Kelly Criterion

The Kelly criterion is a formula for choosing how much of your capital to risk on a bet or trade when you know your edge. It was published by John L. Kelly Jr., a researcher at Bell Labs, in 1956. Kelly showed that betting a specific fraction of capital maximises the long term growth rate of wealth. Betting more than that fraction lowers long term growth and increases the risk of ruin; betting less gives lower growth but a much smoother ride.

The formula#

For a simple bet with two outcomes:

f* = (b × p − q) ÷ b

• f (written f* in the formula) is the fraction of capital to bet.
• p is the probability of winning, q = 1 − p is the probability of losing.
• b is the net payout ratio: how much you win per $1 risked.

For trading, a common form uses win rate and the ratio of average win to average loss:

f* = W − (1 − W) ÷ R

where W is the win rate and R is average win divided by average loss.

Worked examples#

Why full Kelly is dangerous in practice#

1. Your edge is an estimate. Win rates and payoffs from a backtest or a guess are uncertain. Overestimating your edge, which is common, makes Kelly tell you to bet far too much.
2. Huge drawdowns. Even with a correct edge, full Kelly regularly produces drawdowns of 50% or more. Few people can stick to a strategy through that.
3. Changing conditions. Markets change; an edge measured last year may be smaller now.
4. Correlated bets. Kelly for single bets ignores that several trades may lose together.
5. Fat tails and gaps. Real losses can exceed the assumed loss when stops gap.

Overbetting beyond Kelly is especially harmful: betting twice the Kelly fraction gives zero long term growth, and more than that leads to long term decline.

How traders actually use Kelly#

Most practitioners use a fraction of Kelly, commonly half or a quarter, and cap it at their normal risk limits. Kelly is more useful as a sense check than as a sizing rule:

• If Kelly for your strategy is tiny or negative, your edge is too small to trade.
• If you are risking more than Kelly, you are definitely overbetting.
• If Kelly suggests 25% but you risk 1%, you have a large margin of safety for estimation errors.

See Fractional Kelly.

Kelly and expectancy#

Kelly only gives a positive bet size when your expected value is positive. A strategy with negative expectancy should never be traded at any size, and Kelly makes that explicit by returning a negative fraction. See Expectancy.

Common mistakes#

• Using backtest statistics at face value in the formula.
• Applying full Kelly to real trading.
• Ignoring correlation between simultaneous trades.

Frequently asked questions#

What does the Kelly criterion tell you?#

The fraction of capital to bet that maximises long term growth, given your probability of winning and the payout.

Should I use the full Kelly criterion?#

Almost never. Because edges are uncertain and drawdowns are severe, most traders use a fraction such as half or quarter Kelly, often capped further.

What happens if I bet more than Kelly?#

Long term growth falls and the risk of large drawdowns rises. At twice the Kelly fraction, expected long term growth drops to zero.

Next, learn the practical version: Fractional Kelly.

Sources#

• Wikipedia, Kelly criterion