What the Kelly Criterion is and the idea behind it
The Kelly Criterion is a mathematical rule that tells you what fraction of your capital to risk on a repeated bet if your goal is to maximise the long‑term growth of your account. It was devised in the 1950s for information theory and became popular among gamblers and later investors because it gives a clear, quantitative answer to the question “how much should I stake when I have an edge?”
Applied to trading, Kelly does not tell you where to enter or exit a trade. Instead it uses your edge — how often you win and how big your wins are compared with your losses — to compute a single fraction of your account to risk. The result is the size that, in theory, maximises the expected geometric growth of wealth when the same opportunity is repeated many times.
Trading carries risk. The Kelly Criterion assumes you can estimate probabilities and payoffs reliably and that trades are repeated under similar conditions — assumptions that often do not hold in real markets. This article explains the formula, shows how to convert the Kelly fraction into an FX lot size, and covers practical adjustments traders commonly make.
The formula and how to interpret its inputs
The most common form of the Kelly formula used in trading is
f = (b p − q) / b
where f is the fraction of your capital to risk on a single trade, p is the probability of a winning trade, q = 1 − p is the probability of a losing trade, and b is the average win expressed in units of the loss (the “win:loss” ratio). In plain terms b = (average winning amount) / (average losing amount).
Another way people write the formula when they work with win rate W and win/loss ratio R (average win ÷ average loss) is
K% = W − (1 − W) / R
Both expressions represent the same idea: if your probability of winning and your reward-to-risk are large enough, Kelly returns a positive fraction; if not, it returns zero or a negative number (meaning the trade has negative expectancy and you should avoid it).
A concrete worked example makes this clearer. Suppose your system produces a 60% win rate (p = 0.6). Your average winning trade makes 120 pips and your average losing trade loses 60 pips, so b = 120/60 = 2. Plugging into the formula gives
f = (2 × 0.6 − 0.4) / 2 = (1.2 − 0.4) / 2 = 0.8 / 2 = 0.4
Kelly suggests risking 40% of your capital on each repeat of that opportunity. That number looks large because the example assumes a large, reliable edge and repeatability. In real trading you rarely trust raw Kelly at full size for reasons covered below.
Converting a Kelly fraction into a forex position size
Kelly gives you a fraction of account equity to risk, not the number of lots or the margin requirement. To use it in forex you must translate the risk fraction into a monetary risk per trade and then into lot size using your planned stop loss.
Step by step:
- Calculate f (Kelly fraction) from your system statistics.
- Multiply your account balance by f to get the dollar amount you may risk on the next trade.
- Decide a realistic stop‑loss distance in pips and determine the pip value per lot for the currency pair and your account currency.
- Compute lot size = (account × f) / (stop_loss_pips × pip_value_per_lot).
Example: you have a $10,000 account and your adjusted Kelly fraction (see next section) is 3% (f = 0.03). You plan a 50‑pip stop loss on EUR/USD and your broker’s pip value for a standard lot on EUR/USD is about $10 per pip. The dollar risk per trade is $10,000 × 0.03 = $300. The per‑lot risk for a 50‑pip stop is 50 pips × $10 = $500. Lot size = $300 / $500 = 0.6 standard lots, or 6 mini lots (0.6 lots = 6 × 0.1). That is the trade size that risks about 3% of equity on the stop loss.
A couple of practical notes: pip values change with pair and quote currency, so compute pip_value_per_lot for the instrument and account currency you use. Kelly determines how much to risk, not how much margin you need. Margin is a separate calculation: margin = notional / leverage. Kelly is about money at risk, not required margin.
Practical adjustments traders commonly use
Full Kelly often produces larger position sizes and higher volatility than most traders are comfortable with. Because of estimation error, non‑stationary markets and psychological limits, most practitioners use a fractional Kelly — a reduced portion of the full Kelly suggestion — or impose caps.
Typical fractional choices traders commonly use are:
- Full Kelly (100% of f): mathematically optimal for geometric growth if assumptions hold, but usually too aggressive in practice.
- Half‑Kelly (50% of f): a popular compromise that reduces variance and drawdown significantly while keeping much of the growth benefit.
- Quarter‑Kelly or smaller: used by conservative traders or when statistical confidence in estimates is limited.
Beyond fractional Kelly, traders also limit exposure by setting an absolute maximum risk per trade (for example 1–2% of account), treating correlated positions as a single exposure, and re‑estimating statistics frequently. Kelly can be applied separately to independent strategies and aggregated more carefully for a portfolio, but portfolio Kelly is mathematically more complex and requires handling correlations between trades.
Testing Kelly before you use it live
Because Kelly depends on estimated p and b, testing is essential. Start by compiling your historical trade log or backtest results and compute the empirical win probability, average win, average loss and the resulting Kelly fraction. Then run sensitivity and Monte Carlo simulations: randomly sample sequences of wins and losses using your estimated probabilities and reward distribution, and measure typical growth paths, drawdowns and time to recovery.
A simple test plan:
Begin with historical results to compute p and b. Use those to compute full Kelly and several fractional Kelly values. Simulate 1,000 random paths of 1,000 trades for each risk fraction, tracking terminal equity and maximum drawdown. Compare distributions and choose a fraction that gives acceptable drawdowns while preserving reasonable growth. Finally, forward test on a demo account or with small real capital before scaling up.
Risks, limitations and important caveats
The Kelly Criterion can be a helpful mathematical guide but it has important limitations when applied to forex. First, Kelly requires reliable estimates of win probability and payoff ratio. In live markets those parameters change with regime shifts, news events, and overfitting in backtests. Small errors in p or b can materially alter the recommended fraction.
Second, full Kelly can create very large drawdowns. Even if long‑term growth is maximised mathematically, the path to that growth may include sequences of losses that are financially or psychologically intolerable; this is why fractional Kelly is widely used. Third, Kelly ignores transaction costs, slippage and the effect of leverage limits and margin calls; these practical factors can make a theoretically profitable sizing scheme ruinous in practice.
Kelly also assumes independent, identically distributed trades. In forex many trades are correlated (same currency exposures, macro drivers), so sizing each trade independently can dramatically increase portfolio risk. Withdrawals and external cash flows also change the optimal policy, but Kelly in its simplest form doesn’t account for them.
Finally, using Kelly without adequate backtesting, robustness checks and risk controls is risky. This is educational information, not personalised advice. Trading carries risk and you may lose part or all of your capital.
How experienced traders typically incorporate Kelly
Experienced traders use Kelly as one input in a broader risk management framework rather than as an absolute rule. They estimate Kelly from reliable, recent, and relevant trade samples; they reduce the raw result (half‑Kelly, quarter‑Kelly); and they combine it with absolute risk limits, position caps, diversification rules and stress tests. Kelly becomes a disciplined way to think about position sizing and tradeoffs between growth and volatility, rather than a mechanical instruction to deploy a specific lot size.
Final thoughts
The Kelly Criterion offers a mathematically neat answer to “how much to risk?” when you have a repeatable edge, but real forex trading complicates the picture. Use Kelly as a structured starting point: estimate your edge honestly, test extensively, reduce the raw recommendation to account for estimation error and correlation, and always pair position‑sizing rules with stop losses, portfolio limits and contingency plans for tail events.
Trading carries risk. This article provides general information to help you understand position sizing ideas and is not personalised trading advice.
Key takeaways
- The Kelly Criterion computes the fraction of capital to risk that, under ideal assumptions, maximises long‑term geometric growth.
- To use Kelly in forex convert the fraction to a dollar risk and then to lot size using your stop loss (lot size = account × f / (stop_pips × pip_value)).
- Full Kelly is often too aggressive; traders usually apply fractional Kelly (half, quarter) and add caps and diversification controls.
- Always test Kelly assumptions with backtests and Monte Carlo simulations, and remember that estimation error, slippage, leverage and correlated positions can make Kelly recommendations dangerous if applied blindly.
References
- https://www.linkedin.com/pulse/kelly-criterion-enhancing-forex-position-sizing-profit-maximization
- https://www.orbex.com/blog/en/2020/04/what-is-the-kelly-criterion-in-forex
- https://www.litefinance.org/blog/for-beginners/best-technical-indicators/kelly-criterion-trading/
- https://corporatefinanceinstitute.com/resources/data-science/kelly-criterion/
- https://www.forexfactory.com/thread/1144543-using-the-kelly-criterion-in-actual-trading
- https://www.investopedia.com/terms/k/kellycriterion.asp