 # Kelly Criterion

The mathematical formula for bet sizing frequently used by investors

## What is the Kelly Criterion?

Kelly criterion is a mathematical formula for bet sizing, which is frequently used by investors to decide how much money they should allocate to each investment or bet through a predetermined fraction of assets. It is popular because it typically leads to higher wealth in the long run compared to other types of strategies. ### Summary

• Kelly criterion is a mathematical formula for bet sizing, which is frequently used by investors and gamblers to decide how much money they should allocate to each investment or bet through a predetermined fraction of assets.
• It is popular due to how it typically leads to higher wealth in the long run compared to other types of strategies.
• It is based on the formula k% = bp–q/b, with p and q equaling the probabilities of winning and losing, respectively.

### History of the Kelly Criterion

Kelly criterion was developed in 1956 by an American scientist, John L. Kelly, who worked as a researcher at AT&T’s Bell Labs in New Jersey. Kelly originally developed the formula to help the company with its long-distance telephone signal noise issues.

Later, it was picked up upon by the betting community, who realized its value as an optimal betting system since it would allow gamblers to maximize the size of their earnings.

Although it was reported that Kelly never used his formula for personal gain, it is still quite popular today and is used as a general money management system for investing. One reason behind its popularity is because of how frequently it is used by prominent investors, such as Warren Buffet of Berkshire Hathaway.

### Understanding the Kelly Criterion

Investors often face a tough decision when trying to decide how much money to allocate, as staking either too much or too little will result in a large impact either way.

The Kelly criterion is a money-management formula that calculates the optimal amount to ensure the greatest chance of success. The formula is as follows: Where:

• K % = The Kelly percentage that is the fraction of the portfolio to bet
• b = The decimal odds that is always equal to 1
• p = The probability of winning
• q = The probability of losing, which is 1 – p

### Example

When a dice is thrown, the chance of it landing on a 1, 2, or 3 is 50%, while the same percentage applies to an outcome of 4, 5, or 6.

Now, let us imagine that the dice can rest on a 1, 2, or 3 with a probability of 60%, meaning the probability of it landing on 4, 5, or 6 is 40%. The variables will look as follows:

• b = 1
• p = 0.60
• q = 1 – 0.60 = 0.40

Based on the Kelly criterion, K% = (1 × 0.60 – 0.40) / 1 = 0.20 or 20%

The formula is therefore suggesting that 20% of the portfolio be stake 20% of your bankroll. If the dice bias were less, at 53%, the Kelly criterion recommends staking 6%.

In such a case, the Kelly criterion suggests that if one were to go over 20% repeatedly on a low number, there is a high chance one would eventually go broke.

Under-betting less than 20%, on the other hand, would lead to a smaller profit, which means that adhering to the Kelly criterion will maximize the rate of capital growth for the long-term.

### Analysis of the Results

The Kelly criterion results in the K%, which refers to a percentage that represents the size of the portfolio to devote to each investment. Basically, the Kelly percentage provides information on how much one should diversify.

One should not commit more than 20% to 25% of the capital into single equity regardless of what the Kelly criterion says, since diversification itself is important and essential to avoid a large loss in the event a stock fails.

Some investors prefer to bet less than the Kelly percentage due to being risk-averse, which is understandable, as it means that it reduces the impact of possible over-estimation and depleting the bankroll. It is known as Fractional Kelly.

On the other hand, if the Kelly percentage results in a percentage less than 0%, it means that the Kelly criterion is recommending that one walk away and not bet anything at all since the odds do not seem to be in one’s favor based on the formula and mathematical calculation.

Following the Kelly criterion typically results in success due to the formula is based on a simple formula using pure mathematics.

However, factors that can impact the success include accurate inputs of the probabilities of winning and losing, as an incorrect percentage would be detrimental.

In addition to that, there may be unexpected events such as stock market crashes, which would impact all stocks regardless if the Kelly criterion was used or not.