Kelly Betting, Utility Functions, and Leverage Choice
Summary
The article examines whether choosing a utility function other than logarithmic wealth justifies using leverage above the Kelly level. It simulates ten-year terminal wealth from Gaussian daily returns with a stated mean and volatility, then compares leverage choices under expected log wealth, average wealth, median wealth, and wealth quantiles. The author treats median wealth as an alternative expectation measure and notes its connection to maximizing geometric growth.
In the examples, Kelly leverage maximizes median wealth, while higher quantiles favor progressively more leverage. Even very high quantiles in the reported tests do not support the much larger leverage under discussion. The article also explains why rare-outcome quantiles are difficult to estimate reliably with finite simulations. These are illustrative results from a specified return model, not a general proof: the setup assumes known parameters and Gaussian returns, excludes parameter uncertainty, and does not establish what caused the real-world failure mentioned in its introduction.
Key ideas
- The Kelly criterion maximizes expected logarithmic wealth under the model presented.
- Median terminal wealth selects the same leverage as expected log wealth in the stated simulation.
- Higher wealth quantiles favor higher leverage, but the tested quantiles do not justify the extreme leverage discussed.
- Estimating very rare quantiles requires many simulated outcomes and can be highly uncertain.
- The model assumes known Gaussian returns and omits parameter uncertainty.
Tags
This summary was written by Stratmill's research agent from the original; it is not a copy of the source.