The Kelly Criterion: How Much to Bet When You Have an Edge
The Kelly criterion is a formula for the position size that maximizes long-term growth given your win rate and payoff. We explain the math, why full Kelly is too aggressive, and how traders use half-Kelly.
The question every strategy must answer
You have a strategy with a real edge. How much of your capital should you risk on each trade? Too little and you barely grow; too much and one bad streak wipes you out. The Kelly criterion is a formula that answers this precisely: it gives the fraction that maximizes your long-term compounded growth.
The formula
For a simple bet, Kelly says risk a fraction:
f = W β (1 β W) / R
- W = your win rate (probability a trade wins).
- R = your reward-to-risk ratio β how much you win versus lose per trade (see risk-reward ratio).
Example: you win 50% of the time (W = 0.5) and your winners are twice your losers (R = 2). Then f = 0.5 β 0.5/2 = 0.25, meaning Kelly suggests risking 25% of capital per bet. That already sounds like a lot β which is the whole warning.
Why full Kelly is too aggressive
Full Kelly maximizes growth in theory, but it assumes you know W and R exactly. In real trading you do not β you estimate them, and you are usually too optimistic. The consequences of overestimating are brutal: full Kelly produces stomach-churning drawdowns, and betting above Kelly actually reduces long-term growth while adding huge risk.
Half-Kelly: what practitioners actually do
Most serious traders use half-Kelly or less β take the Kelly fraction and cut it in half (or to a quarter). This keeps most of the growth (roughly three-quarters of it) while dramatically reducing drawdowns and the damage from bad estimates. Combined with a hard position-sizing rule, it turns a fragile edge into a survivable one.
Reality checks
- Kelly needs a genuine edge. If W and R do not actually beat break-even, Kelly says bet zero β and no sizing rule saves a losing system.
- Estimates drift. Recompute W and R from a real trading journal, not from hope.
- Correlation breaks it. Kelly assumes independent bets; ten correlated positions act like one oversized bet.
Conclusion
The Kelly criterion, f = W β (1 β W)/R, gives the bet size that maximizes long-term growth from your win rate and payoff. Full Kelly is mathematically optimal but too aggressive in practice because you only estimate your edge β overbetting cripples growth and creates savage drawdowns. Use half-Kelly or less, demand a real edge, and recompute from actual results.
Next step
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