Fractional Kelly Meets Drawdown Zones: Optimal Sizing Under FTMO

The Kelly Problem

Full Kelly sizing maximizes long-run geometric growth. It also produces drawdowns that would breach FTMO limits within the first month. The theoretical optimal bet size for a 59.2% win rate system with 1.5:1 reward-to-risk is around 15% per trade. That is insane for a funded account.

Quarter-Kelly brings the theoretical optimal down to about 3.75%. That is still aggressive. S05 further caps this with the DD-triggered risk zones from S40, starting at 0.30% in normal conditions and scaling down to 0.15% during critical drawdowns. The interaction between Kelly-derived sizing and drawdown-based caps creates a system that grows during good periods and turtles during bad ones.

How the Zones Interact

In the NORMAL zone (0-4% DD), the system uses 0.30% risk per trade. This is well below quarter-Kelly but reflects the FTMO constraint reality. You are not optimizing for maximum growth. You are optimizing for never breaching 10% total drawdown while still generating meaningful returns.

The CAUTION zone (4-6% DD) drops to 0.25%. DANGER (6-8%) goes to 0.20%. CRITICAL (8-10%) floors at 0.15%. Each step down reduces the probability of the drawdown deepening. Monte Carlo simulations with these zones showed breach probability at 0.08%, compared to 2.1% with fixed 0.30% sizing.

Honest Sizing Conclusions

Position sizing is the most important decision in the system, more important than signal quality, entry timing, or exit management. A mediocre signal with great sizing beats a great signal with mediocre sizing over any meaningful sample. S05 does not try to be clever about sizing. It starts conservative, gets more conservative when things go wrong, and lets the 59.2% win rate and 1.60 profit factor do the compounding work. The projected 4.35% monthly return comes not from aggressive sizing but from consistent execution at controlled risk.