Introduction to Fixed Income Analytics: Relative Value Analysis, Risk Measures, and Valuation, Second Edition

CHAPTER 13

Value-at-Risk Measure and Extensions

As financial markets increase in complexity, portfolio managers anguish over how to accurately communicate their portfolio’s risk exposure to investors. Value-at-Risk (VaR) is a widely-used methodology for quantifying risk (e.g., interest rate and credit risk). Following its introduction in October 1994 when J.P. Morgan launched RiskMetrics™, its adoption by bank regulators is an indicator of its acceptance as a risk management tool. The application of VaR extends beyond its initial use in investment banks to commercial banks and corporations. Despite its popularity, however, there are problems with the use of VaR as a measure of risk. In this chapter, we explain the concept of VaR and its limitations. Then we describe another measure, Conditional Value-at-Risk (CVaR) that overcomes the problems associated with VaR.

VALUE-AT-RISK

The basic idea of VaR is a simple one.VaR is a measure of the worst expected loss that a portfolio may suffer over a period of time that has been specified by the user, under normal market conditions and a specified level of confidence. Specifically, VaR is a portfolio’s expected loss over a specified time period for a set (i.e., prespecified) level of probability. For example, suppose a daily VaR is stated as $2 million for a 95% level of confidence. This means there is a only a 5% chance that the loss the next day will be greater than $2 million. Stated another way, we expect this portfolio to lose ...