Kelly Criterion
Definition
The Kelly Criterion is a position-sizing formula that maximises long-term geometric growth: f* = (bp − q) / b, where b is the win/loss ratio, p is win probability, and q is loss probability. Full Kelly is mathematically optimal but variance-aggressive; most retail traders use 'fractional Kelly' (1/4 or 1/2 Kelly) to reduce drawdown variance.
Formula
f^* = \frac{bp - q}{b}f* = (b × p − q) / b, where b = win/loss ratio, p = win probability, q = loss probability
In-depth: Kelly Criterion
The Kelly Criterion, developed by Bell Labs physicist John L. Kelly Jr. for analysing signal noise in long-distance telephone calls, was rapidly adopted by Edward Thorp and others for gambling and later trading applications. Kelly proved that betting f* fraction of capital on each opportunity maximises the long-term logarithm of wealth — equivalent to maximising geometric mean growth.
Basic formula (binary outcome): f* = (bp − q) / b Where: - f* = fraction of capital to risk - b = win/loss payoff ratio (avgWin / avgLoss) - p = probability of win - q = 1 − p = probability of loss
Example: a strategy with 55% win rate and 1.5 win/loss ratio. f* = (1.5 × 0.55 − 0.45) / 1.5 = (0.825 − 0.45) / 1.5 = 0.25. Full Kelly says risk 25% of capital per trade. This is extreme variance — drawdowns of 50%+ are mathematically expected at full Kelly.
Why fractional Kelly: full Kelly maximises geometric growth but produces drawdown distributions that are psychologically and practically intolerable for most traders. A standard practice is 0.5 Kelly (half-Kelly) or 0.25 Kelly (quarter-Kelly), which reduces growth rate moderately but reduces drawdown variance substantially.
For the example above: - Full Kelly: 25% risk per trade, expected drawdowns 50%+ - Half Kelly: 12.5% risk per trade, drawdowns more manageable - Quarter Kelly: 6.25% risk per trade, conservative
Most retail forex traders use position sizing of 0.5-2% per trade, which is typically well below Kelly for any positive-expectancy strategy. This is appropriate because: 1. Kelly assumes known probabilities; real edges are uncertain and probabilities are estimates 2. Kelly assumes returns are independent; trade outcomes are often correlated 3. Variance at Kelly is psychologically destructive; survival matters more than optimal growth
Kelly is most valuable as a theoretical ceiling: position sizing above Kelly is provably suboptimal for long-term growth (over-betting produces eventual ruin even with positive expectancy). Position sizing well below Kelly is just sub-optimal growth, not destructive.
Limitations: Kelly assumes (1) you know p and b precisely, (2) outcomes are independent, (3) you can adjust position size continuously, (4) ruin has infinite negative utility. None of these hold strictly in forex trading; real Kelly application requires substantial fractional adjustment.