A rational risk policy: the importance of randomness, leverage and heavy tails on portfolio drawdowns

Abstract

This paper studies the importance of path dependence under randomness for a tradingoperation. Many studies focus on the importance of maximizing the expected growth rate.Path dependent risk measures, such as drawdown risk measures are getting more and moreattention. We show that given a certain set of profitable trading characteristics, a risk-taker canstill be faced with significant drawdowns, to the point where a strategy becomes unsustainable.Based on Monte Carlo simulation, we analyze the medium term behavior of the differentcumulative return paths. We start from a trading operation assuming a 2 point distributionof trading outcomes, after which we investigate the impact of the presence of heavier tails inthe return distribution both for additive and multiplicative dynamics. Under the presence ofrandomness and especially in the case of heavier tailed outcomes, extra care is needed, andoptimal might not be so optimal in the end.