Position Sizing & Leverage: Kelly Criterion Strategy › Summary

Position sizing determines whether a trading edge compounds into wealth or destruction. This chapter developed the mathematical foundations and practical frameworks for optimal sizing:

Kelly Criterion fundamentals: The Kelly formula maximizes long-term geometric growth by betting a fraction $f^* = \frac{pb - q}{b}$ in the discrete case or applying leverage $\ell^* = \frac{\mu}{\sigma^2}$ in the continuous case. Full Kelly betting is aggressive, often too aggressive for practical use.

Fractional Kelly: Using 25-50% of Kelly-optimal sizing sacrifices modest growth for substantially reduced variance and drawdown risk. Half-Kelly achieves 75% of Kelly growth with 25% of the variance, an attractive tradeoff for most investors.

Multi-strategy allocation: For portfolios of strategies, optimal allocation follows $\mathbf{w}^* \propto \boldsymbol{\Sigma}^{-1} \boldsymbol{\mu}$, generalizing Kelly to account for correlations. Strategies with better risk-adjusted returns and lower correlation receive higher weights.

Risk budgeting: When expected returns are uncertain, risk parity approaches allocate based on risk contribution rather than expected return. This produces portfolios that are less sensitive to expected-return estimation error, though potentially at the cost of expected return.

Leverage dangers: Leverage amplifies both gains and losses nonlinearly. Maximum drawdown probability increases dramatically with leverage, and numerous historical examples demonstrate how excessive leverage has destroyed sophisticated investors. Practical constraints on gross leverage, position limits, and margin requirements provide essential guardrails.

Volatility targeting: Dynamic position sizing based on current volatility estimates automatically reduces risk during dangerous periods. This approach has demonstrated ability to improve risk-adjusted returns across many asset classes and strategies.

The next chapter addresses ethical and regulatory considerations in quantitative trading, examining how position sizing and trading practices intersect with market integrity and investor protection requirements.