Calculator
Kelly criterion optimal fraction calculator
The Kelly criterion finds the fraction of capital to allocate to a repeatable positive-expectancy strategy to maximise long-run geometric wealth growth while avoiding ruin. Institutional desks typically trade Half-Kelly or Quarter-Kelly to dampen drawdown variance.
Half-Kelly allocation (desk standard)
11.70%
29,259.26 position size
- Full-Kelly fraction
- 23.41%
- 58,518.52 position size
- Quarter-Kelly fraction
- 5.85%
- 14,629.63 position size
- Expected edge per unit risked
- 31.60%
- Optimal geometric growth rate
- 3.644%
| Sizing tier | Capital fraction | Position size | Log growth rate |
|---|---|---|---|
| 25% Kelly | 5.85% | 14,629.63 | 1.605% |
| 50% Kelly | 11.70% | 29,259.26 | 2.738% |
| 75% Kelly | 17.56% | 43,888.89 | 3.417% |
| 100% Kelly | 23.41% | 58,518.52 | 3.644% |
| 125% Kelly | 29.26% | 73,148.15 | 3.412% |
Formula
f* = p − (1 − p) ÷ b, where b = Average win ÷ Average loss
Expected edge = p × b − (1 − p)
Expected log growth g(f) = p × ln(1 + f × b) + (1 − p) × ln(1 − f)
How to use it
Enter your portfolio capital, estimated win probability, payoff ratio (average win divided by average loss) and maximum leverage cap.
Review Full Kelly, Half Kelly and Quarter Kelly allocations along with the fractional sensitivity table.
Assumptions and limits
- Assumes independent, identically distributed trials with known win probability and payoff odds.
- Parameter estimation error in real markets makes Full Kelly overly aggressive; Half Kelly achieves 75% of the log growth with half the volatility.
Common questions
Why do quantitative desks prefer Half Kelly?
Overbetting beyond Full Kelly reduces growth and increases the risk of severe drawdowns. Because true win rates and payoff ratios are estimated with noise, scaling down to Half Kelly provides a vital margin of safety.
What if the Kelly fraction is zero or negative?
A non-positive Kelly fraction means the strategy has zero or negative expected value; the optimal allocation is zero.
For education only, not investment advice. Results depend entirely on the inputs and assumptions above; check important numbers independently.