Kelly criterion trading: the formula and why you should use less

The Kelly criterion answers a question most position sizing methods dodge: given your edge, exactly how much of your capital should you risk per trade to grow it fastest? The math returns a precise number. The catch is that the precise number is almost always too large to actually use.

What the Kelly criterion is

The Kelly criterion is the bet size that maximizes the long-run growth rate of your capital. It came out of a 1956 paper by J. L. Kelly Jr. at Bell Labs, written about signal transmission, and was later carried into gambling and markets by Ed Thorp. For trading it needs two inputs you should already be tracking: how often you win, and how much you make when right versus what you lose when wrong.

The formula:

f* = W − (1 − W) / R

Where:

• f* is the fraction of capital to risk
• W is your win probability (0.55 for a 55% win rate)
• R is your payoff ratio (average win divided by average loss)

It is the same two numbers that drive expectancy, arranged to answer a different question. Expectancy tells you whether the edge is positive. Kelly tells you how hard to press it.

A worked example

Say you win half your trades, and your average winner is twice your average loser. So W = 0.50 and R = 2.

f* = 0.50 − (1 − 0.50) / 2
f* = 0.50 − 0.25
f* = 0.25

Kelly says risk 25% of your capital on the trade. On a $50,000 account that is $12,500 of risk on a single position. No disciplined trader does this, and that instinct is correct. Hold the thought.

Change the win rate to 40% with the same 2:1 payoff:

f* = 0.40 − (0.60 / 2) = 0.40 − 0.30 = 0.10

Now Kelly says 10%. Drop the payoff to 1:1 at a 60% win rate:

f* = 0.60 − (0.40 / 1) = 0.20

The formula rewards a higher win rate and a higher payoff, and it punishes weakness in either. If f* comes out at zero or negative, you have no edge and Kelly's answer is not to trade at all.

Why full Kelly is too aggressive

Two reasons, and the second is the one that matters.

The first is variance. Betting the full Kelly fraction maximizes growth in theory, but the path is violent. Full Kelly regularly produces drawdowns that would end a real trading career or breach a prop firm's limits long before the long run arrives. The growth rate is optimal only across an effectively infinite number of trades, and you do not trade infinitely. You trade a career, with a drawdown limit and a human nervous system.

The second reason is that Kelly assumes you know W and R exactly. You do not. You estimate them from a finite sample of past trades, and both estimates carry error. The asymmetry of that error is brutal: betting above the true optimal fraction lowers your long-run growth and raises ruin risk faster than betting the same distance below it does.

Fractional Kelly

The standard fix is to bet a fixed fraction of the Kelly number. Half Kelly and quarter Kelly are the common choices, and the trade is favorable. Betting half of full Kelly keeps roughly three quarters of the growth rate while cutting the volatility of returns by about half.

A quick way to see it: long-run growth as a fraction of the maximum is approximately c × (2 − c), where c is the fraction of full Kelly you use. At half Kelly, c = 0.5, so 0.5 × 1.5 = 0.75. You keep 75% of the growth for half the bet. At quarter Kelly the figure is 0.25 × 1.75 ≈ 0.44, about 44% of the growth for a quarter of the size. Most professionals who use Kelly at all run somewhere between quarter and half.

Why prop traders rarely get to use Kelly anyway

Here is the practical catch for funded futures traders. Kelly sizes against your total capital and assumes you can ride a losing streak down and recover. A prop account cannot. A trailing drawdown or daily loss limit liquidates you well before a Kelly-sized streak finishes playing out.

That means the binding constraint is almost never Kelly. It is the firm's drawdown rule. If half Kelly says risk 5% per trade but your trailing drawdown is 4% of the account, the drawdown rule wins, and you size to survive the rule rather than to maximize growth. Kelly stays useful as a ceiling: if your edge is real, it tells you the most you could ever justify risking, and your actual size should sit well below it.

How to actually use it

You need honest inputs, which means you need a trade log. W and R are not feelings. They are statistics you compute from your own filled trades, and ideally you compute them per setup, because a single blended number hides the fact that one setup may carry a real edge while another quietly bleeds. Calculate Kelly per setup, apply a fractional multiplier of a quarter or a half, then check the result against your drawdown limit and take the smaller of the two.

You can read the canonical definition and history of the Kelly criterion if you want the derivation. For trading, the working knowledge above is enough.

The takeaway

Kelly is the cleanest answer to "how much should I risk," and almost nobody should use the raw answer. The formula is a ceiling, not a target. Compute it from real logged data, cut it to a quarter or a half, and then let your prop firm's drawdown limit cut it further if it has to. The traders who blow up are not the ones who sized too small. They are the ones who never ran the math and sized on feel, which is almost always above full Kelly without their knowing it.