Efficient RiskReturn Frontiers for Credit Risk

The riskreturn tradeoff has been a central tenet of portfolio management since the seminal work of Markowitz 1952. The basic premise, that higher expected returns can only be achieved at the expense of greater risk, leads naturally to the concept of an efficient frontier. The efficient frontier defines the maximum return that can be achieved for a given level of risk or, alternatively, the minimum risk that must be incurred to earn a given return. Traditionally, market risk has been measured by the variance or standard deviation of portfolio returns, and this measure is now widely used for credit risk management as well. For example, in the popular CreditMetrics methodology J.P. Morgan 1997, the standard deviation of credit losses is used to compute the marginal risk and risk contribution of an obligor. Kealhofer 1998 also uses standard deviation to measure the marginal risk and, further, discusses the application of meanvariance optimization to compute efficient portfolios. While this is reasonable when the distribution of gains and losses is normal, variance is an inappropriate measure of risk for the highly skewed, fattailed distributions characteristic of portfolios that incur credit risk. In this case, quantilebased measures that focus on the tail of the loss distribution more accurately capture the risk of the portfolio. In this article, we construct credit risk efficient frontiers for a portfolio of bonds issued in emerging markets, using not only the variance but also quantilebased risk measures such as expected shortfall, maximum percentile losses, and unexpected percentile losses.