What is the Kelly Criterion? Definition, Formula, and Example
The Kelly Criterion is a position-sizing formula that calculates the fraction of capital to risk on each trade in order to maximize long-term geometric portfolio growth.
What Is the Kelly Criterion?
The Kelly Criterion is a position-sizing formula that determines the optimal fraction of capital to risk on each trade in order to maximize the long-term geometric growth rate of the portfolio. Developed by Bell Labs scientist John L. Kelly Jr. in 1956 and popularized in trading by Edward Thorp, it answers the question that risk-of-ruin and fixed-percent sizing cannot: given a measurable edge, exactly how much should you bet?
How the Kelly Criterion Is Calculated
The classical formula for a binary bet (win or lose with fixed payouts):
**f\* = (bp − q) / b**
Where:
- f* = fraction of bankroll to wager
- b = net odds received on the wager (win amount per unit risked)
- p = probability of winning
- q = probability of losing (1 − p)
For trading with continuous outcomes, the practical form is:
**f\* = W − [(1 − W) / R]**
Where:
- W = historical win rate (decimal)
- R = average winner ÷ average loser (in dollars)
A negative f* means no edge—do not trade. A positive f* is the percentage of equity to allocate per trade. f* > 1 implies leverage is mathematically optimal, but in practice this is rarely deployed because the underlying assumptions (stable parameters, independent trades) are too brittle to bet a portfolio on.
Worked Example: Sizing a Breakout System
A trader's backtest on SPY breakout setups produces:
- Win rate: 55% → W = 0.55
- Average winner: $420
- Average loser: $210
- R = 420 / 210 = 2.0
Plugging in:
f* = 0.55 − (0.45 / 2.0) = 0.55 − 0.225 = 0.325
Full Kelly says size each trade at 32.5% of equity. On a $50,000 account that is $16,250 of risk per trade—a level most traders find intolerable on volatility grounds. Standard practice is half-Kelly (16.25%) or quarter-Kelly (8.1%), which sacrifices some compounding rate in exchange for materially lower drawdowns and robustness to parameter error.
When Traders Use Kelly
- Systematic strategies with stable, measurable edges (statistical arbitrage, trend-following, options-selling programs)
- Bankroll-style frameworks where each trade is approximately independent
- Cross-strategy comparison: higher Kelly f* signals a higher-edge system before live deployment
- Drawdown forecasting: Monte Carlo simulations use Kelly fractions as inputs to estimate the distribution of drawdowns
Renaissance Technologies, Susquehanna, and most quantitative shops use Kelly-derived sizing internally, almost always at fractional Kelly. Edward Thorp ran his blackjack card-counting system and his Princeton-Newport hedge fund on the formula explicitly.
Limitations and Common Misconceptions
Kelly is uncompromising about its inputs. Estimating W or R 5% too high produces dramatically oversized positions, and full-Kelly's expected drawdown can exceed 50% even with correctly specified parameters. Real markets violate independence: trades are correlated, regimes shift, and the "true" win rate drifts. Most professionals use one-quarter to one-half Kelly because:
- Half-Kelly captures roughly 75% of the geometric growth at one-quarter the variance
- Drawdowns scale roughly linearly with the Kelly fraction
- Fractional Kelly compensates for parameter uncertainty without rebuilding the formula
Common misconceptions: Kelly is not a stop-loss—it sizes the position, not the exit. It does not work on a single trade; its guarantees are asymptotic across hundreds of trades. It cannot rescue a negative-expectancy strategy—if W and R produce f* ≤ 0, the only correct size is zero.