Within the past two years, important advances have been made in modeling credit risk at the portfolio level. Practitioners and policy makers have invested in implementing and exploring a variety of new models individually. Less progress has been made, however, with comparative analyses. Direct comparison often is not straightforward, because the different models may be presented within rather different mathematical frameworks. This paper offers a comparative anatomy of two especially influential benchmarks for credit risk models, J.P. Morgan’s CreditMetrics and Credit Suisse Financial Product’s CreditRisk +.Weshow that, despite differences on the surface, the underlying mathematical structures are similar. The structural parallels provide intuition for the relationship between the two models and allow us to describe quite precisely where the models differ in functional form, distributional assumptions, and reliance on approximation formulae. We then design simulation exercises which evaluate the effect of each of these differences individually. JEL Codes: G31, C15, G11 ∗The views expressed herein are my own and do not necessarily reflect those of the Board of Governors or its staff. I would like to thank David Jones for drawing my attention to this issue, and for his helpful comments. I am also grateful to Mark Carey for data and advice useful in calibration of the models, and to Chris Finger and Tom Wilde for helpful comments. Please

conversations.

We develop a framework for modeling conditional loss distributions through the introduction of risk factor dynamics. Asset value changes of a credit portfolio are linked to a dynamic global macroeconometric model, allowing macro effects to be isolated from idiosyncratic shocks from the perspective of default (and hence loss). Default probabilities are driven primarily by how firms are tied to business cycles, both domestic and foreign, and how business cycles are linked across countries. The model is able to control for firm-specific heterogeneity as well as generate multi-period forecasts of the entire loss distribution, conditional on specific macroeconomic scenarios. The approach can be used, for example, to compute the effects of a hypothetical negative equity price shock in South East Asia on the loss distribution of a credit portfolio with global exposures over one or more quarters. The approach has several other features of particular relevance for risk managers, such as the exploration of scale and symmetry of shocks, and the effect of non-normality on credit risk. We show that the effects of such shocks on losses are asymmetric and non-proportional, reflecting the highly non-linear nature of the credit risk model. Non-normal innovations such as Student t generate expected and unexpected losses which increase the fatter the tails of the innovations.

This paper has examined two specific aspects of stage 1 of the (BISs) Bank for International Settlements proposed reforms to the 8% risk-based capital ratio. We argue that relying on traditional agency ratings could produce cyclically lagging rather leading capital requirements, resulting in an enhanced rather than reduced degree of instability in the banking and financial system. Despite this possible shortcoming, we believe that sensible risk based weighting of capital requirements is a step in the right direction. The current risk based bucketing proposal, which is tied to external agency ratings, or possibly to internal bank ratings, however, lacks a sufficient degree of granularity. In particular, lumping A and BBB (investment grade corporate borrowers) together with BB and B (below investment grade borrowers) severely misprices risk within that bucket and calls, at a minimum, for that bucket to be split into two. We examine the default loss experience on corporate bonds for the period 1981-1999 and propose a revised weighting system which more closely resembles the actual loss experience on credit assets. 3 1.

We survey both academic and proprietary models to examine how macroeconomic and systematic risk effects are incorporated into measures of credit risk exposure. Many models consider the correlation between the probability of default (PD) and cyclical factors. Few models adjust loss rates (loss given default) to reflect cyclical effects. We find that the possibility of systematic correlation between PD and LGD is also neglected in currently available models. 2

The views expressed herein are not necessarily those of the Board of Governors, other members

England’s conference on “Credit Risk Modelling and the Regulatory Implications ” for their comments and suggestions. Evaluating Credit Risk Models Over the past decade, commercial banks have devoted many resources to developing internal models to better quantify their financial risks and assign economic capital. These efforts have been recognized and encouraged by bank regulators. Recently, banks have extended these efforts into the field of credit risk modeling. However, an important question for both banks and their regulators is evaluating the accuracy of a model’s forecasts of credit losses, especially given the small number of available forecasts due to their typically long planning horizons. Using a panel data approach, we propose evaluation methods for credit risk models based on crosssectional simulation. Specifically, models are evaluated not only on their forecasts over time, but also on their forecasts at a given point in time for simulated credit portfolios. Once the forecasts corresponding to these portfolios are generated, they can be evaluated using various statistical methods. I.

Procyclicality has emerged as a potential drawback to adoption of risk-sensitive bank capital requirements. Systematic risk factors may result in increases (decreases) in bank capital requirements when the economy is depressed (overheated), thereby decreasing (increasing) bank lending capacity and exacerbating business cycle fluctuations. Procyclicality may result from systematic risk emanating from common macroeconomic influences or from interdependencies across firms as financial markets and institutions consolidate internationally. We survey the literature on cyclical effects on operational risk, credit risk and market risk measures. Incorporating Systemic Influences Into Risk Measurements: A Survey of the Literature Bank regulations focus on individual institutions. The Basel Capital Accords (both current and proposed) base international bank capital requirements on the measurement of risk for each individual bank. Aggregate capital levels are then obtained by simply adding each bank’s individual capital requirement. To the extent that there is any attention paid to aggregate capital levels at all, it is only as a means to calibrate the

Should lenders diversify, as suggested by the financial intermediation literature, or specialize, as suggested by the corporate finance literature? I model a financial institution’s (“bank’s”) choice between these two strategies in a setting where bank failure is costly and loan monitoring adds value. All else equal, diversification across loan sectors helps most when loans have moderate exposure to sector downturns (“downside”) and the bank’s monitoring incentives are weak; when loans have low downside, diversification has little benefit, and when loans have sufficiently high downside, diversification may actually increase the bank’s chance of failure. Also, it is likely that the bank’s monitoring effectiveness is lower in new sectors; in this case, diversification lowers average returns on monitored loans, is less likely to improve monitoring incentives, and is more likely to increase the bank’s chance of failure. Diversified banks may sometimes need more equity capital than specialized banks, and increased competition can make diversification either more or less attractive. These results motivate actual institutions ’ behavior and performance in a number of cases. Key implications for regulators are that an institution’s credit risk depends on its monitoring incentives as much as on its diversification, and that diversification per se is no guarantee of reduced risk of failure.

Using a limiting approach to portfolio credit risk, we obtain analytic expressions for the tail behavior of credit losses. To capture the co-movements in defaults over time, we assume that defaults are triggered by a general, possibly non-linear, factor model involving both systematic and idiosyncratic risk factors. The model encompasses default mechanisms in popular models of portfolio credit risk, such as CreditMetrics and CreditRisk +. We show how the tail characteristics of portfolio credit losses depend directly upon the factor model’s functional form and the tail properties of the model’s risk factors. In many cases the credit loss distribution has a polynomial (rather than exponential) tail. This feature is robust to changes in tail characteristics of the underlying risk factors. Finally, we show that the interaction between portfolio quality and credit loss tail behavior is strikingly different between the CreditMetrics and CreditRisk + approach to modeling portfolio credit risk. Key words: portfolio credit risk; extreme value theory; tail events; tail index; factor models; economic capital; portfolio quality; secondorder expansions.