Glossary
Kelly Criterion
Position-sizing formula maximizing geometric (compounded) growth. Mathematically optimal in theory, almost always too aggressive in practice.
The Kelly criterion is the position size that maximizes the long-run geometric growth rate of capital. Derived by John Kelly in 1956, it gives a closed-form answer to "how much should I bet?" given known edge and volatility.
Formula
For a continuous-return strategy:
f* = μ / σ²
- f* — fraction of capital to allocate
- μ — expected excess return
- σ² — variance of returns
For a binary bet with probability p and win/loss ratio b:
f* = (bp − (1 − p)) / b
Why "Kelly-optimal" rarely means "optimal"
Kelly assumes:
- Edge is known with certainty.
- Returns are stationary.
- You can rebalance continuously and frictionlessly.
In practice all three fail. Estimation error in μ inflates the recommended bet. Edge degrades. Rebalancing has costs. Half-Kelly (f* / 2) and fractional-Kelly (typically 0.25× to 0.5×) are the institutional defaults — they sacrifice a modest amount of theoretical growth for a much smaller drawdown profile.
The math: betting double-Kelly produces zero long-run growth. Betting full-Kelly maximizes expected log wealth but with stomach-churning volatility. Betting quarter-Kelly cuts the drawdown by ~75% while only giving up ~30% of the expected return.
Practical use
- Use Kelly to upper-bound position size, not to set it directly.
- Estimate μ and σ on robust, post-cost OOS data.
- Re-estimate quarterly; edge decays.