Kelly vs Fixed Risk
Assume an idealized system with a 50% win probability and a 2:1 reward-to-risk ratio. Under the Kelly formula, the full Kelly fraction is 25% of capital. Half Kelly would risk 12.5%, while a conservative fixed-risk approach might use 1%. Full Kelly maximizes expected logarithmic growth within the assumptions of the model, but it also produces much larger equity fluctuations. Fractional Kelly sacrifices some theoretical growth in exchange for lower volatility. A small fixed fraction grows more slowly but places much less capital at risk on each outcome.The sizing rule that maximizes theoretical growth is not the same as the sizing rule that minimizes drawdown or maximizes stability.Real trading adds parameter uncertainty and changing market conditions, which makes aggressive Kelly sizing especially sensitive to estimation error.