Optimal Leverage: A Quantitative Approach to Position Sizing
Applying the Kelly Criterion and its fractional variants to crypto trading for mathematically optimal position sizing under uncertainty.
The Kelly Criterion
The Kelly Criterion, developed by John Kelly at Bell Labs in 1956, determines the optimal fraction of capital to risk on a bet. The formula is: f* = (bp - q) / b, where b = odds, p = win probability, q = loss probability.
Adapted for Crypto Trading
For trading with asymmetric payoffs: f* = (W/L * p - q) / (W/L) where W = average win, L = average loss, p = win rate, q = 1-p.
Example Calculations
| Strategy | Win Rate | Avg W/L | Full Kelly | Half Kelly | Quarter Kelly |
|---|---|---|---|---|---|
| Trend Following | 42% | 2.8 | 21.3% | 10.6% | 5.3% |
| Mean Reversion | 63% | 1.2 | 31.7% | 15.8% | 7.9% |
| Breakout | 35% | 3.5 | 16.4% | 8.2% | 4.1% |
| RSI Divergence | 53% | 1.8 | 26.7% | 13.3% | 6.7% |
Why Fractional Kelly?
- Estimation error: Our win rate and W/L estimates have uncertainty. Full Kelly assumes perfect knowledge.
- Non-normal distributions: Crypto returns have fat tails. Kelly assumes normal distributions.
- Drawdown tolerance: Full Kelly can produce 50%+ drawdowns. Half Kelly reduces max drawdown by ~40% with only ~25% reduction in long-run growth.
- Psychological comfort: Most traders cannot stomach Full Kelly volatility.
Practical Recommendation
Use Quarter Kelly for crypto trading. This provides roughly 50% of the theoretical growth rate with dramatically reduced drawdowns. For a strategy with a 53% win rate and 1.8 W/L ratio, this means risking approximately 6.7% of capital per trade, or roughly 3x leverage on a 2% stop loss.
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