Kelly criterion

Kelly criterion gives the bet fraction that maximizes the long-run geometric growth rate of a portfolio: f* = p - (1 - p) / b, where p is the probability of a winning trade and b is the ratio of average win size to average loss size (the payoff ratio).

Example. A strategy wins 55% of the time (p = 0.55) with an average win twice the size of the average loss (b = 2). f* = 0.55 - 0.45 / 2 = 0.55 - 0.225 = 0.325. Full Kelly says risk 32.5% of capital per trade — a figure almost nobody uses in practice.

In real trading, Kelly is almost always scaled down. Half Kelly (f*/2 = 16.25% here) cuts variance roughly in half while keeping most of the growth benefit. Many systematic traders use quarter Kelly or less, because win rate and payoff estimates from backtests are noisy, and over-betting with a wrong estimate destroys capital faster than under-betting costs growth.

Kelly requires accurate estimates of win rate and payoff ratio. Out-of-sample validation matters enormously — inflated backtest stats will produce a Kelly fraction that is too large. See position sizing for the risk-based alternative. Research output only — this is not investment advice.