded asset volatility estimation processIterative solution techniqueOutlier handlingCorporate event trackingModeled volatility i.e. shrinkage estimation (industry, country, size)

Empirical specification of default point

Empirical calibration of default probability distribution


Implementation of MKMV Model

Use barrier, perpetual option formula to relate asset value and equity value.Estimate market asset value and market asset volatility using iterative technique on 3 years of weekly data for North American firms and 5 years of monthly data for international firms.Employ trimming algorithm on outliers.Track corporate events to adjust for significant changes in capital structure.Combine “raw” empirical volatility calculated with this process with “modeled” volatility determined from a non-linear regression relating size, country, and industry.Calculate distance-to-default (DD).Map DD into EDF credit measure using empirical mapping based on 30 years of default history.


Equity Value as a Function of Asset Value

E = f(A,σA,κ)σE = ∆*(A/E)* σA

where E = equity valueA = asset valueσE = equity volatility σA = asset volatilityκ = capital structure∆ = hedge ratio


Distance-to-Default (DD)

DD is the distance between the market value of assets and default point measured in standard deviations.

2*

0

0,

ln ln2

AA T

TA

A T Payouts DDD

T

σµ

σ

⎛ ⎞+ − − −⎜ ⎟⎝ ⎠=

*T

AD≡

≡

Market Value of AssetsDefault Point


Asset Volatility: A Measure of Business Risk

Asset V o latility

0%

5%

10%

15%

20%

25%

30%

35%

200 500 1,000 10,000 50,000 100,000 200,000

To ta l Asse ts ($m )

Ann

ualis

ed V

olat

ility

CO M P UTE R S O F TW A REA E RO S P A CE & DE F E NS EF O O D & B E V E RA G E RE TL/W HS LUTILITIE S , E LE CTRICB A NK S A ND S & LS


MKMV Database

MKMV Public FirmDefault Database (Global)

1973-2005

Def

aults

Quarter

• Over 30 years of data• Over 7,600 defaults

• Over 30 years of data• Over 7,600 defaults


Naïve Alternative (NA) Model Specification

E = Market value of firm’s equityF = Face value of firm’s debt

= Firm’s stock return over the previous year

= Equity volatility

( ) ( )21ln 0.5it V

V

E F F r Naive TNaiveDD

Naive T

σ

σ−+ + −⎡ ⎤⎣ ⎦=

1itr −

( )0.05 0.25V E EE FNaive

E F E Fσ σ σ= + +

+ +Eσ


Power Test: Public firm EDF™ power dominates ratings

Random Chance

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