The Kelly criterion gives the bet size that maximizes long-run logarithmic wealth. It is mathematically beautiful, theoretically optimal, and operationally dangerous when applied without modification. This article covers what Kelly says, why Full Kelly is rarely the right choice, and what most practitioners actually do.
The Formula
For a binary bet with probability of winning p, win amount b, and loss amount 1:
where f* is the optimal fraction of bankroll to bet. For continuous returns, the analog is:
where μ is mean excess return per period and σ² is its variance. This is the form that appears in most quantitative-trading contexts.
What Kelly Optimizes
Kelly maximizes the geometric growth rate of wealth — equivalently, the median final wealth after many periods. It does not maximize expected wealth, terminal Sharpe, or any drawdown-related metric. The trade-off it accepts: very high mean return at the cost of very high variance, including catastrophic drawdowns.
A strategy with Sharpe 1.0 traded at Full Kelly has roughly a 50% probability of drawing down 50% of its peak equity at some point. Most humans cannot trade through a 50% drawdown without making mistakes — quitting at the bottom, doubling down inappropriately, or pulling money. So Full Kelly is mathematically optimal but psychologically and operationally destructive.
Why Full Kelly Fails in Practice
- You don't know the true edge. Kelly is optimal given the true probabilities. You estimate them from finite data with error. If you over-estimate edge by 50%, Full Kelly becomes the disastrous "1.5×" Kelly.
- Returns aren't i.i.d. Kelly assumes independent, identically distributed returns. Real return streams have autocorrelation, regime changes, and fat tails — all of which make actual drawdowns worse than the Kelly model predicts.
- The formula is sensitive to the input. A small change in estimated edge produces a large change in optimal size, especially when edge is small.
What Practitioners Actually Use
Half-Kelly
Bet half the Kelly fraction. Cuts expected geometric growth by ~25% but cuts drawdown variance by ~75%. The standard pragmatic choice.
Quarter-Kelly
Bet a quarter of the Kelly fraction. Common in institutional risk-managed systems. Sacrifices more expected growth for further drawdown protection.
Capped Kelly
Compute Kelly, then cap the result at some fixed maximum (often 2× to 5× of equity for leveraged products, or 100% for cash equity). Prevents Kelly from suggesting absurdly large positions when the variance estimate is small.
How to Use Kelly in QuanterLab
- Treat the platform's Kelly% output as a ceiling, not a target. If Kelly says 60%, you can confidently size at 30% (Half-Kelly) and know you have a safety margin.
- Re-estimate Kelly periodically as you accumulate live data. Live edge is almost always smaller than backtest edge — your live Kelly should be smaller too.
- Combine with volatility targeting. Kelly tells you how aggressive to be; volatility targeting normalizes for which name you are trading.
- Never lever past Kelly. Beyond Full Kelly, expected geometric growth turns negative — more leverage produces less wealth in the long run.
The Bottom Line
Kelly is the right framework for thinking about position size in proportion to edge. Full Kelly is the wrong implementation for everyone except simulation studies. Trade Half-Kelly or smaller, accept the modest reduction in expected return, and keep the ride survivable enough that you can stay in the game.
Further Reading
Foundational papers
- Kelly, J. L. (1956). A New Interpretation of Information Rate. Bell System Technical Journal, 35(4), 917–926.
- Thorp, E. O. (2006). The Kelly Criterion in Blackjack, Sports Betting, and the Stock Market. In: Handbook of Asset and Liability Management, Vol. 1.
Textbook references
- MacLean, L. C., Thorp, E. O. & Ziemba, W. T. (2010). The Kelly Capital Growth Investment Criterion. World Scientific.
Related QuanterLab articles
Try it in QuanterLab
Use SC001STCB's Kelly% output as a ceiling, not a target. Most practitioners trade Half-Kelly or Quarter-Kelly to survive the inevitable parameter mis-estimation.