Position Sizing in Trading with Kelly Criterion

How much of your portfolio should you put in a given trade or investment? That's something that intrigues all traders and investors. While discretionary traders approach this as more of an art and gut feel, for systematic traders, there are a few time-tested scientific solutions to this problem. The most common of them is the Kelly Criterion.

The Kelly Criterion is a mathematical formula used to determine the optimal size of a bet or investment in order to maximize the growth of an individual's wealth over time. It was developed by John L. Kelly Jr., a scientist and mathematician who worked at Bell Labs in the 1950s. This is based on the idea that an individual should bet a certain fraction of their wealth on each trade or investment, in order to maximize their long-term growth. The specific fraction to bet is determined by the probability of success and the potential payout of the trade or investment.

One of the most famous applications of the Kelly Criterion is in the field of blackjack. In the 1960s, mathematician and professional blackjack player Ed Thorp used the Kelly Criterion to determine the optimal size of his bets in order to maximize his winnings. Thorp's successful use of the Kelly Criterion helped to popularize the concept among gamblers and investors. Thorp has written about this in his bestselling book "Beat the Dealer".

The Kelly Criterion has been successful in helping many people to maximize their wealth and minimize their losses in the real world. In addition to its application in blackjack and trading, the Kelly Criterion has also been used in other fields where probabilities and payouts are involved, such as horse racing and sports betting.

William Poundstone has also written in details about various uses of Kelly Criterion in his book "Fortune's Formula: The Untold Story of the Scientific Betting System That Beat the Casinos and Wall Street"

One of the famous use of the Kelly Criterion is Ed Seykota's commodities trading program. Seykota's program consisted of two computers that traded futures contracts electronically 24 hours a day. From 1971 to 1989, this program generated an annual return of more than 30%. Seykota's wealth management firm still uses the Kelly Criterion today to manage money for clients. The firm has an algorithmic trading system that determines which trades to make based on when certain conditions are met. These conditions include things like price action, market trends, and volatility levels.

Another well-known example of the success of the Kelly Criterion is the story of Bill Miller, a legendary investor who used the Kelly Criterion to manage his mutual fund at Legg Mason. In the 1990s and early 2000s, Miller's fund consistently outperformed the S&P 500, thanks in part to his use of the Kelly Criterion to determine the optimal size of his bets on stocks.

The Kelly Criterion is used in position sizing in trading. For example, if an individual has a portfolio of $100,000 and they are considering making a trade with a 60% probability of success (win-rate) and a potential payout of 1.5 times the amount risked in the trade (reward:risk), the Kelly Criterion would dictate that they should bet 33.33% of their portfolio on the trade. This is calculated by taking probability of success (0.6), and then subtracting the probability of failure (1 - 0.6 = 0.4) divided by the potential payout (1.5). The result, 0.6 - 0.4/1.5 = 0.33333 (33.33%), is then multiplied by the individual's total portfolio ($100,000) to determine the optimal bet size, which in this case would be $33,333.

Charlie Munger had famously said - "The wise ones bet heavily when the world offers them that opportunity. They bet big when they have the odds. And the rest of the time, they don't. It is just that simple!". The Kelly Criterion is a valuable tool for determining the optimal size of bets and investments in order to maximize an individual's wealth when the world offers them the opportunity.


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