The Kelly criterion is a position-sizing method that asks one blunt question: if you know your edge and payoff, what fraction of capital maximizes long-run compound growth? It is elegant math, but in trading the hard part is not the formula. The hard part is proving that the inputs are real.
That is why Kelly is useful and dangerous at the same time. It forces a trader to connect win rate, payoff, and size in one framework. It also punishes overconfidence when the edge is estimated from a fragile backtest.
What the Kelly criterion actually is
The Kelly criterion chooses the bet size that maximizes expected logarithmic wealth, often described as maximizing long-run geometric growth. Kelly's original 1956 Bell System Technical Journal paper framed the problem through information and betting, while a later Frontiers review describes the same criterion as a growth-optimal portfolio method used in gambling and investing (Kelly 1956: A New Interpretation of Information Rate, Frontiers: Practical Implementation of the Kelly Criterion).
For a simple binary bet where the losing outcome loses the whole stake, the common formula is:
f* = p - q / b
f* = Kelly fraction of capital
p = probability of winning
q = probability of losing, or 1 - p
b = net payoff received per 1 unit riskedCAIA's review gives the same win/loss framing with edge based on payoff odds and win/loss probabilities, and Thorp's Kelly paper treats the criterion as a way to size favorable wagers across blackjack, sports betting, and the stock market (CAIA: Understanding the Kelly Capital Growth Investment Strategy, Thorp: The Kelly Criterion in Blackjack, Sports Betting, and the Stock Market).
How the formula behaves
Kelly position sizing grows when the estimated edge improves, and shrinks when the payoff or probability weakens. That sounds obvious until you put numbers on it.
| Setup | Formula | Kelly fraction |
|---|---|---|
| 55% win rate, 1:1 payoff | 0.55 - 0.45 / 1 | 10% |
| 40% win rate, 2:1 payoff | 0.40 - 0.60 / 2 | 10% |
| 50% win rate, 1:1 payoff | 0.50 - 0.50 / 1 | 0% |
| 45% win rate, 1:1 payoff | 0.45 - 0.55 / 1 | -10% |
The table is not trading advice. It is arithmetic. A lower win rate can still produce the same Kelly fraction if the payoff is larger. A coin-flip with no payoff advantage says to bet nothing. A negative result means the assumed trade has no long-side edge under those inputs.
That makes Kelly a useful lie detector for strategy claims. If a system cannot state its win probability, average win, average loss, and cost model, it cannot honestly state a Kelly size either.
Why traders rarely use full Kelly
Full Kelly is aggressive because it optimizes long-run growth, not the smoothness of the path. MacLean, Thorp, and Ziemba summarize the good and bad properties of Kelly and fractional Kelly, including the tradeoff between growth and security; the Frontiers review also notes that Kelly portfolios can carry higher risk and poorer drawdown behavior than more conservative allocations (MacLean, Thorp, Ziemba: Good and bad properties of the Kelly criterion, Frontiers: Practical Implementation of the Kelly Criterion).
Fractional Kelly means using only part of the calculated Kelly size, such as half Kelly or quarter Kelly. MacLean, Thorp, Zhao, and Ziemba's simulations show the growth-versus-security tradeoff across full and fractional Kelly strategies, while the CAIA review discusses cases where full Kelly wagers can become very large and where practitioners moved to fractional Kelly to control risk (MacLean, Thorp, Zhao, Ziemba: Full and Fractional Kelly simulations, CAIA: Understanding the Kelly Capital Growth Investment Strategy).
Full Kelly = maximum theoretical growth if inputs are right
Half Kelly = lower growth, usually a calmer path
Quarter Kelly = lower again, more conservative
Over Kelly = more risk without a reliable growth benefitThe problem for traders is input error. Backtests estimate the edge; they do not reveal it perfectly. Frontiers warns that bad estimates of mean and variance, or overbetting, can produce worse outcomes or even ruin; the CAIA review also highlights how errors in return estimates can make expected-log decisions overbet (Frontiers: Practical Implementation of the Kelly Criterion, CAIA: Understanding the Kelly Capital Growth Investment Strategy).
That is the honest reason many systematic traders treat Kelly as an upper bound, not a command.
What the critics get right
The main criticism is not that Kelly is wrong. It is that trading inputs are noisy.
Kelly assumes the edge estimate is good enough to size from. Markets do not hand you a clean probability like a solved card-counting game. A backtest gives a sample of trades, and that sample can be distorted by overfitting, regime selection, survivorship bias, execution assumptions, and plain randomness.
There is also a goal mismatch. Kelly optimizes compound growth over repeated favorable bets. A prop-firm trader may care more about daily loss limits, max drawdown, payout stability, or simply staying alive through a bad cluster. Those constraints can make a smaller size more rational than the growth-optimal size.
So the useful question is not "what does Kelly say I should risk?" The useful question is "what would Kelly say if my edge were real, and how much smaller should I be because I might be wrong?"
How you'd actually test it
To test Kelly criterion position sizing, start with a strategy that already has fixed, repeatable rules. Then measure whether Kelly-style sizing improves the strategy after costs and under realistic constraints.
Minimum test design:
- Define the entry, exit, stop, and time rules before sizing changes.
- Include spread, slippage, commission, and swap where relevant.
- Split the data into in-sample and out-of-sample periods.
- Estimate win probability, average win, and average loss only from the training window.
- Apply fixed fractional, full Kelly, half Kelly, and quarter Kelly to the next unseen window.
- Track CAGR, max drawdown, equity drawdown, loss streaks, and rule breaches.
- Repeat with walk-forward windows so the edge estimate is refreshed without seeing the future.
The important comparison is not which curve looks highest in-sample. It is which sizing method survives unseen data without making the account path unacceptable.
| Sizing method | What it tests |
|---|---|
| Fixed fractional | Baseline: does simple risk stay robust? |
| Full Kelly | Does the theoretical growth target survive real drawdowns? |
| Half Kelly | How much growth remains after cutting path risk? |
| Quarter Kelly | Is a conservative fraction still enough to beat the baseline? |
| Capped Kelly | Does a hard maximum risk cap protect against input error? |
This is the same reason risk of ruin, losing streaks, and out-of-sample testing matter. A formula can be mathematically clean and still fail the account if the backtest edge was overstated.
At realbacktesting, the working standard is not "trust the curve." It is define the rule, include real costs, hold out unseen data, and make the sizing prove itself under the same constraints the trader actually faces. The broader proof method is laid out in real-cost backtesting.
Frequently asked
Is the Kelly criterion a trading strategy?
No. The Kelly criterion is a position-sizing rule. It does not tell you when to enter, where to exit, or whether a market has an edge.
Is full Kelly safe?
Full Kelly is growth-optimal under its assumptions, but those assumptions are fragile in trading. If the edge estimate is wrong, full Kelly can become an overbet.
What is fractional Kelly?
Fractional Kelly uses part of the full Kelly size, such as half or quarter Kelly. Traders use it to reduce volatility, drawdown pressure, and sensitivity to estimation error.
Can Kelly be backtested?
Yes, but only as part of a complete rule set. You need a fixed strategy, realistic costs, out-of-sample testing, and a comparison against simpler sizing methods.
Takeaway
Kelly is a sharp tool for sizing a proven edge. If the edge is only guessed from a flattering backtest, Kelly just makes the guess bigger.