Position Sizing Showdown: Fixed Fractional vs. Kelly Criterion Backtest

# Position Sizing Showdown: Fixed Fractional vs. Kelly Criterion Backtest

Most traders obsess over entries and exits while ignoring position sizing, the element that often determines whether a profitable strategy actually makes money or blows up. We ran the same trend-following strategy with four different position sizing methods to quantify the differences.

The Base Strategy

We used a simple 50-day breakout system on a portfolio of 20 futures markets. The strategy has a historical win rate of 38% with an average winner 2.8 times the size of the average loser. This is typical of trend-following systems and provides a good testbed for position sizing comparisons.

Method 1: Fixed Dollar Amount

The simplest approach: risk $1,000 per trade regardless of account size. Starting with $100,000, this produced 8.4% annualized returns with a maximum drawdown of 24%. The problem is obvious: as the account grows, each trade becomes proportionally less meaningful. As it shrinks, risk becomes proportionally larger.

Method 2: Fixed Fractional (2% Risk)

Risking 2% of current equity per trade produced 12.1% annualized returns with a maximum drawdown of 31%. The geometric growth advantage of sizing proportionally to equity is clear. The strategy naturally reduced exposure during drawdowns and increased it during winning streaks.

Method 3: Full Kelly Criterion

The Kelly formula suggested optimal sizing of approximately 8% risk per trade based on the win rate and payoff ratio. Full Kelly produced a stunning 28.4% annualized return but with a soul-crushing 67% maximum drawdown. Few humans could psychologically survive watching two-thirds of their capital disappear.

Method 4: Half Kelly

Half Kelly (4% risk per trade) achieved 19.8% annualized returns with a 42% maximum drawdown. This represents 75% of full Kelly returns with significantly less risk. The mathematical relationship is that half Kelly captures 75% of the growth rate with dramatically less variance.

The Geometric Return Insight

The key lesson from this backtest is that maximizing arithmetic returns (full Kelly) does not maximize geometric returns (actual wealth growth) for most practical time horizons. Volatility drag means that high-variance paths often underperform lower-variance paths even when the expected arithmetic return is higher.

Drawdown Duration Matters Too

Full Kelly experienced drawdowns lasting over 18 months on four separate occasions. Half Kelly had drawdowns exceeding 12 months twice. The 2% fixed fractional method never had a drawdown lasting more than 9 months. Time in drawdown affects psychology and opportunity cost even if the eventual recovery is larger.

Estimation Error Is the Real Killer

The Kelly criterion requires accurate estimates of win rate and payoff ratio. In our backtest, we used the true historical values. In practice, these parameters shift over time. Using estimated parameters that were off by just 20% from true values caused full Kelly to underperform half Kelly in total return due to over-sizing during adverse periods.

Practical Recommendations

For most traders, fixed fractional sizing between 1-3% risk per trade offers the best balance of growth and survivability. Half Kelly is appropriate for systematic traders with high confidence in their edge estimates and the ability to withstand 40%+ drawdowns. Full Kelly should remain a theoretical concept rather than a practical position sizing method.

The Bottom Line

Position sizing transformed the same entry and exit signals from an 8.4% to a 28.4% annualized return. Nothing else in trading has this kind of leverage over outcomes. Before optimizing your next indicator, optimize your sizing. The backtest proves that how much you bet matters far more than what you bet on.