Probability distribution of drawdowns in risky investments
Sergei Maslov, Yi-Cheng Zhang
TL;DR
This paper investigates the distribution of investment drawdowns based on risk attitudes, revealing a power law behavior with a critical exponent at the Kelly-optimal risk level, indicating diverging average drawdowns.
Contribution
It introduces a general power law model for drawdowns depending on investor risk preferences, highlighting the special case at Kelly-optimal risk exposure.
Findings
Drawdowns follow a power law distribution.
At Kelly-optimal risk, the power law exponent is 2.
Average drawdown diverges at Kelly-optimal risk level.
Abstract
We study the risk criterion for investments based on the drawdown from the maximal value of the capital in the past. Depending on investor's 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
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Taxonomy
TopicsRisk and Portfolio Optimization · Stochastic processes and financial applications · Financial Markets and Investment Strategies