Kelly criterion
Choose exposure by expected compound growth, subject to survival.
Library note. Check the assumptions and further reading before applying a formula.
What Is This?
Kelly asks how much of your wealth to expose to an uncertain payoff when you will face the decision repeatedly. R is the net return and f is the exposure. The allowed set of exposures must keep wealth positive. Bigger positions can raise gains, but they also make losses harder to recover from. Kelly weighs both through the logarithm, rather than optimising the win rate.
Try an example
In a hypothetical repeated coin bet that wins £1 per £1 staked with probability 60%, binary Kelly gives a stake of 20% of current wealth. That number depends on the stated odds and payout. It is not a general rule for stock trades.
Where it needs care
Market returns are not binary bets. Use their full net payoff distribution, including costs and tail losses. Estimated probabilities are uncertain; smaller stakes and drawdown limits may be needed. Margin liquidation changes the problem further.
Historical Context
John L. Kelly Jr. developed the criterion in "A New Interpretation of Information Rate" (1956), linking information theory with repeated gambling.
Real-World Applications
- Study the trade-off between exposure and long-run wealth.
- Compare fractional exposure rules under stressed return paths.
