Kelly Criterion position-sizing formula: Full Kelly, Half-Kelly & edge guard

A binary payoff model with known probabilities

In this simplified model a stake either earns net profit b times the stake, with probability p, or loses the entire stake, with probability 1-p. Maximizing expected log wealth produces f = p-(1-p)/b. A no-short constraint floors a negative result at zero.

At p=0.55 and b=2, the model gives 0.325. Multiplying by 0.5 gives 0.1625. This is a mathematical example, not a recommended portfolio position: real return distributions, changing probabilities, correlated positions, costs and estimation errors are not represented.

Fractional Kelly reduces the fraction at risk but does not guarantee a particular drawdown, absence of ruin, or a universal 75% growth/25% variance relationship. An average win/loss ratio alone does not make a variable-return strategy equivalent to this binary model.

Zero-floored Full Kelly and Fractional Half-Kelly position-sizing formulas

The zero floor is a constraint of this illustrative model, not a safety guarantee. Use p between 0 and 1, positive net payoff b, and a fractional multiplier between 0 and 1.

=IF(OR(COUNT(A2:B2)<>2,A2<0,A2>1,B2<=0),"Invalid inputs",ROUND(MAX(0,A2-(1-A2)/B2),4))

Fractional Kelly (e.g. C2 = 0.5 for Half-Kelly drawdown control)

Multiplies zero-floored Full Kelly by risk-scaling fraction C2 (0.5 = Half-Kelly, 0.25 = Quarter-Kelly).

=IF(OR(OR(COUNT(A2:B2)<>2,A2<0,A2>1,B2<=0),NOT(ISNUMBER(C2)),C2<0,C2>1),"Invalid inputs",ROUND(C2*MAX(0,A2-(1-A2)/B2),4))

Further reading

• Microsoft Support — MAX function
• Thorp — The Kelly Criterion in Blackjack, Sports Betting, and the Stock Market