The Kelly Criterion is a mathematical formula for determining the optimal bet size to maximise long-term growth rate. Kelly = (bp - q) / b, where b = odds received, p = probability of winning, q = probability of losing. While theoretically optimal, full Kelly is too aggressive for most traders — half-Kelly or quarter-Kelly is more practical.
Kelly % = (Win% × Average Win/Average Loss - Loss%) / (Average Win/Average Loss). Full Kelly maximises geometric growth but with extreme variance. Half-Kelly: 75% of full Kelly's growth with significantly less variance. Requires accurate estimation of win rate and payoff ratio. Overestimating edge leads to ruin with Kelly.
Calculate the Kelly percentage from your historical trade data. Apply half-Kelly for practical use. Example: 55% win rate, 1:1.5 payoff ratio → Kelly = (0.55 × 1.5 - 0.45) / 1.5 = 25%. Half-Kelly = 12.5%.
If your measured edge (win rate, payoff) decreases, Kelly size decreases. During drawdowns, reduce to quarter-Kelly. Review and recalculate monthly with updated statistics.
Applies to overall position sizing strategy, not individual trade management
Kelly Criterion is theoretically elegant but dangerous with imperfect data. Most traders don't have enough trade history for reliable win rate and payoff ratio estimates. Use Kelly as a ceiling, not a floor.
The Sharpe ratio measures risk-adjusted return by dividing excess return (above the risk-free rate) by the standard deviation of returns. The Sortino ratio improves on Sharpe by penalising only downside deviation, recognising that upside volatility is desirable. Both ratios help traders compare strategies on a level playing field and identify which approaches deliver the best returns for their level of risk.
Fixed-fractional position sizing risks a fixed percentage of your account on every trade (commonly 1-2%). This ensures that a string of losses reduces position sizes proportionally, protecting capital during drawdowns. It's the most widely recommended position sizing method for discretionary traders because it's simple, sustainable, and mathematically sound.
A maximum drawdown limit is a predefined loss threshold that triggers mandatory action — reducing size, stopping trading, or reviewing strategy. Common limits: daily max loss (e.g., 3%), weekly max loss (e.g., 5%), monthly max loss (e.g., 10%), and total max drawdown (e.g., 20%). Professional trading firms and prop firms enforce strict drawdown rules.
Risk of ruin calculates the probability that a trader will lose a specified percentage of their account — typically enough to end their trading career — given their win rate, average reward-to-risk ratio, and percentage risked per trade. This mathematical framework quantifies whether a trading strategy is survivable over the long run and helps traders set appropriate risk limits to ensure longevity.