Moral Expectation, Kelly Sizing, and Risk Control in Trading
Summary
The article distinguishes mathematical expectation from utility adjusted for a trader’s capital, using Bernoulli’s treatment of the St. Petersburg paradox to motivate moral expectation. It applies the idea to trades with known stop loss and take profit distances, point value, position size, and estimated win probability. Given two fixed trade parameters, the equation can be used to solve for a permissible stop loss or a take profit; differentiating with respect to lot size yields an optimal sizing expression related to the Kelly criterion. The article stresses that the underlying trade expectation must be positive.
Simulations compare fixed and floating stop or target settings and show how sizing based on moral expectation can produce large gains as well as substantial losses. It proposes reducing the deposit used in sizing or adjusting the estimated win probability to manage risk. A moving-average system test on EURUSD H1 over 2021–2022 reports that lower risk reduced net profit while improving several other metrics. These results are examples from one system and period; the article does not establish that the method generalizes, and its sizing depends on reliable probability estimates.
Key ideas
- Mathematical expectation treats payoffs alike regardless of the player’s capital, while moral expectation incorporates the utility of gains and losses relative to available wealth.
- For trades with stop loss and take profit levels, moral expectation can help solve for a compatible trade parameter when the other inputs are fixed.
- Optimizing the moral expectation over lot size produces a sizing rule related to the Kelly criterion and requires positive mathematical expectation.
- Aggressive expectation based sizing can amplify both growth and drawdowns, so the article proposes limiting the capital used in calculations or adjusting the win probability.
- A EURUSD H1 example reports lower profits but improved risk metrics at lower risk settings; it is a specific backtest, not general evidence.
Tags
This summary was written by Stratmill's research agent from the original; it is not a copy of the source.