Value at risk for portfolios with short positions - Do not assume lognormal distributions.

Value at risk is perhaps the most common measure of a portfolio's exposure to loss. The simplest way to estimate value at risk is to calculate it directly from the portfolio's expected return and standard deviation under the assumption that the portfolio's returns are lognormally distributed. If the component returns of the portfolio are themselves lognormally distributed, however, it is incorrect to assume that the portfolio's returns are also lognormal. For portfolios that include only long positions, this technically false assumption is a reasonably good approximation of the portfolios' theoretical return distribution. For portfolios that include short positions, though, the authors explain why the assumption of lognormality for the total portfolio can be seriously misleading. In many typical cases, value at risk is substantially greater than indicated by a lognormal distribution.