Calculating hedge fund risk: the draw down and the maximum draw down

Hedge funds, defined in this context as geared financial entities, frequently use some measure of point loss as a risk measure. This paper considers the statistical properties of an uninterrupted fall in a security price; called a draw down. The distribution of the draw downs in an N-trading period is derived together with an approximation to the distribution of the maximum. Complementary results are provided which are useful for risk calculations. A brief empirical study of the S&P futures is included in order to highlight some of the limitations in the presence of extreme events.