2013issue C138-13

Kelly fraction versus risk of ruin

Editorial view: treat the Kelly criterion as a pre-trade exposure filter. First confirm that expectancy is greater than zero, then choose a fraction that keeps risk of ruin inside a personal bound instead of taking the theoretically maximum growth bet.

A positive edge exists only when expectancy is greater than zero. A non-positive expectancy implies no trading edge and is treated as a reason not to trade at all.
The Kelly optimum fraction simplifies to FO = E / R, linking bet size directly to expectancy and the win-to-loss ratio.
Raising the bet fraction produces an exponential rise in risk of ruin, described as increasing at a square rate with betting level.
A half-Kelly fraction lowers risk of ruin relative to a full-Kelly fraction, at the cost of a lower profit level and lower ending equity.

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Current trackKelly criterion10 readings Risk of ruin13 readings Risk-reward ratio19 readings

Confirm a positive edge first

Expectancy is defined as E = B * (1 + R) - 1, so a positive edge exists only when expectancy is greater than zero. A non-positive expectancy implies no trading edge and is treated as a reason not to trade at all.

Set the Kelly fraction from expectancy and the ratio

The Kelly optimum fraction simplifies to FO = E / R, linking bet size directly to expectancy and the win-to-loss ratio. At the same expectancy, a low win-to-loss ratio allows a higher win rate and a larger Kelly fraction than a high win-to-loss ratio.

Fixed-dollar betting and fixed-fraction betting

Fixed-dollar betting produces linear, noncompounded equity change, while fixed-fraction betting compounds equity at a nonlinear rate.

Risk of ruin and a half-Kelly fraction

Raising the bet fraction produces an exponential rise in risk of ruin, described as increasing at a square rate with betting level. When profit per trade is matched across setups, a high win-to-loss-ratio case can show substantially worse risk of ruin than a low-ratio case.

A half-Kelly fraction lowers risk of ruin relative to a full-Kelly fraction, at the cost of a lower profit level and lower ending equity.

Ruin risk at full Kelly versus half Kelly

Cutting the stake from full Kelly to half Kelly at even odds drops ruin risk from 11.1 percent to 1.23 percent, while profit per trade only falls from 14 percent to 10 percent. High payoff-ratio bets stay a worse ruin-to-profit tradeoff even at half Kelly. Figures are taken from the article comparison table with expectancy held at 0.50.

Expectancy is fixed at 0.50. The R = 1 rows use win bias B = 0.75; the R = 10 rows use B = 0.136.

Educational research material, not investment advice. Historical source context does not establish present-day performance.

6 of 9 in the Kelly criterion track

201622-25 pp.Next on Kelly criterionExpected value versus leverage, drawdown, and Kelly sizingThree betting styles with 35-to-1, 1-to-1, and 1-to-35 odds can share a negative expected value of -5.26% while producing very different equity spreads and drawdowns.

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