Financial Risk Management: Models, History, and Institutions

CHAPTER 3

Value-at-Risk

Value at Risk (VaR) is a technique for analyzing portfolio market risk based on a known—or at least posited—return model. VaR has dreadful limitations, both as a model and as a practice of risk managers in real-world applications. We talk about these at length in Chapters 10 and 11. And VaR has come under ferocious, and to a large extent justified, attack from many quarters. But it is nonetheless an extremely important technique, for a number of reasons. It is worth laying these out carefully, lest the poor reputation of VaR lead to the neglect of an important analytical tool:

• Uniquely among risk measures, VaR provides a single number summarizing the risk of even large and complex portfolios. That number may be inaccurate. But in situations that require at least an order-of-magnitude estimate of the potential loss of a portfolio, or in which a comparison must be made as to which of two portfolios is riskier, it is hard to avoid using some sort of VaR estimate, at least as one among other risk measures.
• Examining VaR, its assumptions, the different ways to compute it, and its pitfalls, is an excellent way to understand the issues involved in risk measurement. We study VaR techniques not because we believe in them or in any particular distributional hypothesis literally, but so that we can learn to ask the right questions.
• VaR is a reasonably accurate guide to the “main body” risks of most portfolios, that is, losses that are large, but nonetheless routine. ...