Kelly Criterion

What Is Kelly Criterion?

The Kelly criterion is a mathematical formula relating to the long-term growth of capital developed by John L. Kelly Jr. while working at AT&T's Bell Laboratories.

Understanding Kelly Criterion

Kelly criterion 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.

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 that 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.

There are two key components to the formula for the Kelly criterion:

1. winning probability factor (W) - the probability a trade will have a positive return.
2. win/loss ratio (R) - 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 they should apply to each investment.

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

K e l l y   % = W − [ ( 1 − W ) R ] where: K e l l y   % =  Percent of investor’s capital to put into  a single trade W = Historical win percentage of trading system R = Trader’s historical win/loss ratio \begin{aligned} &Kelly~\% = W - \Big[\dfrac{(1-W)}{R}\Big] \\ &\textbf{where:}\\ &\begin{aligned} Kelly~\% = &\text{ Percent of investor's capital to put into}\\ &\text{ a single trade} \end{aligned}\\ &W = \text{Historical win percentage of trading system}\\ &R = \text{Trader's historical win/loss ratio}\\ \end{aligned} Kelly %=W−[R(1−W)]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

Kelly Criterion Limitations

The Kelly Criterion formula is not without its share of skeptics. Although the strategy's promise of outperforming all others in the long run looks compelling, some economists have argued 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.