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What is the Kelly Criterion?
The Kelly criterion, named after the mathematician John L. Kelly Jr., is a formula used to determine the optimal allocation of capital in order to maximize long-term growth in a sequence of investments or bets. It provides a guideline for determining the size of each bet or investment based on the expected return and risk. The Kelly criterion is widely used in various fields, including gambling, trading, and investment management. It is expressed as a mathematical formula:
f* = (bp - q) / b
where:
- f* is the fraction of capital to be wagered or invested,
- b is the net odds received on the bet (the profit if the bet wins divided by the initial stake),
- p is the probability of winning,
- q is the probability of losing (1 - p).
The key aspects of the Kelly criterion are as follows:
The Kelly criterion is based on the expected value, which is the average return that can be anticipated from each bet or investment. It considers both the probability of winning and the magnitude of the potential gain or loss. The goal is to maximize the long-term growth rate of wealth. It aims to strike a balance between risk and reward, allowing for aggressive growth while managing the risk of ruin. The Kelly criterion suggests investing a fraction of capital that is proportional to the expected edge or advantage of the bet. It indicates that the optimal bet size is directly related to the perceived value and probability of success.
While the Kelly criterion maximizes long-term growth, it is important to consider the risk of ruin or substantial losses. Aggressive use of the Kelly fraction can result in significant drawdowns or potential loss of capital, especially in situations with imperfect information or volatile markets. Variations and modifications have also been proposed to handle multiple investment choices, constraints, and practical considerations, such as transaction costs and portfolio diversification.
It is essential to carefully consider the assumptions, limitations, and practical considerations when applying the Kelly criterion in real-world scenarios. Risk management, diversification, and individual risk preferences should also be taken into account alongside the Kelly criterion.