Kelly from your hit rate and win/loss ratio

Question

Your trades win with probability p = 0.40. When you win, the average gain is 3 times the average loss (payoff ratio R = W/L = 3). What fraction of your risk capital does Kelly say to put on each trade, even though you lose more often than you win?

Accepted Answer

Model each trade as a bet at net odds b = R: you risk one unit, and you either gain R units (prob p) or lose your 1 unit (prob q = 1-p). The general-odds Kelly fraction is f^ = \frac{pb - q}{b} = p - \frac{q}{R}. Plug in p = 0.40, q = 0.60, R = 3: f^ = 0.40 - \frac{0.60}{3} = 0.40 - 0.20 = 0.20. Bet 20\% of your risk capital per trade, despite a sub-50\% hit rate. The reason is the favorable payoff: the numerator pb - q = 0.40	imes 3 - 0.60 = 1.2 - 0.6 = 0.6 is your edge per unit staked (expected profit), and it is positive because the big winners outweigh the frequent small losses. Expected…

Kelly from your hit rate and win/loss ratio

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