The Kelly Criterion — Is It a Good Position-Sizing Tool?

The Kelly criterion is seductive: a formula promising to tell you exactly how much to stake so capital grows fastest in the long run. It sounds like the holy grail of position sizing. In the right environment — blackjack with properly counted cards — Kelly is beautiful. In retail forex it stops being the grail and becomes an elegant way to blow up an account in six months. This article explains why, and when Kelly is worth using.

Who Kelly was and what he actually wrote in 1956

John Larry Kelly Jr. was a physicist at Bell Labs in New Jersey, in the same lab where Claude Shannon had laid the foundations of information theory a few years earlier. Kelly tackled an apparently unrelated question: if someone plays a game with a known positive expected value, and plays it repeatedly while reinvesting capital, what fraction of the bankroll should be staked each time so wealth grows fastest? The answer appeared in July 1956 in the Bell System Technical Journal under the title A New Interpretation of Information Rate. It was an elegant application of expected value to the logarithm of capital: Kelly showed that f = (bp − q) / b maximises the logarithmic growth rate. Here b is the win-to-loss ratio, p the probability of winning, q the probability of losing. Everything else is consequence.

What Kelly is really about, with a walk through the numbers

This is where most lay readings of the formula go wrong. Kelly does not maximise the win rate of a single trade, the arithmetic mean of returns, or minimise drawdowns. Kelly maximises the geometric growth rate of capital over a very long horizon, assuming you reinvest every zloty. Geometric growth is not arithmetic growth — one large loss hits much harder than an average winner compensates for it. That is precisely why Kelly deliberately gives up some potential average gain in exchange for lower ruin risk.

An illustrative trader has kept an honest journal for two years. Hit rate is 55 percent, average winners are 1.5 times average losers. Plug those into the formula: b is 1.5, p is 0.55, q is 0.45. The numerator becomes 0.55 times 1.5 minus 0.45, which is 0.825 minus 0.45, which is 0.375. The denominator is 1.5. Divide and you get 0.25. Full Kelly tells this trader to risk a quarter of the account on every trade. On a €40,000 account that means a €10,000 loss if the stop is hit. That is the moment when the mathematician smiles and the practitioner reaches for a glass of cold water.

Why full Kelly is suicidal for a retail trader

For three reasons. The first is that Kelly assumes you know p and b exactly. In counted blackjack that holds — the deck has a precisely defined distribution. In forex it never holds. Your hit rate and your win-to-loss ratio are estimates from a few hundred trades, burdened with sampling error, regime error, and often optimism bias from backtests where you unconsciously kept only the winning variants.

The second reason is mathematical, with a brutal asymmetry. If you under-estimate p by five points, the formula tells you to bet less — you give up some growth but survive. If you over-estimate p by five points, the formula tells you to bet much more, and drawdowns scale non-linearly. A small input error turns into a catastrophic output.

The third reason is psychological and probably the most important. Monte Carlo simulations of our example strategy show that under full Kelly, hitting a 50-percent drawdown within a few hundred trades is practically certain. After a 50-percent drawdown you have to double the capital to break even — not „minus fifty, then plus fifty", but „minus fifty, then plus one hundred". Very few retail traders, whose money is really their own, sit through that bottom. They quit on the worst possible day. Statistically right as traders, lost as humans.

„Kelly’s system is a way of betting which, in the long run, gives the player a larger fortune than any other betting system." — William Poundstone, Fortune’s Formula, Hill and Wang, 2005

Fractional Kelly — a compromise that sometimes makes sense

Because full Kelly is practically unusable, the professional world has long worked with its fractional version. Take the formula value and multiply by 0.5 or 0.25. You trade away some theoretical growth for radically lower volatility. If full Kelly said 25 percent, the quarter version says 6.25 percent — still more than the one-percent rule, but drawdowns become bearable and ruin risk under realistic estimation error drops by an order of magnitude. Edward Thorp, the first serious practitioner of Kelly (see the basics of risk management), publicly disclosed using strongly fractional variants at Princeton Newport Partners.

Fractional Kelly makes sense only if you satisfy three conditions at once. First: you have an honest track record of at least a few hundred trades with a single strategy across different market states. Second: you can estimate how much your p and b wobble between yearly samples — only that range tells you what multiplier is safe. Third: you accept 20-to-30-percent drawdowns and treat the maximum drawdown as part of the strategy, not an excuse to quit. Most retail traders meet none of those conditions.

Why the one-percent rule usually wins

Here comes the punchline most readers do not expect: for a typical retail forex trader, the classic one-percent rule systematically beats Kelly in practice. Not because it is mathematically superior — in pure theory Kelly is by definition optimal. It wins because it is robust to what a retail trader does not know. The one-percent rule needs no probabilities, no statistically significant sample, no assumption about market stationarity. It simply says: risk one percent of capital, size the lot so that the stop in pips matches that amount, end of discussion. Mathematically that is dramatically less than any sensible Kelly. In practice, it is the difference between „I lived through five years and capital is growing" and „I cut the account in half and quit". This sits well with the data: in its 2018 product-intervention review, ESMA found that 74 to 89 percent of retail CFD accounts lose money — strongly suggesting the retail problem is sizing too aggressive, not too conservative.

Put differently, Kelly assumes you know p. The one-percent rule assumes you do not. The second is much closer to retail reality. If one day you cross into professional trading, with a journal of thousands of trades across different regimes, fractional Kelly becomes sensible. Until then, one percent wins. Some retail traders also like comparing the two-percent rule against the one-percent rule — both still firmly in conservative territory, far below full Kelly.

What to do tomorrow

1. Open your trade journal and honestly compute, from at least the last two hundred positions, your own p (percentage of winning trades) and b (ratio of average winner to average loser); if the sample is smaller, do not attempt any version of Kelly yet — first gather a statistically meaningful dataset.
2. Plug those numbers into the formula f = (bp − q) / b for your own curiosity, then compare the result with one percent — if your fractional Kelly (half or quarter of the full value) lands close to one percent, you are safe; if much higher, you almost certainly have an over-estimated p.
3. Run a simple sensitivity test: repeat the calculation with p lowered by five percentage points and see how much the recommended sizing changes — if the jump is large, that is direct evidence that your strategy is too sensitive to Kelly and the one-percent rule remains the only sensible choice.
4. Independent of those calculations, set hard daily and monthly loss limits (for example three percent per day, eight percent per month) and write them into your strategy file — per-trade sizing is only one of three blades of risk management, alongside time-based limits and live psychological discipline.
5. Put a reminder in the calendar to repeat these calculations in six months — Kelly is not a one-off decision but a parameter that needs recalibration as market data accumulates and macro conditions shift; without periodic review, any sizing based on historical p and b quietly stops describing reality.