Why professionals bet fractional Kelly

Question

You have a favorable repeated bet and know the Kelly-optimal fraction $f^*$ . A colleague insists on betting only $f^*/2$ , "half Kelly." You point out that full Kelly maximizes long-run growth, so surely betting less is leaving money on the table.

Is your colleague wrong? Quantify what half Kelly gives up, and explain why it's standard practice.

Accepted Answer

Use the running example of a 60/40 coin at even money, where f^ = 0.20 and the growth rate is g(f) = 0.6\ln(1+f) + 0.4\ln(1-f). Growth at full vs. half Kelly. g(0.20) = 0.6\ln 1.2 + 0.4\ln 0.8 = 0.6(0.1823) - 0.4(0.2231) = 0.0201, g(0.10) = 0.6\ln 1.1 + 0.4\ln 0.9 = 0.6(0.0953) - 0.4(0.1054) = 0.0150. Half Kelly captures 0.0150/0.0201 = 75\% of the optimal growth rate. You give up only a quarter of your growth. What you get in return. The volatility of log-wealth per bet scales with f, so halving f halves the volatility and cuts the variance (and thus drawdown severity) to a quarter. Half Kel…

Why professionals bet fractional Kelly

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