What Is the Kelly Criterion?

The Kelly criterion is a mathematical formula relating to the long-term growth of capital developed by John L. Kelly, Jr. The formula was developed by Kelly while working at AT&T's Bell Laboratories. The formula is currently used by gamblers and investors for risk and money management purposes, to determine what percentage of their bankroll/capital should be used in each bet/trade to maximize long-term growth.

The Formula for the Kelly Criterion Is

The term is often also called the Kelly strategy, Kelly formula or Kelly bet, and the formula is as follows:

Kelly %=W[(1W)R]where:Kelly %=percent of investor’s capital to put into a single tradeW=historical win percentage of trading systemR=trader’s historical win/loss ratio\begin{aligned} &Kelly~\% = W - \Big[\dfrac{(1-W)}{R}\Big] \\ &\textbf{where:}\\ &Kelly~\% = \text{percent of investor's capital to put into a single trade}\\ &W = \text{historical win percentage of trading system}\\ &R = \text{trader's historical win/loss ratio}\\ \end{aligned}Kelly %=W[R(1W)]where:Kelly %=percent of investor’s capital to put into a single tradeW=historical win percentage of trading systemR=trader’s historical win/loss ratio

How to Calculate the Kelly Criterion

There are two key components to the formula for the Kelly criterion: the winning probability factor (W) and the win/loss ratio (R). The winning probability is the probability a trade will have a positive return.

The win/loss ratio is equal to the total positive trade amounts, divided by the total negative trading amounts. The result of the formula will tell investors what percentage of their total capital that they should apply to each investment.

What Does the Kelly Criterion Tell You?

After being published in 1956, the Kelly criterion was picked up quickly by gamblers who were able to apply the formula to horse racing. It was not until later that the formula was applied to investing. More recently, the strategy has seen a renaissance, in response to claims legendary investors Warren Buffet and Bill Gross use a variant of the Kelly criterion.

The formula is used by investors who want to trade with the objective of growing capital, and it assumes that the investor will reinvest profits and put them at risk for future trades. The goal of the formula is to determine the optimal amount to put into any one trade.

Key Takeaways

  • Although used for investing and other applications, the Kelly Criterion formula was originally presented as a system for gambling on horse races.
  • The formula is used to determine the optimal amount of money to put into a single trade or bet.
  • Some argue that an individual investor's constraints can affect the formula's usefulness.


Limitations of Using the Kelly Criterion

The Kelly Criterion formula is not without its share of skepticism. Although the Kelly strategy's promise of outperforming any other strategy, in the long run, looks compelling, some economists have argued strenuously against it—primarily because an individual's specific investing constraints may override the desire for optimal growth rate.

In reality, an investor's constraints, whether self-imposed or not, are a significant factor in decision-making capability. The conventional alternative includes expected utility theory, which asserts that bets should be sized to maximize the expected utility of outcomes.