The statistics of random walks: how long can you go and when should you panic?

Investors inevitably focus on the short term performance of the components of their portfolio and often attempt to make sense of recent bouts of consecutive negative returns or drawdowns in a given asset or strategy. These return streams can be modelled using random walks, a numerical technique that provides insight into the probability of observing a recent performance pattern given the assumptions about the quality of the investment. We demonstrate, given the modest Sharpe ratios that one should expect from an individual investment, that the depth and length of a cumulative period of negative performance can be surprisingly large. This observation leads us to the conjecture that investors systematically underestimate the length and depth of ‘normal’ drawdowns.