Bet sizing to maximise long-run growth

Question

What is the Kelly criterion, and what does it recommend?

Short answer

Kelly sizes each bet to maximise the expected logarithm of wealth, which maximises the long-run growth rate. For a bet paying $b$ to $1$ with win probability $p$ , stake the fraction $f^*=p-(1-p)/b$ of wealth; for a continuous investment, roughly $f^*=(\mu-r)/\sigma^2$ . Full Kelly is very volatile and over-betting is disastrous, so practitioners often use half-Kelly.

Adapted from Wilmott, Frequently Asked Questions in Quantitative Finance, FAQ 14, p.70; question and answer rewritten by SelfMadeQuant.com.

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Lessons behind this question

Optimisation Problems
Constrained Optimisation and Lagrange Multipliers
Mean-Variance Optimisation

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