Kelly criterion intuition
Derive a sensible per-trade risk from winrate and reward-to-risk using the Kelly framework.
Lesson path
Market Foundations + Forex Mechanics
Risk Management Math
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Derive a sensible per-trade risk from winrate and reward-to-risk using the Kelly framework.
What Kelly is actually saying
The Kelly criterion is a formula that suggests the bet fraction that grows a bankroll fastest over the long run. The simple version: fraction equals winrate times b, minus loss rate, divided by b. Here b is the ratio of your average win to your average loss. In plain English: if you know your winrate and your reward-to-risk, Kelly tells you the size that maximizes long-term growth, mathematically.
Worked example. Your system wins 50 percent of the time. Your average win is $20 and average loss is $10, so b equals 2. Plug into Kelly: (0.50 times 2 minus 0.50) divided by 2 = (1.0 minus 0.5) / 2 = 0.5 / 2 = 0.25. Kelly says risk 25 percent of your bankroll per trade. That number is correct in theory and dangerous in practice.
Why is full Kelly dangerous? Because Kelly assumes your winrate and reward-to-risk are exactly known. In real trading, those numbers wobble. They change with market regime, with sample size, with your discipline. If your true winrate is 5 percent lower than you think, full Kelly turns into ruin. Half Kelly (12.5 percent here) gives up some growth in exchange for huge robustness against parameter error.
On a $500 retail account, even half Kelly is too aggressive in practice because you cannot afford the variance. That is why the 1 percent rule from earlier lessons exists. It is roughly quarter-Kelly to one-eighth-Kelly for most realistic retail systems. The intuition you should keep: better edge plus better reward-to-risk justifies slightly more size. But the gap between theory and survivable real-world sizing is huge, and you stay on the safe side of that gap.
Recap: Kelly says risk a fraction tied to your edge and your reward-to-risk. Full Kelly is too aggressive. Use a quarter to a half of Kelly. On $500, 1 percent stays well inside the safe zone.
Knowledge check
Answer before moving on.
1. System: 50 percent winrate, avg win $20, avg loss $10. What does the Kelly formula return?
2. Why do most pros use a fraction of Kelly, like half or a quarter?
3. On a $500 retail account, what is the practical implication of Kelly intuition?
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