Kelly Criterion Position Sizing with Drawdown-Adjusted Scaling

Apex's early position sizing used a fixed 5% of capital per trade regardless of signal confidence, historical win rate, or current drawdown. The result was symmetric exposure across wildly asymmetric opportunities. A signal with 72% win rate and 1.8:1 reward-to-risk received the same allocation as a signal with 48% win rate and 0.9:1 reward-to-risk. Capital was poorly distributed, and drawdown episodes were uncontrolled because the system continued full allocation through losing streaks.

The position sizing problem had three distinct subproblems. Optimal fraction given signal quality: given a win probability estimate and an expected payoff ratio, what fraction of capital maximizes long-run growth without risking ruin? Signal quality estimation: the win probability input to Kelly could not be assumed known and had to be estimated from signal score and calibrated against backtest outcomes. Dynamic scaling under drawdown: full Kelly allocations during adverse market regimes amplified losses.

The full Kelly formula for a binary outcome is f* = (p * b - q) / b where p is win probability, q is loss probability, and b is the net payoff ratio. Full Kelly was capped at 0.25 as an absolute ceiling, because full Kelly at high win rates can produce allocations above 40%, which is ruin-adjacent in practice due to execution slippage and estimation error.

The implementation used 50% Kelly as the default scaling factor. Half Kelly reduces growth rate by approximately 25% relative to full Kelly but reduces variance and maximum drawdown by approximately 50%. For a system with estimation error in p, half Kelly is generally superior to full Kelly on a risk-adjusted basis.

Calibration mapping was built using isotonic regression of observed win rate against score decile across 10,486 historical trades. The result was a monotone mapping from score to calibrated win probability: P(win | score = 0.82) = 0.712, P(win | score = 0.61) = 0.438.

Drawdown scaling: current equity drawdown was computed continuously as dd = 1 - (current_equity / hwm) where hwm is the rolling high-water mark. Below 5% drawdown, full half-Kelly was used. Between 5 and 25% drawdown, sizing scaled down linearly to 20% of half-Kelly. At or beyond 25% drawdown, position size was capped at 20% of half-Kelly regardless of signal quality until the portfolio recovered above the 5% drawdown threshold. The 25% hard floor was set rather than zero to prevent complete inactivity during drawdown.

The position sizer was implemented as a Rust module. The calibration table was loaded at startup from a ClickHouse query into a sorted Vec, then binary-searched at runtime for each sizing call. The market hours enforcement blocked new entries within 30 minutes of the relevant market's close. US equities blocked new entries after 15:30 ET. Crypto used a 4-hour maximum hold time as a proxy.

One postmortem issue: early implementation computed drawdown using mark-to-market equity including open position unrealized PnL. This caused drawdown scaling to fire mid-trend when unrealized losses were temporarily large but would recover. The fix changed the high-water mark computation to use only realized equity.

The shift from fixed sizing to Kelly-based sizing improved Sharpe from 0.79 to 1.34 on the same signal set over the same 4-week period. Maximum drawdown dropped from 18.3% to 9.7%. The drawdown scaling mechanism activated 9 times over the 4-week period, each time reducing exposure automatically without human intervention. In 7 of 9 activations, the drawdown was temporary and the portfolio recovered within 3 to 5 trading days.