The Kelly Criterion Formulation
Formulated by J.L. Kelly Jr. in 1956 at Bell Labs, the Kelly Criterion computes the optimal fraction \(f^*\) of capital to allocate to maximize long-term geometric capital growth:
f^* = rac{b \cdot p - q}{b} = p - rac{q}{b}
Where:
- \(b\) = Net odds received (Payoff ratio = Avg Win / Avg Loss)
- \(p\) = Probability of winning
- \(q\) = Probability of losing (\(1 - p\))
Why Full Kelly Is Dangerous in Live Markets
Full Kelly betting assumes you know the true underlying probabilities with absolute certainty. In real financial markets, parameters are non-stationary and estimated with statistical error. Sizing at full Kelly results in violent drawdowns (often exceeding 50% to 70%), which cause psychological capitulation or broker liquidation.
Industry Standard Practice: Fractional Kelly. Production quant desks size positions at Half-Kelly (0.50) or Quarter-Kelly (0.25), achieving roughly 75% to 85% of theoretical growth while reducing portfolio variance and drawdown risk by more than 50%.