Contemporary Finance

8Market Risk

8.1 Definition of Value-at-Risk

8.1.1 Why Value-at-Risk?

Value-at-Risk (VaR) is a single number summarizing the risk of a position or a portfolio. Ahead, we’ll define VaR and analyze its many drawbacks and limitations as a risk measure, but it’s important to be aware of the virtues that led to its wide and long-standing adoption.

VaR can be computed for portfolios encompassing very different asset types. It can be roughly accurate for many portfolios. It is applicable even to large and complex portfolios and can be computed using a broad range of return models, estimation methods, and data sources.

The most salient criticism of VaR is that in most practical applications, if it is accurate at all, it is as a measure of the risk of unusual but recurrent losses. VaR loses all accuracy if used to estimate extreme losses. But this should be understood not as a criticism but as stating the appropriate use of VaR. Any asset portfolio will routinely display fluctuations in value, and VaR can be a reasonably accurate measure of them. A bank’s trading desk, for example, may wish to estimate the size of the losses that it can expect to recur on a regular basis, say, monthly. But VaR will be a far less useful guide to the likelihood of losses large enough to endanger the bank, require public or regulatory reporting, or impel it to fundamentally reassess its trading business.

In large trading operations, VaR limit systems have been widely used to set position size limits based ...