Asset Correlation Research Articles

The Basel Committee proposals for a new capital accord: implications for Italian banks

AbstractFollowing a few general considerations on the recently proposed revision of the Basel Agreement on capital adequacy, this paper focuses on the first pillar of the Basel Committee proposals, the handling of capital requirements for credit risk in the banking book. The Basel Committee envisages an approach alternatively based on external ratings or on internal rating systems for the determination of the minimum capital requirement related to bank loan portfolios. This approach supports a system of capital requirements that is more sensitive to credit risk. On the basis of specific assumptions, these requirements provide a measure of the value at risk (VaR) produced by models used by major international banks. We first address the impact of the standardised and (internal ratings‐based) IRB foundation approach using general data on Italian banks loans' portfolios default rates. We then simulate the impact of the proposed new rules on the corporate loan portfolios of Italian banks, using the unique data set of mortality rates recently published by the Bank of Italy. Three main conclusions emerge from the analysis: (i) the standardised approach implicitly penalizes Italian banks in their interbank funding as their rating is generally below AA/Aa, (ii) the average default rate experienced by Italian banks is higher than the one implied in the benchmark risk weight (BRW) proposed by the Basel Committee for the IRB foundation approach, thereby potentially leading to an increase in the regulatory risk weights, and (iii) the risk‐weight is based on an average asset correlation that is significantly higher than the one historically recorded within the Italian banks' corporate borrowers. These findings support the need for a significant revision of the basic inputs and assumptions of the Basel proposals. Finally, in relation to the conditions that allow the capital market to effectively discipline banks, we comment on the proposals advanced in relation to the third pillar of the new capital adequacy scheme.

The Empirical Relationship between Average Asset Correlation, Firm Probability of Default and Asset Size

The asymptotic single risk factor (ASRF) approach is a simplified framework for determining regulatory capital charges for credit risk and has become an integral part of how credit risk capital requirements are to be determined under the second Basel Accord. Within this approach, a key regulatory parameter is the average asset correlation. In this paper, we examine the empirical relationship between the average asset correlation, firm probability of default and firm asset size measured by the book value of assets by imposing the ASRF approach within the KMV methodology for determining credit risk capital requirements. Using data from year-end 2000, credit portfolios consisting of U.S., Japanese and European firms are analyzed. The empirical results suggest that average asset correlation is a decreasing function of probability of default and an increasing function of asset size. When compared with the average asset correlations proposed by the Basel Committee on Banking Supervision in November 2001, the empirical average asset correlations further suggest that accounting for firm asset size, especially for larger firms, may be important. In conclusion, the empirical results suggest that a variety of factors may impact average asset correlations within an ASRF framework, and these factors may need to be accounted for in the final calculation of regulatory capital requirements for credit risk.

The empirical relationship between average asset correlation, firm probability of default and asset size

The asymptotic single risk factor (ASRF) approach is a simplified framework for determining regulatory capital charges for credit risk and has become an integral part of how credit risk capital requirements are to be determined under the second Basel Accord. Within this approach, a key regulatory parameter is the average asset correlation. In this paper, we examine the empirical relationship between the average asset correlation, firm probability of default and firm asset size measured by the book value of assets by imposing the ASRF approach within the KMV methodology for determining credit risk capital requirements. Using data from year-end 2000, credit portfolios consisting of U.S., Japanese and European firms are analyzed. The empirical results suggest that average asset correlation is a decreasing function of probability of default and an increasing function of asset size. When compared with the average asset correlations proposed by the Basel Committee on Banking Supervision in November 2001, the empirical average asset correlations further suggest that accounting for firm asset size, especially for larger firms, may be important. In conclusion, the empirical results suggest that a variety of factors may impact average asset correlations within an ASRF framework, and these factors may need to be accounted for in the final calculation of regulatory capital requirements for credit risk.

Asset Allocation Models and Market Volatility

Asset allocation and risk management models assume at least short–term stability of the covariance structure of asset returns, but actual covariance and correlation relationships fluctuate dramatically. Moreover, correlations tend to increase in volatile periods, which reduces the power of diversification when it might most be desired. We propose a framework to both explain these phenomena and to predict changes in correlation structure. We model correlations between assets as resulting from the common dependence of returns on a marketwide factor. Through this link, an increase in market volatility increases the relative importance of systematic risk compared with the unsystematic component of returns. The increase in the importance of systematic risk results, in turn, in an increase in asset correlations. We report that a large portion of the variation in correlation structures can be attributed to variation in market volatility. Moreover, market volatility contains enough predictability to construct useful forecasts of covariance.

The Correlation Effect

We examine how the correlations of bank loan defaults depend on the correlations of asset returns and how correlations and diversification are affected by macroeconomic risks. We highlight the main properties of the relationship between asset returns and default correlations, illustrating how adverse macroeconomic shocks raise not only the likelihood of defaults, but also the of defaults. The latter called correlation effect, may account for more than 50% of the increase in the credit risk.

On Default Correlation

This article studies the problem of default correlation. It introduces a random variable called “time-until-default” to denote the survival time of each defaultable entity or financial instrument, and defines the default correlation between two credit risks as the correlation coefficient between their survival times. The author explains why a copula function approach should be used to specify the joint distribution of survival times after marginal distributions of survival times are derived from market information, such as risky bond prices or asset swap spreads. He shows that the current approach to default correlation through asset correlation is equivalent to using a normal copula function. Numerical examples illustrate the use of copula functions in the valuation of some credit derivatives, such as credit default swaps and first-to-default contracts.

On Default Correlation: A Copula Function Approach

This paper studies the problem of default correlation. We first introduce a random variable called time-until-default to denote the survival time of each defaultable entity or financial instrument, and define the default correlation between two credit risks as the correlation coefficient between their survival times. Then we argue why a copula function approach should be used to specify the joint distribution of survival times after marginal distributions of survival times are derived from market information, such as risky bond prices or asset swap spreads. The definition and some basic properties of copula functions are given. We show that the current CreditMetrics approach to default correlation through asset correlation is equivalent to using a normal copula function. Finally, we give some numerical examples to illustrate the use of copula functions in the valuation of some credit derivatives, such as credit default swaps and first-to-default contracts.

Mean-variance analysis of portfolios of dependent investments: An extension

This paper extends portfolio-choice theory under risk aversion to the case of dependent investments. It establishes the circumstances in which optimal portfolios of dependent investments will be diversified or completely specialized, and reevaluates earlier statements in this connection arrived at without reference to risk preference. The model, which assumes two risky assets, focuses first on the normal case, in which one asset has both a higher mean and variance of expected returns and, second, on the perverse case, in which one of the two assets is both more profitable and less risky than the other. In the first case diversified portfolios are the rule irrespective of the degree of correlation between assets; completely specialized portfolios may only obtain as corner solutions generally resulting from low-risk aversion; complete specialization obtains when there is high-risk aversion only in the limiting normal case of equally profitable but unequally risky assets. In the second, or perverse case, a wider variety of diversified portfolios than previously thought is found to be optimal. Specifically, diversification may be optimal even if one security has an extremely higher yield and lower variance of returns than the other, provided asset correlation is sufficiently low or negative. There will be complete specialization in the more profitable and less risky asset only if the correlation coefficient between asset returns assumes positive values in an interval that will be narrower or wider depending on the assumed degree of risk aversion and other considerations.