Portfolio Credit Risk Research Articles

Basel II and Bank Credit Risk: Evidence from the Emerging Markets

Existing literature has focused attention on the impact of Basel I and similar capital requirement regulations on developed countries where such regulations were found to be effective in increasing capital ratios and reducing portfolio credit risk of commercial banks. In the present study, we study the impact of such capital requirement regulations on commercial banks in 11 developing countries around the world within a cross-section framework with the widely popular simultaneous equations model of Shrieves and Dhal (1992). Surprisingly, we find that such regulations did not increase the capital ratios of banks in the developing countries. This implies that particular attention should be given to the business, environmental, legal, cultural realities of such countries while designing and implementing such policies for developing countries. However, we find evidence that such regulations did reduce portfolio risk of banks. We also find that capital ratios and portfolio risk are inversely related in contrast to the predictions of buffer capital theory, managerial risk aversion theory, and bankruptcy cost avoidance theory. Our, evidence also shows that level of financial development and credit risk are inversely related implying that as the financial sector of a country develops it opens up avenues for alternative sources of finance, which results in reduced risk. Further evidence shows that liberalization is associated with bank risk.

Parameterizing credit risk models

The present paper shows how the parameters of three popular portfolio credit risk models can be empirically estimated by banks using a Maximum Likelihood framework. We apply the method to a database of German firms provided by Deutsche Bundesbank and analyze the inclusion of macroeconomic and borrower specific rating factors. Given the uniform ML estimation methodology, we compare the parameter estimates and the forecasted loss distributions for the credit risk models and find that they perform in very similar ways, in contrast to the differences found in some previous studies. We also propose an approach for addressing estimation errors. Our findings suggest that for a financial institution model risk, i.e. the risk of choosing the wrong credit model, may be considerably reduced.

Tail approximation for credit risk portfolios with heavy-tailed risk factors

We consider a portfolio credit risk model in the spirit of CreditMetrics [15]. The multivariate normally distributed underlying risk factors in that model are replaced by more general multivariate elliptical factors with heavy-tailed marginals, introducing tail-dependence. We consider a full-scale version of the model, i.e. we incorporate not only the default risk, but also rating migrations, credit spread volatility and recovery risk. We derive an upper bound of the portfolio loss distribution, which is particularly accurate at high loss levels. Given the complexity of our model, we obtain this results using a mixture of analytic techniques and Monte Carlo simulation. We conclude with an approximation of VaR and a new method to determine the contributions of the individual credits to the overall portfolio risk. ∗GKAAM, Munich University of Technology, D-85747 Garching, Germany, tel:(++49)(+89)28917991, email: krassi@ma.tum.de, http://www.ma.tum.de/stat The author is supported financially by a scholarship from DFG (Deutsche Forschungsgemeinschaft) through Graduate Program Applied Algorithmic Mathematics AMS 2000 Mathematics Subject Classification: 62H99, 65C20, 91B28 JEL Classification: G11, G21

Empirical Risk Analysis of Pension Insurance: The Case of Germany

With this paper we seek to contribute to the literature on pension insurance systems. The financial literature tends to focus exclusively on the US pension insurance system. This is the first major empirical study to address the German occupational pension insurance (PSVaG) plan in Germany. The study is based on a Merton-type one-factor model, in which we determine the credit portfolio risk profile of the occupational pension insurance plan and compare two alternative pricing plans. We find that there is a low, yet non-negligible risk of very high losses that may threaten the existence of the occupational pension insurance plan (PSVaG). While relating risk premiums to firms' default probabilities would cause them to diverge widely, a marginal risk contribution method would produce less pronounced differences compared to the current, uniform pricing plan.

Deriving Credit Portfolio Diversification Properties from Large Asset-Backed Security Pools

The present analysis estimates Markowitz portfolio correlations for retail loan portfolios. The correlations are derived from almost $1 trillion of asset backed security pools originated by more than five hundred issuers between January 2000 and September 2003. Such a broad sample, comprised of several hundred thousand pool-month observations, provides a unique opportunity to infer asset correlation structures of commercial bank assets. Since the types of loans analyzed are rarely traded, Markowitz correlations are estimated from five different loan performance measures. The analysis demonstrates that the performance of many different loan credit types is weakly correlated, and is sometimes even negatively correlated. Hence, there is the potential to eliminate a significant amount of risk in diversified credit portfolios.

A credit risk model for large dimensional portfolios with application to economic capital

In this paper we develop a multi-period and multi-state portfolio credit risk model which is applicable to large dimensional portfolios like for example retail and mortgage portfolios. The model includes a methodology for estimation and simulation of systematic transition risk through a model for stochastic migration, a methodology for the modelling of recoveries in the case of stochastic collaterals as well as an approach to dimension reduction of the portfolio. One important application of our model is economic capital (EC) and a concept of EC based on the analogy with classical risk theory is introduced and the questions of allocation as well as risk-adjusted pricing based on the allocation of EC are structured and described. The model is illustrated by an extensive numerical example giving a concretization of the model as well as of several of the concepts introduced.

Asymmetric Information Effects on Loan Spreads

This paper estimates the cost arising from information asymmetry between the lead bank and members of the lending syndicate. In a lending syndicate, the lead bank retains only a fraction of the loan but acts as the intermediary between the borrower and the syndicate participants. Theory predicts that private information in the hands of the lead bank will cause syndicate participants to demand a higher interest rate and that a large loan ownership by the lead bank should reduce asymmetric information and the related premium. Nevertheless, the estimated OLS relation between the loan spread and the lead bank's share is positive. This result, however, ignores the fact that we only observe equilibrium outcomes and, therefore, the asymmetric information premium demanded by participants is offset by the diversification premium demanded by the lead bank. Using exogenous shifts in the credit risk of the lead bank's loan portfolio as an instrument, I measure the asymmetric information effect of the lead's share on the loan spread and find that it has a large economic cost, accounting for approximately 4 percent of the total cost of credit.

The Underlying Dynamics of Credit Correlations

We propose a hybrid model of portfolio credit risk where the dynamics of the underlying latent variables is governed by a one factor GARCH process. The distinctive feature of such processes is that the long-term aggregate return distributions can substantially deviate from the asymptotic Gaussian limit for very long horizons. We introduce the notion of correlation spectrum as a convenient tool for comparing portfolio credit loss generating models and pricing synthetic CDO tranches. Analyzing alternative specifications of the underlying dynamics, we conclude that the asymmetric models with TARCH volatility specification are the preferred choice for generating significant and persistent credit correlation skews.

Importance Sampling for Portfolio Credit Risk

Monte Carlo simulation is widely used to measure the credit risk in portfolios of loans, corporate bonds, and other instruments subject to possible default. The accurate measurement of credit risk is often a rare-event simulation problem because default probabilities are low for highly rated obligors and because risk management is particularly concerned with rare but significant losses resulting from a large number of defaults. This makes importance sampling (IS) potentially attractive. But the application of IS is complicated by the mechanisms used to model dependence between obligors, and capturing this dependence is essential to a portfolio view of credit risk. This paper provides an IS procedure for the widely used normal copula model of portfolio credit risk. The procedure has two parts: One applies IS conditional on a set of common factors affecting multiple obligors, the other applies IS to the factors themselves. The relative importance of the two parts of the procedure is determined by the strength of the dependence between obligors. We provide both theoretical and numerical support for the method.

Credit Risk Versus Capital Requirements under Basel II: Are SME Loans and Retail Credit Really Different?

Under Basel II, retail and SME credit (R&SME) receive special treatment because of a supposedly smaller exposure to systemic risk. Most research on this issue has been based on parameterized credit risk models. We present new evidence by applying Carey's (Carey, Mark. “Credit Risk in Private Debt Portfolios.” Journal of Finance 53, no. 4 (1998), 1363–1387.) nonparametric Monte-Carlo resampling method to two banks' complete loan portfolios. By exploiting that a sub-sample of all borrowers has been assigned an internal rating by both banks, we can compare the credit loss distributions for the three credit types, and compute both economic and regulatory capital under Basel II. We also test if our conclusions are sensitive to the definitions of R&SME credit. Our findings show that R&SME portfolios are usually riskier than corporate credit. Special treatment under Basel II is thus not justified.

The Basel II Reform and Retail Credit Markets

Over the last two decades, many large banks have developed advanced quantitative credit risk models for allocating economic capital, measuring risk-adjusted returns at the businessline and individual credit level, and improving overall risk management. The advent of these new models and their incorporation into bank credit risk management were an important impetus for the effort to reform the Basel Committee’s standards for regulatory capitalV Basel IIVand, in turn, the Basel II proposal is encouraging banks to upgrade their credit risk management approaches. Under the Basel II proposal, banks with sufficiently sophisticated risk measurement and management systems can use their own internal systems to estimate key risk parameters that determine regulatory capital minimums. While general principles of portfolio credit risk modeling are applicable for commercial and retail portfolios, the Basel II framework was built based primarily on industry practices developed for large commercial credits. Over time, the Basel II proposal has explicitly incorporated the unique characteristics of retail credits into this overall framework. The Basel II proposal defines retail loans to include most loans to individuals, including credit card loans, mortgage loans, home equity lines of credit, auto loans, and other consumer loans. In addition, the Basel II proposal includes small loans to businesses as retail credits if those loans are managed on a pooled basis. Basel II’s initial emphasis on corporate credit is not entirely surprising, since many of the models built for estimating capital needs and extreme tails of credit loss distributions (e.g., CreditMetrics, Credit Risk, KMV Portfolio Manager) were explicitly developed for the large commercial bond or loan sector. Moreover, much of the academic research on credit risk also focused on the large corporate credit market where data were more easily available

Default dependence among corporate bond issuers: empirical evidence from time series data

This study shows that the extent to which the asset returns of different obligors are correlated is of vital importance for a realistic assessment credit portfolio risk. The high empirical relevance of this phenomenon is demonstrated by applying a likelihood-based estimation procedure to time series data on historical default frequencies. It turns out that, apparently, the default probabilities of speculative-grade debtors are much more highly correlated than the ones of investment-grade borrowers.

Simulated Credit Loss Distribution

Standard portfolio credit risk models provide an assessment of the potential credit loss that could result from changes to the credit quality of different obligors held in a bond portfolio. In practice, a significant portion of the credit loss can also result from changes to credit spreads that may or may not be directly related to the obligor9s creditworthiness. Comparison of the simulated credit loss distribution for an investment-grade corporate bond portfolio generated using standard credit risk models and the historical credit loss distribution of a similar portfolio indicates that the two are quite dissimilar. Several modifications can be made to the standard portfolio credit risk model to reduce this discrepancy.

Portfolio Credit Risk with Extremal Dependence

We consider the risk of a portfolio comprised of loans, bonds, and financial instruments that are subject to possible default. In particular, we are interested in the probability that the portfolio will incur large losses over a fixed time horizon. Contrary to the normal copula that is commonly used in practice (e.g., in the CreditMetrics system), we assume a portfolio dependence structure that supports {\it extremal dependence} among obligors and does not hinge solely on correlation. A particular instance within this model class is the so-called $t$-copula model that is derived from the multivariate Student $t$ distribution and hence, generalizes the normal copula model. The size of the portfolio, the heterogenous mix of obligors, and the fact that default events are rare and mutually dependent makes it quite complicated to calculate portfolio credit risk either by means of exact analysis or naive Monte Carlo simulation. The main contributions of this paper are twofold. We first derive sharp asymptotics for portfolio credit risk that illustrate the implications of extremal dependence among obligors. Using this as a stepping stone, we develop multi-stage importance sampling algorithms that are shown to be asymptotically optimal and can be used to efficiently compute portfolio credit risk via Monte Carlo simulation.

Small Sample Asymptotics for Credit Risk Portfolios

This article considers small sample asymptotics for the distribution of the total loss Sn of a credit risk portfolio. For portfolios with a few exceptionally high potential loss values, the distribution of Sn turns out to be bimodal. Direct approximation by Esscher tilting does not capture this feature. An improved recursive algorithm is proposed. The new approach leads to a more accurate small sample approximation that models bimodality in the presence of outliers. The results are illustrated by a simulated example as well as an example of an observed credit risk portfolio.

Optimal Importance Sampling for Credit Portfolios with Stochastic Approximation

We introduce an adaptive importance sampling method for the loss distribution of credit portfolios based on the Robbins-Monro stochastic approximation procedure. After presenting the subtle construction of the algorithm, we apply our adaptive scheme for calculating the risk flgures of a typical medium-sized credit risk portfolio with 2000 obligors. Simulating the tail of the loss distribution, we can improve signiflcantly the variance reduction and outperform other recently proposed importance sampling approaches that are based on deterministic methods providing asymptotically optimal importance sampling distributions. Furthermore, the simple structure of the algorithm not only allows a straightforward implementation, but also ofiers a lot of ∞exibility for extensions to more complex models. Therefore, our numerical results motivate interesting future research paths for the application of stochastic approximation methods in risk management.

Capital Allocation for Portfolio Credit Risk

Capital allocation rules are derived that maximize leverage while maintaining a target solvency rate for credit portfolios where risk is driven by a single common factor and idiosyncratic risk is fully diversified. Equilibrium conditions ensure that capital allocations depend on interest earnings as well as credits' probability of default, endogenous loss given default, and asset correlation. Capitalization rates exceed those estimated using Gaussian credit loss models. Results demonstrate that credit risk is undercapitalized by the Basel II AIRB approach in part because of ambiguities regarding the definition of loss given default. An alternative proposed capital rule removes this bias.

Discrete versus continuous state switching models for portfolio credit risk

Dynamic models for credit rating transitions are important ingredients for dynamic credit risk analyses. We compare the properties of two such models that have recently been put forward. The models mainly differ in their treatment of systematic risk, which can be modeled either using discrete states (e.g., expansion versus recession) or continuous states. It turns out that the implied asset correlations and default rate volatilities for discrete state switching models are implausibly low compared to empirical estimates from the literature. We conclude that care has to be taken when discrete state regime switching models are employed for dynamic credit risk management. As a side result of our analysis, we obtain indirect evidence that asset correlations may change over the business cycle.

Credit Portfolio Risk and PD Confidence Sets through the Business Cycle

Transition matrices are an important determinant for risk management and VaR calculations in credit portfolios. It is well known that rating migration behavior is not constant through time. It shows cyclical behavior and signiflcant changes over the years. We investigate the efiect of changes in migration matrices on credit portfolio risk in terms of Expected Loss and Value-at-Risk flgures for exemplary loan portfolios. The estimates are based on historical transition matrices for difierent time horizons and a continuous-time simulation procedure. We further determine confldence sets for the probability of default (PD) in difierent rating classes by a bootstrapping methodology. Our flndings are substantial changes in VaR as well as for the width of estimated PD confldence intervals.

Business Cycle Effects on Portfolio Credit Risk: Scenario Generation through Dynamic Factor Analysis

In this paper, we focus on measuring the risk associated to a bank loan portfolio. In particular, we depart from the standard one factor model representation of portfolio credit risk. In particular, we consider an hetrogeneous portfolio, and we account for stochastic dependent recoveries. We also examine the influence of either one systemic shock (interpreted as the state of the business cycle) or two systemic shocks (interpreted as demand and supply innovations) on portfolio credit risk. The identification and estimation of the common shocks is obtained by fitting a Dynamic Factor model to a large number of macro credit drivers. The scenarios are obtained by employing Montecarlo stochastic simulation.