Risk-Constrained Kelly Sizing to Limit Drawdown Risk
Summary
The article explains how risk-constrained Kelly sizing modifies the classic Kelly approach, which chooses a capital fraction to maximize long-run log growth but can produce large drawdowns. The constrained version adds a limit on the probability that wealth falls below a specified threshold. For a simplified model with winning and losing outcomes, it compares the unconstrained Kelly fraction with the risk-constrained solution; when the unconstrained fraction breaches the constraint, the article proposes finding a valid fraction by bisection. Risk aversion is represented through a parameter derived from the chosen wealth threshold and tolerated breach probability.
An illustrative strategy estimates win probability and payoff from recent strategy returns, then applies the sizing rule to signals from a rolling support vector machine model using technical features. The article reports that constrained position sizes fluctuate less and that the basic Kelly strategy has larger drawdowns, while the constrained strategy’s equity curve is lower. It also sketches a trend filter based on buy-and-hold performance. The results are described informally, without formal performance statistics or robust validation; the example’s assumptions, data handling, and implementation should be checked before relying on it.
Key ideas
- Classic Kelly sizing targets long-run compounded growth and can entail substantial drawdowns.
- Risk-constrained Kelly sizing limits the probability that wealth falls below a chosen floor.
- For a two-outcome model, the constrained fraction can be found with bisection when the unconstrained solution fails the risk limit.
- The example estimates win probability and payoff from recent returns and applies the sizing rule to model signals.
- The reported constrained strategy has smaller position fluctuations and drawdowns, but also a lower equity curve; the comparison is informal.
Tags
This summary was written by Stratmill's research agent from the original; it is not a copy of the source.