Kelly Criterion vs fixed fractional position sizing
Both methods scale risk with equity, but they answer different questions. Fixed fractional sizing starts with a risk limit. Kelly starts with an estimated edge and calculates the fraction that maximizes long-run logarithmic growth under strict assumptions.
Fixed fractional sizing is easier to govern: choose a percentage of current equity and recalculate the cash risk on every trade. Kelly can adapt sizing to an estimated win rate and payoff, but estimation error can make Full Kelly aggressive. Fractional Kelly and a hard maximum-risk cap are more conservative ways to test the idea.
The core difference
With fixed fractional sizing, a trader selects a constant percentage such as 0.5% or 1% of current equity. After a loss, the cash amount falls; after a gain, it rises. The fraction does not change simply because the estimated edge changes.
For a binary win/loss model, the Kelly fraction is f* = p − (q ÷ b), where p is win probability, q = 1 − p, and b is the average net reward for each unit risked. If this produces zero or a negative number, the inputs do not imply a positive Kelly allocation.
At a 45% win rate and 1.5:1 average reward:risk, Full Kelly is 8.33%. Quarter Kelly is about 2.08%. A fixed fractional plan might instead use 1% regardless of that estimate.
Side-by-side comparison
- Input is a chosen equity percentage.
- Simple to audit and enforce.
- Does not automatically respond to a measured edge.
- Still produces compounding and sequence risk.
- Input is estimated win rate and payoff.
- Targets long-run log-growth in the idealized model.
- Highly sensitive to inaccurate inputs.
- Full Kelly can create uncomfortable drawdowns.
Neither method discovers whether a strategy really has an edge. Both inherit the quality of the underlying win-rate and payoff estimates. Spreads, commissions, changing market regimes and correlated trades can make live outcomes worse than the model.
Why traders test fractional Kelly
Fractional Kelly multiplies the Full Kelly result by a chosen fraction. Half Kelly uses 50% of the calculated allocation; quarter Kelly uses 25%. This reduces the sensitivity of position size to estimation error and generally reduces path volatility, while also reducing expected growth under the ideal assumptions.
A maximum-risk cap is a separate safeguard. If quarter Kelly suggests 2.08% but the cap is 1%, the simulation should use 1%. The Kelly Monte Carlo Simulator exposes both controls so the calculated number cannot silently override your risk policy.
The same expectancy can produce different paths
A 45% win rate and 1.5R average win have positive expectancy: (0.45 × 1.5R) − (0.55 × 1R) = 0.125R per trade. That average does not dictate the order of wins and losses. Losing clusters can occur early, late or repeatedly.
Use the Fixed Risk Monte Carlo Simulator and the Kelly simulator with the same win rate, payoff, number of trades and bot paths. Compare median ending equity, the poor P10 path, maximum drawdown, target success and ruin—not only the best outcome.
When each method may be useful
- Use fixed fractional testing when you want a simple risk budget that is independent of a noisy edge estimate.
- Use fractional Kelly testing when you have a large, relevant trade sample and want to examine how the estimated edge could inform sizing.
- Use a cap with either method when broker, prop-firm or personal drawdown constraints matter.
- Use neither result blindly when trades overlap, losses can exceed stops, or the strategy changes across regimes.
A reasonable comparison holds every other input constant and changes only the sizing rule. If the plan survives only under precise win-rate assumptions, treat that fragility as a warning.
A repeatable comparison workflow
First calculate expectancy from a meaningful sample with the Trading Expectancy Calculator. Next run at least 1,000 bot paths under fixed fractional sizing. Then run fractional Kelly with a conservative fraction and maximum cap. Record the median and poor-case drawdowns, not just ending balances. Finally, lower the win rate and payoff to see whether the risk plan survives estimation error.