The Kelly Criterion and the Stock Market
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What they found
Rotando and Thorp applied the Kelly criterion to a continuous investment problem: how much of your wealth to put in the S&P 500 versus Treasury bills. Using historical return and volatility estimates, they derived the growth-optimal fraction (which came out to roughly 117% of wealth, meaning a modest amount of leverage) and showed how the growth rate falls as you move away from it in either direction. The paper is an accessible bridge from Kelly's gambling framework to a continuous-time investing one.
What you can use
- The Kelly fraction for a stock index with historical returns was slightly above 100%, which is why unlevered buy-and-hold is close to growth-optimal.
- The growth rate curve is flat near the optimum: betting half Kelly gives up only a quarter of the growth rate but cuts drawdowns dramatically.
- Over-betting is far more costly than under-betting; the curve falls off a cliff beyond twice Kelly.
Caveats
Uses historical averages as if they were known parameters; small changes in assumed return or volatility swing the optimal fraction a lot. Written for a mathematics audience.
Tags: risk, position-sizing, kelly, leverage
Summaries are our own reading of the paper, not the authors' words. Educational only, not advice. Discuss it in Book Club.