Position sizing & risk
When you know your probability of winning and the payout ratio, the Kelly criterion calculates the share of capital to risk on an opportunity.
Origin
The Kelly criterion goes back to physicist John L. Kelly Jr., who worked on information theory at AT&T Bell Labs in 1956. He studied which share of capital maximises long-term wealth growth when repeated bets have a known win probability and payout ratio. The result is now used in trading and in betting with known odds.
The formula
The formula needs two inputs, either known or estimated realistically: your probability of winning and your payout ratio, meaning how much profit you receive relative to the stake.
The result f* is the share of capital that would maximise long-term growth under those assumptions. It depends entirely on the quality of the probability and payout estimates.
Worked example
Assume a 55% win probability (p = 0.55), a 45% loss probability (q = 0.45) and a payout ratio of 1.2 (b = 1.2).
Small changes in win probability or payout ratio move the result materially. Use actual inputs rather than intuition whenever possible.
Limits
As with retirement withdrawals, the core question is how much risk you can take without putting the capital at serious risk. The answer depends on the whole plan, not only on the formula.
Fractional Kelly
The 22.5% result assumes known probabilities, correct odds and the ability to repeat the same opportunity many times. Real inputs are uncertain. A small overestimate of your win probability can make the recommended share far too high.
Growth does not simply fall to half when using half Kelly, while volatility and the damage from a wrong estimate are reduced. That trade-off is often easier to live with.
Estimation
With fixed odds, the payout ratio is usually visible. The probability of winning must be estimated, and that is where the largest error occurs. “55%” sounds precise, but without data, a method and enough observations it may be only a guess.
A percentage becomes useful through a clear definition, traceable data and a separate evaluation of forecast and outcome. Do not revise it after the result to make the past look right.
Several opportunities
The simple formula treats one opportunity in isolation. Two trades can depend on the same interest rate, industry or market move, so two apparently independent stakes can combine into one large risk.
Set a second boundary: how much of total capital may be tied up in uncertain positions at the same time? This does not compete with Kelly; it prevents several good-looking decisions from becoming one oversized bet.
Implementation
Document the assumed probability, payout ratio and Kelly fraction before every stake. Afterwards, record the result without rewriting the forecast. Over time this creates a dataset: you can see whether your estimates are optimistic, which situations work and how much your capital actually swings.
Without that review, Kelly merely multiplies an imprecise opinion by mathematical precision. My order is: check the edge, justify the probability, calculate Kelly, apply a safety factor and check the portfolio.
Enter win rate, loss rate and payout ratio, then calculate and simulate the suggested stake.
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