Second Generation VaR and Risk-Adjusted Return on Capital

Abstract

Within a period of only a few years, value at risk has become probably the single most widely used measure of financial risk exposure. Yet, by focusing only on the probability of experiencing a loss of a given size at the VaR horizon, it tacitly assumes that a large loss occurring prior to the horizon will be ignored. But this is unrealistic. A firm that monitors its financial position frequently and sees that it has penetrated the VaR level before the horizon is reached will very likely take action to reduce risk exposure, even though in many cases, a recovery would occur such that the loss would not exceed the VaR level by the time the horizon was reached. In this article, Rich shows that the traditional VaR calculation substantially understates the risk that a loss of a given size will occur at some point during the specified VaR horizon, and he offers a set of formulas for computing the relevant “continuous value at risk.” The article also explores related applications of the continuously monitored VaR barrier, including discretely monitored VaR barriers, RAROC using continuous VaR, and modifications for inflation-adjusted VaR and VaR evaluated relative to a benchmark portfolio.