Risk Capital and VaR

Abstract

In a few short years, Value at Risk has become one of the most widely used metrics for evaluating exposure to financial risk. Originally presented as a way to measure exposure to market risk over very short periods — typically overnight, or perhaps up to ten days — the VaR concept has been extended to broader uses, including estimating the need for risk capital to fund a risky business unit or investment project. In this article, Kupiec points out a couple of pitfalls in applying the VaR approach to the longer-horizon problem of allocating risk capital. One issue is how to treat the expected return on the assets: Do you measure VaR relative to the initial value, or to the expected end-of-period value? (Kupiec argues for the former.) Another issue is that when debt is part of the financing mix, the probability of insolvency at maturity depends on the firm9s ability to pay both the principal and the interest on its bonds, but interest payments may not be included in a standard VaR calculation. Moreover, the size of the interest payment will be endogenous, because the rate depends on default risk, which in turn is a function of the firm9s risk capital allocation. Kupiec discusses these issues and illustrates their quantitative importance under different parameter values.

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