Kelly Criterion
Quick Definition
A formula for determining the optimal bet size that maximizes long-term growth rate while accounting for both the probability and magnitude of wins and losses.
What Is Kelly Criterion?
The Kelly Criterion, developed by John L. Kelly Jr. in 1956, calculates the optimal fraction of your capital to risk on each bet or trade to maximize long-term compound growth.
Formula: Kelly % = W - [(1 - W) / R]
Where: W = Win probability, R = Win/Loss ratio (average win ÷ average loss)
Example Calculation:
- Win probability: 55% (W = 0.55)
- Average win: $200, Average loss: $100 (R = 2.0)
- Kelly % = 0.55 - (0.45 / 2.0) = 0.55 - 0.225 = 0.325 = 32.5%
Kelly Criterion Outcomes:
| Fraction of Kelly | Expected Growth | Risk Level |
|---|---|---|
| Full Kelly (1.0x) | Maximum growth | Very volatile |
| Half Kelly (0.5x) | 75% of max growth | Much smoother |
| Quarter Kelly (0.25x) | 50% of max growth | Conservative |
| Over Kelly (>1.0x) | Growth DECREASES | Dangerous |
Why Half Kelly Is Popular:
- Full Kelly produces extreme drawdowns
- Input estimates (win rate, payoff) are uncertain
- Half Kelly gives ~75% of the growth with ~50% of the volatility
- Over-betting (above full Kelly) actually reduces long-term growth
Application to Investing:
- Position sizing for concentrated portfolios
- Determines maximum allocation per stock based on edge
- Prevents over-concentration in single ideas
- Used by famous investors like Warren Buffett (conceptually) and Edward Thorp (mathematically)
Key Insight: The Kelly Criterion proves that overbetting is worse than underbetting. If you're unsure about your edge, bet less than Kelly suggests.
Formula
Formula
f* = W - (1-W)/RKelly Criterion Example
- 1With 60% win rate and 2:1 payoff ratio, Kelly suggests risking 40% of capital — most investors use half-Kelly (20%)
- 2Edward Thorp used Kelly Criterion to beat blackjack and later to manage a highly successful hedge fund
Related Terms
Risk-Reward Ratio
The ratio comparing the potential loss (risk) to the potential gain (reward) of a trade or investment, expressed as risk:reward.
Risk Management
The systematic process of identifying, assessing, and mitigating financial risks to protect portfolio value and achieve investment objectives.
Maximum Drawdown
The largest peak-to-trough decline in portfolio value before a new peak is reached, measuring worst-case loss.
Monte Carlo Simulation
A computational technique that uses random sampling to model the probability of different outcomes, widely used in retirement planning and risk assessment.
Standard Deviation
A statistical measure of how spread out returns are from the average, quantifying investment volatility and risk.
Hedging
An investment strategy that uses offsetting positions to reduce the risk of adverse price movements in an existing asset or portfolio.
Expand Your Financial Vocabulary
Explore 130+ financial terms with definitions, examples, and formulas
Browse Risk Management Terms