Fractional Kelly
Bet a fraction of Kelly, because your edge is only an estimate. · 7 min
Decide first
Kelly is extremely sensitive to the edge. For 2R trades, every percentage point of win rate moves the Kelly fraction by 1.5 points. A backtest that overstates the win rate by six points, which is easy (module C3), puts a "full Kelly" trader at ten times the real Kelly fraction.
A fraction of Kelly is insurance against that error. Half Kelly gives up about a quarter of the growth and removes most of the pain; quarter Kelly gives up about half the growth and survives a large overestimate. Many traders end up near 0.5% to 2% per trade, well below any Kelly they could compute.
10,000 simulated traders
Simulated data · not real pricesEvery trader takes the same 200 trades of a 40% win rate, 2R edge (expectancy +0.2R, Kelly 10.0%). The wins and losses are identical across the four groups; only the size differs. Switch on the error to see what happens when the true win rate is 34%, not the 40% the sizes were chosen for.
| Sizing (true edge 40% at 2R) | Risk | Share of Kelly growth | 10 losses in a row cost |
|---|---|---|---|
| Full Kelly | 10% | 100% | 65% |
| Half Kelly | 5% | 76% | 40% |
| Quarter Kelly | 2.5% | 45% | 22% |
| 1% fixed | 1% | 19% | 10% |
Worked example: choosing a fraction
- Measured edge: 45% wins at 2R. Kelly = 0.45 − 0.55 ÷ 2 = 17.5%.
- If the true win rate could be as low as 38%, true Kelly is 0.38 − 0.31 = 7%.
- Quarter of the measured Kelly: 4.4%, still below the pessimistic Kelly, so growth stays positive in both cases.
- Then check the drawdown: ten losses at 4.4% cost 36%. If that is too much to live with, size lower still.
Common mistake: trusting the backtest win rate
A win rate from 50 or 100 trades has a wide uncertainty band (module C1). Sizing to the point estimate treats a guess as a fact. Size to the low end of what the edge could be.
Check yourself
- Ten losses in a row happen. How much of the account is gone at full Kelly (10% risk) and at quarter Kelly (2.5%)?
- A backtest says 45% wins at 2R, so you size at Kelly, 17.5%. Live, the win rate turns out to be 40%. What is the true Kelly fraction?
- Edge: 40% wins at 2R. What is half Kelly?
Closing round
Pick a risk per trade you could hold through ten losses in a row, then play a mystery market at that size.
Play the round in the simulator →The simulator's markets are generated, not real prices; the round practises the arithmetic, it does not predict anything.
Further reading: Poundstone, Fortune's Formula. The lesson teaches the idea in its own words and exercises.