The Kelly Criterion for Traders: Optimal Bet Size and Its Dangers

The Kelly criterion, published by John Kelly in 1956, gives the fraction of your capital to risk on each bet to maximize the long-term growth rate of your wealth. Bet less and you grow more slowly than you could. Bet more and you grow more slowly too, and eventually risk ruin.

The formula

For a bet that wins with probability p and pays b times your stake when it wins (losing the stake otherwise):

f* = p − (1 − p) ÷ b

Example: a strategy wins 55% of the time, and its average win equals its average loss (b = 1).

f = 0.55 − 0.45 ÷ 1 = 0.10*, or 10% of capital at risk per trade.

With a 45% win rate and an average win twice the average loss (b = 2): f = 0.45 − 0.55 ÷ 2 = 0.175*, or 17.5%.

Why traders rarely use full Kelly

Full Kelly maximizes long-term growth, but the ride is brutal:

• Huge drawdowns. At full Kelly, drawdowns of 50% or more are common over a long series of trades.
• Uncertain inputs. Your true win rate and payoff are estimates. If you overestimate your edge, the Kelly fraction is too large, and betting more than Kelly reduces growth while increasing risk.
• Changing markets. Your edge is not constant.

Notice the shape of the curve: it is flat near the top. Half Kelly gets about three quarters of the growth rate with much smaller drawdowns. That trade-off is why many practitioners use half Kelly or less.

Kelly vs fixed fractional

The Kelly fractions above, 10% and 17.5%, are far larger than the 0.5% to 2% risk per trade most traders use. In practice, many traders treat Kelly as an upper limit and a check: if your risk per trade is above your Kelly fraction, you are risking too much for your edge. See the 1% rule.

Getting the inputs right

Use your own trade history, not hopes. You need:

• Win rate, from a reasonable sample. See sample size.
• Average win and average loss, for the payoff ratio.

Be conservative. If your history is short, shrink your estimate of the edge before calculating.

Try it

Our free Kelly's Simulator shows how full Kelly, half Kelly and other fractions play out over many simulated trades, including the drawdowns. TradeThink also calculates the Kelly fraction from your real results on the statistics page. Related: risk of ruin.