The Kelly Criterion & Position Sizing
John L. Kelly / Edward Thorp · 1956
"Kelly derived the fraction of bankroll to bet to maximize long-run logarithmic growth — bet too little and you compound slowly, bet too much and a single bad run wipes out the geometric advantage even with a positive edge."
Kelly asked Bell Labs' question in 1956: if you have an edge, what fraction should you actually bet? The answer — edge divided by odds — is the fastest sustainable compounding path, and most investors bet far past it.
With a 60/40 edge and even payoff, Kelly says bet 20% of capital; bet 40% and you grow slower, bet 100% and a short streak ruins you despite the edge. The formula maximizes log wealth, which is geometric growth, not expected value alone. Practitioners use half-Kelly because estimates are noisy — volatility is the tax on misestimating your own edge, so position size is inseparable from uncertainty about the edge.
Why does the Kelly Criterion recommend betting less than full expected-value maximization would suggest?
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The explanation above is written with AI assistance. These are the originals — go to them to check it.
- A New Interpretation of Information Rate — the Kelly Criterion (1956)J. L. Kelly / Wikipedia
The Capital Asset Pricing Model (CAPM)
"CAPM isolates the price of systematic risk — expected return rises linearly with beta to the market, so only non-diversifiable risk earns a premium and alpha is excess over that line."