A New Interpretation of Information Rate
Read the paperopens doi.org in a new tab
What they found
Kelly, a Bell Labs physicist, asked how a gambler with private information should bet to maximize the long-run growth rate of his wealth. The answer is to bet a fixed fraction of capital equal to the edge divided by the odds, which maximizes the expected logarithm of wealth. Betting more than this fraction reduces long-run growth and eventually guarantees ruin; betting less is safer but grows slower. The paper connects this optimal fraction to Shannon's information theory: the growth rate equals the information rate of the gambler's private channel.
What you can use
- There is a mathematically optimal bet size for any edge, and it is proportional to the edge and inversely proportional to the variance.
- Betting more than the Kelly fraction does not just add risk; it lowers your long-run growth and can guarantee ruin.
- Because real edges are uncertain and overestimated, practitioners bet a fraction of Kelly.
Caveats
Assumes you know your edge exactly and can bet repeatedly with independent outcomes; neither holds for traders. Kelly sizing produces drawdowns most people cannot tolerate.
Tags: risk, position-sizing, kelly, foundations
Summaries are our own reading of the paper, not the authors' words. Educational only, not advice. Discuss it in Book Club.