  Trading strategies that were profitable in the past often degrade with time.
Since unlucky streaks can also hit "healthy" strategies, how can one detect
that something truly worrying is happening? It is intuitive that a drawdown
that lasts too long or one that is too deep should lead to a downward revision
of the assumed Sharpe ratio of the strategy. In this note, we give a
quantitative answer to this question based on the exact probability
distributions for the length and depth of the last drawdown for upward drifting
Brownian motions. We also point out that both managers and investors tend to
underestimate the length and depth of drawdowns consistent with the Sharpe
ratio of the underlying strategy.
