What is the Kelly criterion?
The Kelly criterion (also the Kelly Criterion, or Kelly formula) is a money-management rule that calculates the optimal fraction to invest in a given opportunity, by maximising the logarithmic growth of capital over the long term.
It was developed in 1956 by John L. Kelly Jr., a mathematician at Bell Labs, in a paper on information transmission. The analogy with betting — then with the stock market — was popularised by Edward Thorp (author of Beat the Dealer and a pioneer of quantitative trading) in the 1960s and 1970s.
The intuition is simple: investing too little holds back capital growth. Investing too much exposes you to catastrophic losses. Kelly mathematically calculates the optimal balance between the two.
Where:
- f*: the optimal fraction of capital to invest
- p: the probability that the trade is a winner
- b: the ratio of the average gain on winning trades / the average loss on losing trades
- q: the probability of losing (= 1 − p)
Interactive Kelly calculator
Which Kelly fraction should you choose?
Full Kelly theoretically maximises growth, but it is rarely used as-is in practice. The reasons are as much psychological as mathematical: the drawdowns generated by full Kelly are often too painful to sit through.
Rule of thumb: Edward Thorp, who used Kelly to generate annual returns of 20% over 30 years, systematically recommends half-Kelly: "Full Kelly is too volatile to be psychologically sustainable over the long term. Half-Kelly gives 75% of the growth for half the volatility — it's the ideal trade-off."
Kelly applied to the screener's signals
Screener Small Caps integrates Kelly directly into its Portfolio module. Here is how the parameters are calculated:
| Kelly parameter | Source in the screener | Typical value |
|---|---|---|
| p (win rate) | Track record of J+30 predictions logged in the database | ~62% |
| b (gain/loss ratio) | Ratio of average gains / average losses on confirmed BUY signals | ~1.30 |
| Fraction | Half-Kelly by default (adjustable in Pro) | 50% |
| Regime adjustment | kelly_mult × 0.7 in a bear market / ×1.0 in a bull market | Variable |
With these parameters (p=0.62, b=1.30), the raw Kelly is:
This result means that with capital of €10,000, the Portfolio module recommends investing around €1,640 on each high-confidence BUY signal — subject to sector-diversification constraints and the minimum cash reserve.
Limitations and precautions
Kelly assumes that bets are independent
The Kelly formula was developed for successive independent bets. In the stock market, positions are correlated — a market correction pushes all your small caps down at the same time. The screener's Portfolio module includes a sector-diversification constraint to limit this correlation risk.
The parameters p and b are uncertain
You never have certainty about the true probability of winning. The p and b estimated from the track record can change if the market shifts regime. That is why half-Kelly is preferable: it is more robust to errors in estimating the parameters.
Kelly does not handle liquidity constraints
On the least liquid European small caps, the position size recommended by Kelly can exceed the daily volume available. The Portfolio module includes a minimum-liquidity filter.
Important: The Kelly criterion is a decision-support tool, not a mechanical rule to follow blindly. It does not constitute investment advice. Past performance from the track record is not a guide to future returns.