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# Kelly Criterion

## Definition

The Kelly Criterion is a mathematical formula used in investing and gambling to determine the optimal bet size based on the odds and the probability of winning. It aims to maximize the long-term growth rate of capital while minimizing the risk of losing the entire funds. Developed by John Larry Kelly Jr., this formula helps investors and gamblers find the right balance between risk-taking and preserving capital.

### Phonetic

The phonetic pronunciation of “Kelly Criterion” is:K-E-L-L-Y: /ˈkɛli/C-R-I-T-E-R-I-O-N: /krɪˈtɪriən/

## Key Takeaways

1. Maximizing long-term growth: The Kelly Criterion is a formula used by investors and gamblers to determine the optimal bet size or position to maximize their long-term growth. It takes into account the probability of winning and the potential return on investment to make calculated decisions.
2. Managing risk: By using the Kelly Criterion, individuals can manage their risk and avoid excessive drawdowns or losses. This helps in preserving capital and maintaining a relatively stable growth trajectory over time, making it an attractive consideration for risk-averse investors.
3. Flexible and adaptable: The Kelly Criterion can be adapted for various types of investments or bets, such as stocks, fixed income, options, or sports betting. This makes the technique valuable for a wide range of applications and for investors with diverse investment profiles.

## Importance

The Kelly Criterion is an important financial concept as it enables investors to determine the optimal amount to invest in each trade while maximizing long-term growth and minimizing risk. Developed by John Larry Kelly Jr., this formula is particularly vital for traders and investors participating in high-risk endeavors, such as stock markets or sports betting, where capital preservation is a key concern. The Kelly Criterion combines probabilities and potential returns to calculate the ideal percentage of one’s capital to invest. By following this strategy, investors can not only strategically allocate their bets to potentially grow their wealth exponentially but also minimize the risk of ruin by avoiding overexposure to any single investment. As a result, the Kelly Criterion establishes itself as an essential tool for those striving to achieve a balanced investment approach, effectively balancing risk and reward in any financial endeavor.

## Explanation

The Kelly Criterion is a mathematical formula designed to maximize the growth rate of repeated bets while minimizing the risk of ruin, commonly employed in finance, most notably in investing and sports betting. The core purpose of the Kelly Criterion is to determine the optimal bet size or investment proportion given the probability of success and the expected return of the investment. This helps individual investors, professional money managers, and gamblers allocate their funds in a systematic manner to achieve long-term returns while mitigating risk.

In practical applications, the Kelly Criterion balances the trade-off between aggressive and conservative strategies, by advising an investor to invest a portion of their funds according to the estimated probability of successful outcomes. The formula takes into account factors such as the odds of winning, the expected return, and the investor’s total capital. By tailoring investment proportions to an individual’s unique circumstances and investment opportunities, the Kelly Criterion assists in maximizing expected returns while reducing the chance of losing a significant portion of their funds. This strategic approach enables individuals and businesses to grow their wealth and manage risk more effectively in various financial and betting scenarios.

## Examples

The Kelly Criterion is a formula that helps determine the optimal bet size based on available information to maximize the growth of wealth over time. Here are three real-world examples:

1. Stock Market Investing: An individual investor who has access to historical data and statistical information on the stock market may use the Kelly Criterion to determine the optimal percentage of his/her investment portfolio that should be allocated to a particular stock. Based on the stock’s anticipated returns, risks, and investment size, the Kelly Criterion can help the investor maximize the long-term growth of his/her wealth.

2. Sports Betting: A sports bettor can use the Kelly Criterion to determine the optimal amount of money to wager on a specific game or event based on the probability of winning, odds offered by the sportsbook, and the available bankroll. By following this betting system, the bettor tries to minimize the risk of losing while maximizing potential reward. For example, if a bettor determines that Team A has a 60% chance of winning against Team B, and the sportsbook offers odds of 2:1, he/she can use the Kelly Criterion to calculate the optimal bet amount to maximize the long-term growth of the bankroll.

3. Blackjack Card Counting: One of the applications of the Kelly Criterion is in the card counting systems in blackjack. A professional blackjack player may use a card counting system that assigns point values to specific cards in a deck and adjusts his/her betting strategy accordingly. Based on the current point values (positive or negative), a player may use the Kelly Criterion to determine the optimal bet amount in order to maximize profits while reducing the risk of ruin or being noticed by the casino. By following the Kelly Criterion betting strategy, the blackjack player tries to balance the risk and reward while exploiting favorable situations in the game.

What is the Kelly Criterion?

The Kelly Criterion is a mathematical formula used to determine the optimal bet size in gambling or investing situations. It helps calculate the percentage of capital to allocate per bet or investment to maximize long-term growth and minimize the risk of ruin. The formula was developed by John Larry Kelly Jr., a scientist at AT&T’s Bell Labs, in 1956.

How does the Kelly Criterion work?

The Kelly Criterion works by assessing the potential return on investment compared to the risk. It calculates the optimal bet size by taking into account the odds of winning, potential profit, and desired risk level. The formula is:K% = (BP – Q) / B where K% is the fraction of the capital to be invested; B is the odds multiplier (net odds but must be converted to decimal); P is the probability of success; and Q is the probability of failure (1 – P).

Why is the Kelly Criterion important in finance and investing?

The Kelly Criterion is important for investors and traders because it helps to determine the optimal amount of capital to risk on a specific trade or investment. By maximizing the potential growth rate while reducing the risk of ruin, it ensures a more sound approach to managing capital and making investment decisions.

When should one use the Kelly Criterion?

The Kelly Criterion should be used when the probabilities or odds of the outcomes are known or can be estimated, and the main goal is to maximize the long-term growth of capital while minimizing the risk. This can be applied to various financial scenarios like gambling, investing in stocks, trading, and portfolio allocation.

Can the Kelly Criterion be used in portfolio management?

Yes, the Kelly Criterion can be adapted for portfolio management. It can be used to determine the optimal allocation of capital to different assets or investments within a portfolio. Using the Kelly Criterion in this way helps achieve the greatest potential for long-term growth while reducing risks associated with volatile markets.

What are the limitations of the Kelly Criterion?

Some limitations of the Kelly Criterion include:1. Assumes accurate estimation of odds or probabilities, which can be difficult to determine in real-world situations.2. Can lead to over-betting if the calculated probabilities are overly optimistic.3. Assumes that the returns from each bet or investment are independent of one another, which may not always be true.4. May not work effectively for those with a relatively small capital base, as it could result in highly concentrated positions.

How can the Kelly Criterion be used in conjunction with other risk management strategies?

The Kelly Criterion can be combined with other risk management strategies such as diversification and stop loss orders to create a more well-rounded approach to managing capital and investments. Proper risk management practices can help reduce exposure to potential losses while enhancing the benefits of using the Kelly Criterion to allocate capital efficiently.

## Related Finance Terms

• Expected Value
• Bankroll Management
• Optimal Bet Sizing
• Probability Theory
• Risk of Ruin

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