What Is the Kelly Criterion?
The Kelly Criterion is a mathematical formula that determines the optimal position size for a trade based on your edge (expected value) and the risk-reward characteristics of your strategy. Originally developed by John Kelly in 1956 for information theory, it has become a cornerstone of professional gambling and trading money management.
The Kelly Formula
The Kelly Criterion formula is: f* = (bp - q) / b
- f* = fraction of capital to bet (position size as % of account)
- b = ratio of average win to average loss (reward/risk ratio)
- p = probability of winning (win rate as decimal)
- q = probability of losing (1 - p)
Why Use Half Kelly Instead of Full Kelly?
While full Kelly maximizes long-term growth rate, it comes with significant volatility. Most professional traders use Half Kelly or Quarter Kelly for these reasons:
- Reduced volatility: Half Kelly cuts volatility roughly in half while sacrificing only 25% of growth rate
- Error tolerance: If your edge estimate is slightly wrong, Half Kelly is much more forgiving
- Psychological comfort: Full Kelly can produce stomach-churning drawdowns that cause traders to abandon the strategy
- Real-world constraints: Liquidity, slippage, and execution quality degrade as position sizes increase
Leverage-Adjusted Kelly
When using leverage, Kelly position sizes must be adjusted downward. This calculator automatically accounts for leverage by dividing the recommended position size by your leverage multiplier. For example, if Kelly suggests 10% and you're using 5x leverage, your actual position should be 2% of capital (controlling 10% notional exposure).
When Kelly Says Zero or Negative
If the calculator shows zero or negative Kelly values, your strategy has no edge or a negative edge. This means:
- Your expected value per trade is zero or negative
- You should not trade this strategy with real money
- Either your win rate is too low, or your average losses are too large relative to your average wins
Worked Example
With a 55% win rate, a 3% average win and a 2% average loss, the formula produces the following approximate allocations:
- Full Kelly: ~25% position size (aggressive)
- Half Kelly: ~12.5% position size
- Quarter Kelly: ~6.25% position size
Practical Tips for Using Kelly Criterion
- Start conservative: Begin with Quarter Kelly until you're confident in your edge estimate
- Track your stats rigorously: Kelly is only as good as your input data. Use at least 100 trades to estimate your win rate and averages
- Account for correlation: If your trades are highly correlated, reduce position sizes further
- Factor in costs: Include trading fees and slippage in your average win/loss calculations
- Rebalance regularly: Recalculate Kelly as your account grows or your edge changes