Optimal f and why full size is a trap

[Shadow Trader]

Ralph Vince's optimal f and the Kelly criterion describe the position size that maximises long-run geometric growth. In theory, betting that fraction produces the fastest compounding. In practice, it also produces gut-wrenching drawdowns and catastrophic outcomes when estimates are off.

The growth curve as a function of bet size is hump-shaped. Growth rises with size up to the optimum, then falls, and beyond about twice the optimum, growth turns negative. The left side of the hump is gentle. The right side is a cliff.

Because the inputs, win rate and payoff, are estimates, the real optimum is uncertain. Overestimating the edge means betting past the peak. Underestimating costs the same. The asymmetry suggests erring on the small side.

Practitioners often use half or quarter of the computed optimum. Half-Kelly gives roughly 75% of the growth with much lower volatility and drawdown.

For a scalper with an uncertain, decaying edge, even smaller sizes are sensible. The goal is to stay in the game while the data accumulates.

A concrete illustration: suppose a strategy's optimal fraction comes out at 10% of equity per trade, which sounds absurdly high. At that size, a run of five losses cuts the account by about 41%. Betting half of that, 5%, still produces drawdowns that would shake most people. Many scalpers settle on 0.25% to 1%, far below any theoretical optimum, because survival and sanity matter more than squeezing out the last bit of growth.

The gap between theory and practice isn't a failure of the mathematics. It reflects uncertainty in the inputs, and the fact that real people have limits.

What fraction of the theoretical optimum is used, and how was the edge estimate stress-tested?