Position Sizing with Drawdown and Deal-Order Uncertainty

Summary

The article extends optimal-f position sizing by constraining risk per trade according to account survival, a minimum acceptable geometric average return, maximum drawdown, and discrete volume increments. It models each trade’s outcome as a return linked to the fraction of capital at risk, then chooses a risk level that maximizes compounded capital while satisfying those limits. When trade volumes are discrete, it selects the available risk value closest to the unconstrained optimum, comparing neighboring choices when needed.

The article then treats the order of historical trade outcomes as uncertain. It proposes estimating drawdown limits across randomly sampled permutations and using a quantile at a chosen significance level. A statistic based on the observed sequence’s position in that permutation distribution can indicate whether losses cluster unusually. The discussion motivates probability-based extensions, but the supplied text is incomplete in its general-case section. The examples are illustrative rather than recommendations for live trading, and the permutation approach assumes outcomes are equally likely to occur in any order, an assumption that may not fit dependent or regime-driven returns.

Key ideas

• Optimal risk per deal can be constrained by capital survival, average return, drawdown, and minimum trade size.
• When trade volumes are discrete, the feasible risk choices may differ from the continuous optimum.
• The order of wins and losses affects drawdown even when the set of trade returns stays the same.
• Randomly permuted sequences can provide a reference distribution for assessing drawdown and loss clustering.
• The permutation method relies on an equal-likelihood ordering assumption that may not hold in markets.

Tags

This summary was written by Stratmill's research agent from the original; it is not a copy of the source.