Kelly Criterion in Practice: Half-Kelly, Fractional Kelly, and the Case Against Full Kelly

The Kelly criterion tells you the position size that maximizes the long-run geometric growth rate of capital. The math is beautiful. Following it literally is operationally insane.

This is one of the most counterintuitive results in systematic trading: the theoretically optimal answer is almost never the practically optimal answer. Understanding why is the difference between using Kelly as a tool and using it as a weapon against your own portfolio.

The math, briefly

For a continuous-return strategy with known expected return μ and known variance σ²:

f* = μ / σ²

f* is the fraction of capital to allocate. With μ = 12% and σ = 20%, f* = 3.0 — Kelly tells you to allocate 300% of capital (3× leverage). Following that prescription leads to a 60%+ maximum drawdown in expectation. Most investors do not survive a 60% drawdown without redeeming.

Why full Kelly is wrong in practice

Three structural problems:

1. μ and σ aren't known; they're estimated

Kelly assumes the inputs are exact. They aren't. A 12% expected return estimate from a backtest carries a standard error that scales with 1 / √T. Even with 10 years of daily data, the estimate is uncertain enough that the recommended Kelly fraction has a wide confidence interval.

The asymmetric problem: betting too much destroys capital catastrophically (compounding kills you when you over-bet); betting too little sacrifices return. The asymmetric loss function alone justifies betting well below the point estimate of f*.

2. Returns aren't stationary

Kelly assumes the edge is constant. Real edges decay, recover, regime-shift. A position size that's correct for last decade's edge is not correct for next decade's. Re-estimating frequently helps but introduces estimation noise.

3. The volatility of wealth is enormous at full Kelly

Even with perfect inputs, full-Kelly betting produces wealth volatility equal to the strategy's volatility — at full leverage. A 20% annualized strategy at full Kelly produces 20% annualized wealth volatility. That means routine 30% drawdowns and occasional 50%+ drawdowns. Most professional allocators would redeem; most retail traders would panic-flatten.

What fractional Kelly does

Multiply f* by a constant fraction (typically 0.25 to 0.5). The result:

Long-run growth rate drops by less than the fraction suggests. Half-Kelly retains roughly 75% of full-Kelly growth.
Volatility of wealth scales linearly with the fraction. Half-Kelly cuts wealth volatility in half.
Drawdown depth scales roughly with the fraction. Quarter-Kelly cuts max drawdown to roughly 25% of full-Kelly's drawdown.

The math: full-Kelly maximizes E[log(W)]. Quarter-Kelly forfeits a small amount of log-wealth in expectation in exchange for dramatically lower drawdown. For any investor with utility curvature stronger than log (which is essentially all investors), quarter- or half-Kelly is preferred.

How to set the fraction

A defensible institutional rubric:

Compute f from out-of-sample, post-cost edge estimates.* Not in-sample, not pre-cost.
Apply a confidence haircut based on edge estimate uncertainty. If μ has a 95% CI from 8% to 16%, use the lower end (8%) for Kelly computation.
Multiply by 0.25 to 0.5. Quarter-Kelly is the institutional default; half-Kelly only when edge is exceptionally well-established.
Cap at a maximum percent of capital regardless of what Kelly recommends. No single position sizes above e.g. 10% of capital.
Re-estimate quarterly. Edge decays.

When full Kelly is approximately right

Edge is known with extreme precision. Closed-form arbitrages, structural mispricings. Even here, fractional Kelly is safer.
Recovery from drawdown is structurally guaranteed. Almost never true in trading.
The investor's utility is exactly log-wealth. Unusual.

Practical takeaways

Full Kelly is never the right answer in practice. The asymmetric loss function alone justifies fractional sizing.
Quarter-Kelly is a defensible institutional default. Sacrifices ~30% of expected return for ~75% drawdown reduction.
Edge estimates are uncertain. Position sizing must respect that uncertainty. Otherwise the math gives you the wrong answer with high confidence.