What is 'The Kelly Criterion'

The Kelly criterion is a mathematical formula relating to the long-term growth of capital developed by John Larry Kelly, Jr. The formula was developed by Kelly while working at the AT&T Bell Laboratories. The formula is currently used by gamblers and investors to determine what percentage of their bankroll/capital should be used in each bet/trade to maximize long-term growth.

The term is often also called the Kelly strategy, Kelly formula or Kelly bet.

Formula for calculating the Kelly criterion.

BREAKING DOWN '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.

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 investor Warren Buffet and Bill Gross use a variant of the Kelly criterion.

The 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 bets should be sized to maximize the expected utility of outcomes.

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