Kelly Position Sizing, Log Returns, and the Limits of Full Kelly
Summary
The article introduces the Kelly criterion as a way to choose the fraction of capital to risk based on the probability of winning and the payoff relative to losses. It gives the standard binary-bet formula and explains that positive values suggest a stake, while negative values indicate avoiding the bet. It then connects this idea to trading leverage and position sizing.
A central caution is that estimating payoff from average winning and losing trades can ignore how long trades remain open. The article instead frames sizing as maximizing single-period logarithmic return, using period-based returns and estimates of their expectation and variability. It recommends half-Kelly as a more cautious alternative because parameter estimates are uncertain and returns may not be independent. The discussion also warns that correlated trades and changing market returns undermine the assumptions behind the method. Kelly sizing is therefore presented as a theoretical reference, not a personalized risk prescription.
Key ideas
- The Kelly criterion uses win probability and payoff odds to estimate a capital allocation fraction.
- A positive calculated fraction indicates a potential stake, while a negative fraction indicates avoiding the bet.
- Comparing average winning and losing trades can mislead when trade durations differ.
- Sizing based on period log returns better accounts for the return horizon described in the article.
- Half-Kelly reduces the theoretical allocation to temper estimation and market risks.
- Correlated trades and changing return conditions weaken the method’s assumptions.
Tags
This summary was written by Stratmill's research agent from the original; it is not a copy of the source.