Evaluation of Value-at-Risk Models Using Historical Data

esearchers in the field of financial economics have long recognized the importance of measuring the risk of a portfolio of financial assets or securities. Indeed, concerns go back at least four decades, when Markowitz’s pioneering work on portfolio selection (1959) explored the appropriate definition and measurement of risk. In recent years, the growth of trading activity and instances of financial market instability have prompted new studies underscoring the need for market participants to develop reliable risk measurement techniques.1 One technique advanced in the literature involves the use of “value-at-risk” models. These models measure the market, or price, risk of a portfolio of financial assets—that is, the risk that the market value of the portfolio will decline as a result of changes in interest rates, foreign exchange rates, equity prices, or commodity prices. Valueat-risk models aggregate the several components of price risk into a single quantitative measure of the potential for losses over a specified time horizon. These models are clearly appealing because they convey the market risk of the entire portfolio in one number. Moreover, value-at-risk measures focus directly, and in dollar terms, on a major reason for assessing risk in the first place—a loss of portfolio value. Recognition of these models by the financial and regulatory communities is evidence of their growing use. For example, in its recent risk-based capital proposal (1996a), the Basle Committee on Banking Supervision endorsed the use of such models, contingent on important qualitative and quantitative standards. In addition, the Bank for International Settlements Fisher report (1994) urged financial intermediaries to disclose measures of value-at-risk publicly. The Derivatives Policy Group, affiliated with six large U.S. securities firms, has also advocated the use of value-at-risk models as an important way to measure market risk. The introduction of the RiskMetrics database compiled by J.P. Morgan for use with third-party value-at-risk software also highlights the growing use of these models by financial as well as nonfinancial firms. Clearly, the use of value-at-risk models is increasThe views expressed in this article are those of the authors and do not necessarily reflect the position of the Federal Reserve Bank of New York or the Federal Reserve System.