The Origins of the Kelly Criterion and Its Application to Investing
The Kelly criterion is a formula published in 1956 by mathematician John Kelly of Bell Labs in the context of information theory. Originally a theory for optimizing information transmission over noisy communication channels, its mathematical structure was found to be identical to the problem of determining optimal bet sizes in gambling and investing, leading to its widespread application in money management. The core of the Kelly criterion is calculating the "investment ratio that maximizes the long-term compound growth rate of assets."
In its simplest form, the Kelly formula is expressed as f* = (bp - q) / b, where f* is the optimal investment ratio relative to assets, b is the profit multiplier when winning, p is the probability of winning, and q is the probability of losing (1 - p). For example, given an investment opportunity with a 60% win rate where winning yields 100% profit and losing means 100% loss, the Kelly criterion calculates f* = (1 x 0.6 - 0.4) / 1 = 0.2, meaning investing 20% of assets is optimal. Investing beyond this ratio may yield larger returns in the short term, but the long-term compound growth rate actually decreases.
The Dangers of Full Kelly and Fractional Kelly
Full Kelly (investing at the exact ratio indicated by the Kelly criterion) is extremely dangerous in practice for three reasons. First, if the estimates of win probability and profit multiplier are inaccurate, the Kelly criterion's output will also be inaccurate. In the investment world, accurately estimating probabilities is difficult, and estimation errors directly translate into overinvestment risk. Second, full Kelly results in very large drawdowns (temporary asset declines). Theoretically, maximum drawdowns exceeding 50% of assets are not uncommon, and few investors can psychologically endure this.Books on the Kelly criterion and risk management also provide detailed analysis of the practical dangers of full Kelly.
Third, the Kelly criterion assumes a logarithmic utility function, which does not accurately reflect every investor's risk preferences. In practice, "fractional Kelly" is widely used - investing at half (half Kelly) or one-quarter (quarter Kelly) of the Kelly criterion. Half Kelly reduces the compound growth rate to approximately 75% of full Kelly while significantly reducing drawdowns. It also improves robustness against estimation errors, which is why many practitioners recommend half Kelly or less.
Considerations When Applying the Kelly Criterion to Stock Investing
When applying the Kelly criterion to stock investing, you need to handle continuous return distributions rather than simple binary win/lose outcomes. The continuous distribution version of the Kelly criterion is approximated as f* = (mu - r) / sigma-squared, where mu is the expected return, r is the risk-free rate, and sigma-squared is the variance of returns. For example, for a stock portfolio with an expected return of 10%, a risk-free rate of 2%, and a standard deviation of 20%, f* = (0.10 - 0.02) / 0.04 = 2.0, indicating that 2x leverage is optimal.
However, executing this result directly is dangerous. Real-world constraints such as estimation errors in expected returns, deviations from normality in return distributions (fat tails), and transaction and leverage costs must be considered.Books on position sizing and quantitative analysis introduce specific adjustment methods for applying the Kelly criterion to actual portfolio management. It is wise to use the Kelly criterion as an indicator of the upper limit of "how much to invest" and keep the actual investment ratio at half or less.
Next Actions for Incorporating the Kelly Criterion into Money Management
To incorporate the Kelly criterion's thinking into your investing, start by identifying the riskiest position in your current portfolio and calculating what percentage of your total assets it represents. If you have more than 30% of your assets concentrated in a single stock, it is likely far exceeding full Kelly, and your drawdown risk is excessive. Following the half Kelly principle, aim to keep any single position below 10-15% of total assets.
As a more practical approach, before making a new investment, decide in advance "what is the maximum percentage loss I can tolerate on this investment" and reverse-calculate the position size so that the loss amount stays within 2-5% of the total portfolio. Use our compound interest calculator to simulate long-term asset growth at different position sizes and experience firsthand how excessive concentration reduces compound growth rates through volatility drag.