Kelly Criterion
Kelly Criterion for Optimal Position Sizing · Also known as: Kelly Formula, Optimal Bet Sizing
The Kelly Criterion (1956) is a formula for optimal bet sizing that maximizes the long-run logarithmic growth of wealth. It specifies the optimal fraction of capital to risk on each trade based on win probability and payoff ratio. The criterion has become foundational in quantitative trading, portfolio management, and behavioral economics.
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When to use it
Use Kelly for trading systems with repeated independent trades and known win rate. Essential for hedge funds and systematic traders. Use with caution in markets with correlated trades or time-varying edges—reduce bet size (half-Kelly) to manage model error.
Strengths & limitations
- Optimal growth: Kelly maximizes expected logarithmic growth, leading to highest long-term returns for any risk level
- Mathematically rigorous: derived from information theory; optimal in both discrete and continuous settings
- Intuitive: bet size proportional to edge makes intuitive sense; higher p and b warrant larger bets
- Widely applicable: Kelly works for any repeatable trade or investment with positive expected value
- Model error: Kelly assumes known win probability; estimation error leads to over-betting and ruin risk
- Correlation assumption: Kelly assumes independent trades; correlated losses amplify ruin probability
- Discrete stakes: Kelly formula applies exactly to binary outcomes; exotic payoffs require numerical optimization
- Behavioral hurdles: full Kelly implies portfolio volatility that many investors find intolerable (drawdowns can exceed 50%)
Frequently asked
What is full Kelly vs. half-Kelly?
Full Kelly bets the fraction f* that maximizes growth. Half-Kelly bets f*/2. Half-Kelly trades lower volatility and drawdown risk for slower growth. In practice, practitioners use quarter-Kelly or 10%-Kelly to hedge model error and comfort with volatility.
What if my win probability is 51% and the odds are even?
f* = (0.51 * 1 - 0.49) / 1 = 0.02 or 2%. You should risk 2% of capital per trade. This tiny bet reflects the tiny edge (1% win probability advantage).
How do I handle multiple simultaneous trades?
Use portfolio Kelly, which accounts for correlations between trades. Compute the covariance matrix of trade returns, then solve for the portfolio weight vector that maximizes growth. This is more complex than single-trade Kelly.
What if my edge varies over time?
Use dynamic Kelly: estimate p(t) at each time and adjust f(t) accordingly. This requires constantly updating win probability estimates. Alternatively, use a lower fixed fraction (half-Kelly) to hedge time-varying edge risk.
Sources
- Kelly, J. L. (1956). A new interpretation of information rate. Bell System Technical Journal, 35(4), 917-926. DOI: 10.1002/j.1538-7305.1956.tb03809.x ↗
- Thorp, E. O. (2017). A Man for All Markets: From Las Vegas to Wall Street. Random House. link ↗
How to cite this page
ScholarGate. (2026, June 3). Kelly Criterion for Optimal Position Sizing. ScholarGate. https://scholargate.app/en/quantitative-finance/kelly-criterion
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