being based on stock market data rather than “historic” book value account- ing data, it is forward looking. Third, it has strong theoretical underpinnings because it is a “structural model” based on the modern theory of corporate finance, where equity is viewed as a call option on the assets of a firm, and loans are viewed as put options written on the value of a firm’s assets.
Against these strengths are four weaknesses: (1) it is difficult to construct theoretical EDFs without the assumption of normality of asset returns; (2) private firms’ EDFs can be calculated only by using some comparability analysis based on accounting data and other observable characteristics of the borrower;27(3) it does not distinguish among different types of debt accord- ing to their seniority, collateral, covenants, or convertibility;28 and (4) it is
“static” in that the Merton model assumes that once management puts a debt structure in place, it leaves it unchanged—even if the value of a firm’s assets has doubled. As a result, the Merton model cannot capture the behavior of those firms that seek to maintain a constant or target leverage ratio across time [see Jarrow and van Deventer (1999) and Collin-Dufresne and Goldstein (2001)]. In contrast, Mueller (2000) models leverage as a function of sensi- tivity to macroeconomic factors (e.g., GDP growth and risk-free interest rates). Thus, the long-run leverage ratio changes stochastically over time, thereby fitting the model to observed term structures of default.29
equity growth, distance to default, return on assets (ROA), and leverage all signaled significantly higher EDFs.
The data used to estimate and validate the Moody’s empirical EDF scores consist of 14,447 public, nonfinancial firms during the period from 1980 to 1999; more than 100,000 firm-year observations; and 1,406 de- fault events.32The Moody’s model has been criticized as being overfit to a particular sample, and therefore unlikely to perform well out-of-sample; see Kealhofer (2000).33However, Sobehart, Keenan, and Stein (2000) showed an out-of-sample, out-of-time Type 1 error of only 26 percent and a Type 2 error of 17 percent. In addition, Sobehart, Keenan, and Stein (2000) con- ducted a performance test of Moody’s empirical EDFversus the theoretical EDF(not the KMV empirical EDF) and versus several statistical models, in- cluding: two variants of the Z-score discriminant model (see the discussion of credit scoring models in Chapter 2), a hazard model based on financial data, and a univariate model based on return on assets (ROA) only. The power curve, shown in Figure 4.11, suggests that the Moody’s empirical EDFoutperforms all other methods; for example, if the bottom 20 percent of the rankings using each of the methods are denied credit (i.e., Type 2 er- rors are held to 20 percent), then the Moody’s empirical EDFs eliminate 80 percent of the defaults. This may be compared to the results for the KMV empirical EDFshown in Figure 4.9, which shows a power of 84 percent for the 20 percent cutoff point.34However, this is not proof of superiority for either model because statistical significance tests are subject to sample TABLE 4.1 Key Variables of the Moody’s Default Prediction Model
Model Variable Definition Frequency
Credit quality Moody’s Rating when available. Credit history Proprietary rating model for when available.
unrated firms.
Return on assets Net income/assets Annual
Firm size Log (assets) Annual
Operating liquidity Working capital/assets Annual
Leverage Liabilities/assets Annual
Market sensitivity Stock price volatility Monthly
Equity growth Equity growth rate Monthly
Return on equity Net income/equity Monthly
Distance to default Merton model DD Monthly
(equation 4.5)
Source: Sobehart, Stein, Mikityanskaya, and Li (2000), p. 10.
62
FIGURE 4.10 An example of influence analysis of model factors. Source:
Sobehart, Keenan, and Stein (2000).
0.012
0.01
0.008
0.006
0.004
Relative Influence
0.002
0 Equity
Growth ROA Distance to Default
Leverage Operating Liquidity Panel (B) January 1999
Market Sensitivity Credit
Quality ROE Firm Size
Applied Magnetics Corp.
0.012
0.01
0.008
Relative Influence 0.006 0.004
0.002
–0.002
–0.004 0
Equity Growth
ROA Distance to Default
Leverage Operating Liquidity Panel (A) January 1998
Market Sensitivity
Credit Quality
ROE Firm Size
variations, and it is unclear whether 84 percent is statistically significantly higher than 80 percent.35
SUMMARY
The economic cause of default (or insolvency), as modeled by structural models of default probability, is the decline in the market value of the firm’s assets below the value of the firm’s debt obligations at a given horizon. Only FIGURE 4.11 Power curves for the tested models. Notes: All models were tested on the same validation data set. The 45˚ line represents the naive case which is equivalent to a random assignment of scores. All models perform considerably better than the random case. The Merton model variant performs almost as well as the Moody’s model in the case of extremely poor quality firms. However, the Moody’s model clearly performs better beyond about the bottom 10% of the population and is much better at discriminating defaults in the middle ranges of credit.
Source:Sobehart, Keenan, and Stein (2000).
0 100
90 80 70 60 50 40 30 20 10 0
20 40
Percent of Population Excluded
Percent
60 80 100
Random ROA Z Score
ReducedZ Score
Hazard Model Merton Model Variant Moody’s Model
if the assets’ value exceeds the debt value will it be rational for shareholders to exercise their “call option” on the firm’s assets and repay the firm’s debt.
Thus, debt can be viewed as a short put option on the firm’s assets; the shareholders will “sell” the firm’s assets to the lenders (i.e., exercise the put option and default on the debt) if the market value of assets is less than the put’s exercise price, which is the repayment value of the debt. The probabil- ity of default (the risk-neutral expected default frequency, EDF) is the area under the asset value probability distribution below the default point. The distance to default (DD) is the number of standard deviations of the asset probability distribution between current asset value and the default point.
The KMV Corporation applies structural models of default to its sub- stantial credit history database in order to determine an empirical EDFby examining the historical likelihood of default for any given DD level.
Moody’s incorporates ratings and financial statement variables together with the theoretical risk-neutral EDFin an artificial neural network that measures another empirical EDFscore. Both empirical EDFs outperform ratings and statistical models in terms of their accuracy at predicting de- faults. The primary advantage of structural models is that they utilize stock price data that are predictive and highly responsive to changes in the firm’s financial condition. The primary disadvantage of structural models is their reliance on distributional assumptions (i.e., normality) that imply default probabilities that are not reflected in observed bond spreads.