Leverage and uncertainty

Abstract

How risk and uncertainty are perceived depends on experience, luck, skills and mod- eling. Unsurprisingly, these are hard to disentangle. Yet, asset allocation (leverage) should depend on accurately assessing quantifiable return and risk, and unquantifi- able uncertainty. In this paper, we look beyond risk and evaluate how uncertainty constrains optimal leverage. We do this 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 port- folio theory and risk parity as limiting cases. The fat-tailed distributions we see in markets, which stem from the transient nature and uncertainty of markets, underscore loss aversion and the use of leverage. The Markowitz efficient risk–return frontier becomes concave due to loss aversion and fat tails. Decisions about uncertainty and leverage are among the most important aspects of financial markets and global macro investing.