Probability distribution of drawdowns in risky investments

We study the risk criterion for investments based on the drawdown from the maximal value of the capital in the past. Depending on investorʹs risk attitude, thus his risk exposure, we find that the distribution of these drawdowns follows a general power law. In particular, if the risk exposure is Kelly-optimal, the exponent of this power law has the borderline value of 2, i.e. the average drawdown is just about to diverge.