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9
A Summary and Comparison of New Internal Model Approaches
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n Chapters 4 through 8, we described key features of some of the more prominent new models of credit risk measurement. At first sight, these ap- proaches appear to be very different and likely to produce considerably dif- ferent loan loss exposures and VARfigures. This chapter summarizes these new models and discusses key differences and similarities among them.Empirical evidence on predictive differences among these models is also discussed.
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TABLE 9.1Comparison of Different Credit Risk Measurement Models Merton OPMReduced F CreditMetricsCreditPortfolio ViewCredit Risk PlusKMV/Moody’sKPMG/Kam Definition of riskMTMMTM or DMDMMTM or DMMTM Risk driversAsset valuesMacroeconomic factorsExpected default ratesAsset valuesDebt and equity pr Data requirementsHistorical transition matrix, credit spreads and yield curves, LGD, correlations, exposures Historical transition matrix, macroeconomic variables, credit spreads, LGD,exposures Default rates and volatility, macro fac- tors, LGD,exposures Equity prices, credit spreads, correlations, exposures
Debt and equity prices, historical tran- sition matrix, co tions, exposure Characterization of credit eventsCredit migrationMigration conditional on macroeconomic factors
Actuarial random default rateDistance to default: structural and empirical
Default intensity Volatility of credit eventsConstant or variableVariableVariableVariableVariable Correlation of credit eventsMultivariate normal asset returnsMacroeconomic factor loadingsIndependence assump- tion or correlation with expected default rate
Multivariate normal asset returnsPoisson intensity processes with j systemic factors Recovery ratesRandom (beta distri- bution)RandomConstant within bandConstant or randomConstant or random Numerical approachSimulation or analyticSimulationAnalyticAnalytic and econo- metricEconometric Interest ratesConstantConstantConstantConstantStochastic Risk classificationRatingsRatingsExposure bandsEmpirical EDFRatings or credit spreads
Definition of Risk
As described in Chapters 4 through 8, we need to distinguish between mod- els that calculate VAR based on the change in the market value of loans [mark-to-market (MTM) models], and models that concentrate on predict- ing default losses [default mode (DM) models]. The MTM models allow for credit upgrades and downgrades as well as defaults in calculating loan value losses and gains and hence capital reserves. The DM models consider only two states of the world: default and no-default.
As discussed earlier, the key difference between the MTM and DM ap- proaches is the inclusion of credit migration risk in MTM models. This is often referred to as spread risk.However, spread risk also includes the risk of changes in credit spreads for any given rating classification. Therefore, changes in valuation may result from (1) default, (2) changes in credit quality (e.g., ratings migration), and (3) changes in credit spreads that are not caused by credit quality changes. MTM models measure the first two of these com- ponents of valuation changes; the third is considered market risk and the 1996 market risk amendment of BIS I levies capital requirements to cover this component of spread risk.1In contrast, DM models measure changes in valu- ation resulting from default only. Not surprisingly, if models measure differ- ent things, they are likely to produce different results. CreditMetrics is an MTM model. Credit Risk Plus and KMV are essentially DM models. (Al- though, as discussed in Chapter 11, KMV also offers an MTM version.)2 CreditPortfolio View can be used as either an MTM or a DM model. Re- duced form models such as KPMG’s LAS is an MTM model.
Risk Drivers
At first sight, the key risk drivers of these models appear to be quite differ- ent. CreditMetrics, KMV,and Moody’s have their analytic foundations in a Merton-type options pricing model (OPM); a firm’s asset values and the volatility of asset values are the key drivers of default risk. In CreditPort- folio View, the risk drivers are macroeconomic factors (such as the unem- ployment rate); in Credit Risk Plus, it is the mean level of default risk and its volatility; in reduced form models, it is the credit spreads obtained from risky debt yields. Yet, if couched in terms of multifactor models, all five models can be viewed as having similar roots.3Specifically, the variability of a firm’s asset returns in CreditMetrics (as in KMV and Moody’s) is modeled as being directly linked to the variability in a firm’s stock returns. To the ex- tent that multifactor asset pricing models drive all risky security prices, the credit spreads of reduced form models are driven by the same risk factors.
In turn, in calculating correlations among firms’ asset returns (see Chapter 11), the equities of individual firms are viewed as being driven by a set of
systematic risk factors (industry factors, country factors, and so on) and un- systematic risk factors. The systematic risk factors, along with correlations among systematic risk factors (and their weighted importance), drive the asset returns of individual firms and the default correlations among firms.4
The risk drivers in CreditPortfolio View have origins similar to those of CreditMetrics. In particular, systematic countrywide macroeconomic fac- tors and unsystematic macroeconomic shocks drive default risk and the cor- relations of default risks among borrowers. The key risk driver in Credit Risk Plus is the variable mean default rate in the economy. This mean de- fault rate can be viewed as being linked systematically to the “state of the macroeconomy”; when the macro economy deteriorates, the mean default rate is likely to rise, as are default losses. An improvement in economic con- ditions has the opposite effect.
Thus, the risk drivers and correlations in all five models can be viewed as being linked, to some degree, to a set of macroeconomic and systematic risk factors that describe the evolution of economywide conditions.
Data Requirements
Where the five models differ considerably is in the format of the data re- quired to estimate credit risk exposure. Indeed, participants in the IIF/ISDA study of credit risk modeling (to be discussed later in this chapter) noted the critical role of data management and standardization in obtaining usable es- timates from any model. Historical transition matrices represent the funda- mental data input for CreditMetrics, CreditPortfolio View, and KPMG’s LAS. In contrast, Credit Risk Plus is built around mortality tables used to es- timate the default rate distribution for each exposure band. Because of Credit Risk Plus’ light data requirements, it can be most readily applied to retail portfolios. In contrast, KMV,Moody’s, and Kamakura require a series of security prices consisting of risky debt, risk-free debt, and equity prices.
All models input credit exposures from the portfolio’s composition. As Table 9.1 shows, most models input asset correlations, with the exception of Cred- itPortfolio View, which estimates asset correlations with common macroeco- nomic risk factors and Credit Risk Plus, in which correlations are obtained from default distributions conditional on macroeconomic factors.
Characterization of Credit Events
A credit event is said to occur when there is a material change in the credit- worthiness of a particular obligation. In CreditMetrics and CreditPortfolio View, a credit event occurs whenever there is a rating migration. KMV and Moody’s characterize a credit event as a change in the distance to default, resulting in a change in the empirical EDF.In Chapter 4, we demonstrated
that rating changes lag behind empirical EDF changes in forecasting changes in credit quality. Therefore, credit events are realized with greater speed and frequency in KMV and Moody’s than in CreditMetrics and Cred- itPortfolio View.
Similar in focus to KMV and Moody’s is the reduced form KPMG LAS and Kamakura models. Because they also rely on market prices (of debt and equity), reduced form models show greater sensitivity to credit events, de- fined as changes in the default intensity, than a model such as Credit Risk Plus, which limits characterization of credit events to default since it is a pure DM.However, changes in the actuarial default rate could be consid- ered a deterioration in credit quality. Because the distribution of the mean actuarial default rate is estimated from mortality rates, Credit Risk Plus def- initions of credit events are related to ratings transitions, at least for the entry that measures the probability of default.
Volatility of Credit Events
A key difference among the models is in the modeling of the one-year default probability or the probability of default distribution function. In CreditMet- rics, the probability of default (as well as upgrades and downgrades) is mod- eled as a fixed or discrete value based on historic data. In KMV and Moody’s, expected default frequencies (EDFs) vary as new information is impounded in stock prices. Changes in stock prices and the volatility of stock prices underlie empirical EDFscores. Similarly, changes in debt and equity prices drive changes in default intensities estimated by Kamakura’s re- duced form model. In CreditPortfolio View, the probability of default is a lo- gistic function of a set of macroeconomic factors and shocks that are normally distributed; thus, as the macroeconomy evolves, so will the proba- bility of default and the cells, or probabilities, in the rest of the transition matrix. In Credit Risk Plus, the probability of each loan’s defaulting is viewed as variable, conforming to a Poisson distribution around some mean default rate. In turn, the mean default rate is modeled as a variable with a gamma distribution. This produces a distribution of losses that may have fat- ter tails than those produced by either CreditMetrics or CreditPortfolio View.
Correlation of Credit Events
The similarity of the determinants of credit risk correlations has already been discussed in the context of risk drivers. Specifically, the correlation structure in all five models can be linked to systematic linkages of loans to key factors. The correlations among borrowers will be discussed in greater length in Chapters 10 through 12, where the application of the new models, and modern portfolio theory, to the credit portfolio decision is analyzed.
Recovery Rates
The distribution of losses and VAR calculations depend not only on the probability of defaults but also on the severity of losses or loss given default.
Empirical evidence suggests that default severities and recoveries are quite volatile over time. Further, building in a volatile recovery rate is likely to in- crease the VARor unexpected loss rate. (See, for example, the discussion on CreditMetrics in Chapter 6.)
CreditMetrics, in the context of its VARcalculations, allows for recov- eries to be variable. In the normal distribution version of the model, the es- timated standard deviation of recoveries is built in to the VARcalculation.
In the “actual” distribution version which recognizes a skew in the tail of the loan value loss distribution function, recoveries are assumed to follow a beta distribution, and the VARof loans is calculated via a Monte Carlo sim- ulation. In KMV’s simplest model, recoveries are viewed as a constant. In extended versions of the model, recoveries are allowed to follow a beta dis- tribution as well. In CreditPortfolio View, recoveries are also estimated via a Monte Carlo simulation approach and severities are drawn from a beta distribution. By contrast, under Credit Risk Plus, loss severities are rounded and banded into subportfolios, and the loss severity in any subportfolio is viewed as a constant. In reduced form models, the recovery rate is estimated from debt and equity prices, and either follows a stochastic process (Ka- makura) or else is assumed to be constant (KPMG).
Numerical Approach
The numerical approach to estimation of VARs, or unexpected losses, also differs across models. A VAR, at both the individual loan level and the port- folio-of-loans level, can be calculated analytically under CreditMetrics, but this approach becomes increasingly intractable as the number of loans in the portfolio increases. (This is discussed in more detail in Chapter 11.) As a re- sult, for large loan portfolios, Monte Carlo simulation techniques are used to generate an “approximate” aggregate distribution of portfolio loan values and hence a VAR. Similarly, CreditPortfolio View uses repeated Monte Carlo simulations to generate macro shocks and the distribution of losses (or loan values) on a loan portfolio. By comparison, Credit Risk Plus, based on its convenient distributional assumptions (the Poisson distribution for indi- vidual loans and the gamma distribution for the mean default rate, along with the fixed recovery assumption for loan losses in each subportfolio of loans), allows an analytic or closed-form solution to be generated for the probability density function of losses. KMV also allows an analytic solution to the loss function as well as a Monte Carlo simulation solution. Moody’s
combines the analytic and econometric approaches. Finally, the reduced form models utilize a closed form, econometric approach to solve for the form of the intensity process.
Interest Rates
Although several academic (structural) models have incorporated stochastic interest rates into the credit risk measurement models, most of the basic commercial models assume constant interest rates (i.e., assuming a stable yield curve). Indeed, CreditMetrics even assumes a fixed credit spread. Only reduced form models (e.g., Kamakura) explicitly model the stochastic processes governing interest rate fluctuations.
Risk Classification
A critical step in implementing credit risk models is the risk classification of each obligation. This is particularly difficult for loan portfolios, since most of the obligations are untraded. That is, there is no external risk classifica- tion of loans for the most part, whereas rating systems and credit spreads are available for risky debt securities. In Chapter 2, we discussed the inter- nal ratings systems and credit scoring models that have been developed by financial institutions to remedy this problem. CreditMetrics, CreditPortfo- lio View, and KPMG’s LAS utilize ratings (either external or internal) to classify risk. Credit Risk Plus uses exposure bands to classify the default risk of any obligation. Reduced form models use default intensity levels. Fi- nally, KMV and Moody’s estimate empirical EDFs. The differences in these methodologies imply that the same loan may be classified differently by each of the different models. The question is whether these classification differences significantly impact the measure of credit risk. To answer this question, we examine comparative studies that measure the credit risk of a standardized portfolio using each of the different credit risk models.