Risk-Constrained Kelly Sizing for Trading Strategies

Summary

The document explains how the risk-constrained Kelly criterion modifies standard Kelly position sizing. Standard Kelly sizing seeks to maximize long-run log growth using estimated win probability and win/loss payoff, but can lead to prolonged, deep drawdowns. The constrained version adds a limit on the probability that wealth falls below a chosen threshold. For a strategy with two outcomes, the article describes checking the unconstrained Kelly fraction against the risk limit and, if needed, finding an acceptable fraction with bisection.

A worked example applies the method to an SVM signal strategy using Microsoft historical data and technical indicators. It compares basic Kelly sizing, risk-constrained sizing, and versions gated by a buy-and-hold moving-average condition. The article reports informally that constrained sizing has lower position-size variability and drawdowns, alongside a lower cumulative equity curve. It provides no formal performance statistics, and the example’s findings are specific to its setup. Leverage, stop-losses, take-profits, and meta-labelling are suggested as possible extensions, not demonstrated results.

Key ideas

• Standard Kelly sizing maximizes theoretical long-run log growth using estimated win probability and payoff.
• The risk-constrained version limits the probability that wealth falls below a chosen minimum threshold.
• For a two-outcome bet, the article describes using bisection when the unconstrained Kelly fraction violates the risk limit.
• The Microsoft example reports smoother sizing and lower drawdowns with constrained sizing, but also lower cumulative returns.
• The example does not provide formal performance statistics, so its comparisons remain informal.

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