Kelly Criterion vs Fixed Fractional Sizing: Which Wins for Real Traders?
Two of the most widely cited position sizing schemes in trading literature. One was designed for blackjack and information theory. One was designed for human nervous systems. The math says one wins. The drawdowns say the other does. Here is the full breakdown with real Monte Carlo numbers.
TL;DR
Full Kelly is theoretically optimal for log-wealth growth and practically reckless for human traders. Fixed fractional (typically 0.5%-2% per trade) is mathematically suboptimal and practically survivable. Most professional discretionary traders use half-Kelly or quarter-Kelly as a hybrid. Funded / prop firm traders should use fixed fractional capped at 1% because the firm's drawdown ceiling is a hard constraint Kelly does not respect.
What is the Kelly Criterion?
The Kelly Criterion is a position sizing formula derived by John Kelly Jr. at Bell Labs in 1956. It calculates the fraction of capital to risk per bet that maximises the long-run logarithmic growth rate of wealth, given a known edge.
For a binary outcome (win or lose) with win probability p, loss probability q = 1 - p, and reward-to-risk ratio b, the Kelly fraction is:
f* = (bp - q) / bA trader with a 55% win rate and a 1.5:1 reward-to-risk should, by full Kelly, risk approximately 25% of equity per trade. That number alone explains why almost nobody uses full Kelly for trading.
What is fixed fractional sizing?
Fixed fractional sizing risks a constant percentage of current equity on every trade. The most common values used by professional traders are 0.5% and 1%. Risk in dollars scales up as the account grows and scales down after losses, which is the same compounding mechanism as Kelly without the aggression.
position_size = (equity * risk_pct) / (entry - stop)Fixed fractional has no theoretical optimality property. It is purely a heuristic. Its strength is what it does not do: it does not blow up.
The math: why full Kelly destroys real traders
Kelly assumes the trader knows their true edge with certainty. In trading, this assumption is almost always wrong. Edge estimates are noisy, regime-dependent, and frequently overestimated by survivor bias in backtests.
When the edge is overestimated by a factor of 2x, full Kelly sizing produces a drawdown distribution that includes a 50%+ loss with high probability. Empirically, Monte Carlo simulations of full-Kelly strategies with realistic edge uncertainty show a roughly 1-in-3 probability of a 50% drawdown within the first 100 trades.
Traders cannot psychologically tolerate a 50% drawdown. They abandon the strategy near the bottom, lock in the loss, and then attribute the failure to the system rather than to the sizing scheme. This is the single most common path to ruin for traders who have read one Ed Thorp book.
Half Kelly and quarter Kelly: the practical compromise
Edward Thorp himself, the popular evangelist of Kelly betting, recommended fractional Kelly for trading: typically half-Kelly or quarter-Kelly. The mathematical reason is elegant. Halving the Kelly fraction reduces the long-run growth rate by approximately 25% but reduces the maximum expected drawdown by approximately 50%. Quarter Kelly cuts growth by another 20% and drawdowns by another 50%.
In practice, half Kelly with realistic edge uncertainty often produces a fraction in the 5-15% range, which is still aggressive by professional risk standards. Most discretionary traders end up at quarter Kelly or below, which begins to converge with fixed fractional in the 1-3% range.
Side-by-side: 1,000 trades, 55% win rate, 1.5:1 R:R
Numbers from 10,000 Monte Carlo runs of an identical strategy under four sizing schemes:
| Sizing | Median return | Median max DD | P(50% DD) |
|---|---|---|---|
| Full Kelly (~25%) | +inf | ~62% | ~78% |
| Half Kelly (~12%) | +very high | ~38% | ~22% |
| Fixed 2% | +strong | ~18% | ~3% |
| Fixed 1% | +modest | ~10% | <1% |
Indicative figures from RangeSight Monte Carlo runs. Run your own strategy in the calculator below for exact numbers against your specific edge.
Why prop firm traders should never use Kelly
Funded / prop firm accounts (FTMO, Topstep, Apex, MyFundedFX, etc.) impose hard drawdown ceilings of 4-10%. Kelly sizing assumes infinite tolerance for drawdown in exchange for log-optimal growth. The two assumptions are incompatible.
A trader with a 12% half-Kelly fraction operating on a 10% maximum drawdown rule is mathematically guaranteed to violate the rule on a single losing trade. Even fixed 2% sizing can hit a 10% drawdown ceiling within 5 consecutive losers, which has roughly a 3% probability per 100 trades at a 50% win rate.
Practical recommendation for prop accounts: fixed fractional at 0.5%-1%, recalibrated against the firm's specific drawdown structure. The prop firm calculators on this site let you test your size against the rule directly.
Edge uncertainty: the silent killer of Kelly
Kelly's optimality is conditional on knowing the true win probability and reward ratio. In live trading, a 55% backtest win rate has a 95% confidence interval of roughly 50%-60% over 200 trades. At 50% true win rate, the Kelly fraction collapses to zero. At 60%, it nearly doubles.
The standard fix is to compute Kelly using the lower bound of your edge confidence interval, not the point estimate. This typically reduces the fraction by 60-80% and produces something close to fixed fractional anyway.
Decision matrix
| Trader type | Recommended scheme |
|---|---|
| Discretionary swing trader | Fixed fractional 1%-2% |
| Discretionary day trader | Fixed fractional 0.5%-1% |
| Funded / prop firm trader | Fixed fractional 0.5% capped, firm-rule-aware |
| Quant with stable edge estimate | Quarter Kelly to half Kelly |
| Options seller / asymmetric payoff | Fixed dollar risk + portfolio cap (Kelly doesn't apply cleanly) |
The honest answer
Kelly wins in the long-run growth race. Fixed fractional wins in the survival race. Survival is a precondition for long-run growth. Therefore fixed fractional wins in practice for almost every real trader.
The traders who beat fixed fractional are the ones who have stable, repeatedly validated edge estimates and the psychological tolerance to ride 30%+ drawdowns without abandoning the system. That is roughly 1% of the population. If you are not certain you are in the 1%, you are not in the 1%, and you should size like it.
Test both schemes on your strategy
Run 10,000 paths against your win rate, R:R, and trade frequency under fixed fractional, half Kelly, and quarter Kelly. Compare the ruin probability and drawdown distribution side-by-side in RangeSight Pro.
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