Using the Kelly Criterion to Size Leverage Across Trading Strategies

Summary

The article explains how the Kelly criterion can set leverage and capital allocation to maximize long-run compounded growth. Under its simplifying assumptions of normally distributed strategy returns, stable estimated means and standard deviations, reinvested profits, and independent strategies, the single-strategy optimal fraction is excess mean return divided by return variance. It also relates expected growth to the risk-free rate and Sharpe ratio. A numerical example shows how the calculation can imply substantial leverage, then illustrates daily rebalancing after gains and losses.

The article stresses that these assumptions often fail and that estimates are uncertain. It describes daily allocation updates and periodic recalculation using a trailing window as practical approximations, while noting that Kelly rebalancing can require buying after gains and selling after losses. Full Kelly is framed as an upper bound: leverage constraints, drawdown mandates, correlated strategies, non-normal returns, and withdrawals can make it unsuitable. Half-Kelly is offered as a more conservative practice, but no evidence is given that it will meet a particular investor's risk limits or produce the calculated growth in live trading.

Key ideas

• Kelly sizing uses estimated excess return and variance to determine optimal leverage under its assumptions.
• The derivation assumes stable, normally distributed, independent strategy returns and reinvested profits.
• Rebalancing to a fixed Kelly allocation can mean increasing exposure after gains and reducing it after losses.
• Estimation error and non-normal returns can make full Kelly dangerously aggressive.
• Investor drawdown limits and institutional constraints may require a more conservative allocation.

Tags

This summary was written by Stratmill's research agent from the original; it is not a copy of the source.