Leverage and Uncertainty

Abstract

How risk and uncertainty are perceived depends on experience, luck, skills, and modelling, and, unsurprisingly, they are hard to disentangle. Yet asset allocation – leverage – should depend on accurately assessing quantifiable return and risk and unquantifiable uncertainty. Looking beyond risk and evaluating how uncertainty constrains optimal leverage is explored by extending the Kelly Criterion to a simple probabilistic model with an additional tail risk outcome associated with uncertainty. For a single asset, the fractional Kelly Criterion is justified by the negative skew and positive kurtosis of the probability distribution. The Portfolio Theory based on the Kelly Criterion is shown to be a general theory, which includes the Markowitz Portfolio Theory and Risk Parity as limiting cases. The fat tail distributions we see in markets, which stem from the transient nature and uncertainty of markets, underscore loss aversion and the use of leverage. Markowitz efficient risk-return frontier becomes concave due to the loss aversion and fat tails. Decisions about uncertainty and leverage are among the most important aspects of financial markets and global macro investing.