Leverage and uncertainty

Abstract

Risk and uncertainty will always be a matter of experience, luck, skills, and modelling. Leverage is another concept, which is critical for the investor's decisions and results. Adaptive skills and quantitative probabilistic methods need to be used in successful management of risk, uncertainty and leverage. The author explores how uncertainty beyond risk determines consistent leverage in a simple model of the world with fat tails due to significant, not fully quantifiable and not too rare events. Among particular technical results, for the single asset fractional Kelly criterion is derived in the presence of the fat tails associated with subjective uncertainty. For the multi-asset portfolio, Kelly criterion provides an insightful perspective on Risk Parity strategies, which can be extended for the assets with fat tails.