The Holy Grail Formula

Discover the Kelly Formula, a mathematical tool for managing risk and optimizing position sizing in financial markets.

Jun 19, 2023

#keypoints
Daily Educational Content [Free]:
The Kelly Formula: A Key Financial Market Strategy
Understanding the Kelly Formula
What is the formula for Kelly rule?
What is the Kelly multiplier formula?
Kelly Formula in Financial Markets
What is an example of Kelly formula?
Case Study on S&P 500 Leveraged ETF
Bottom Line
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Properly sizing your positions is the Holy Grail of the Financial Market.

The formula to outperform the market is simply to maintain assets in an upward trend in your portfolio, limit losses through sell stops, and manage risk with optimal position sizing.

Let's take a step forward in risk management and apply the position sizing theory that has allowed great investors to decipher and outperform the market - the Kelly Formula.

The formula you're about to learn was created by computer scientist John Kelly in a 1956 paper, referenced in William Poundstone's book "Fortune's Formula," and later popularized by Edward Thorp (A Man for All Markets) when he applied the theory to beat the game of Blackjack. It was also applied by Jim Simons, founder of the Hedge Funds Medallion and Renaissance.

The Kelly Formula: A Key Financial Market Strategy

The formula is based on the principle of maximizing the expected logarithm of wealth, which is equivalent to maximizing the expected geometric growth rate.

The formula provides a strategy for bet sizing that leads to the highest possible growth rate in the long run.

Understanding the Kelly Formula

In the financial market, the Kelly Formula can be used to manage risk and optimize position sizing.

By correctly sizing your positions, you can limit losses through sell stops and maintain assets in an upward trend in your portfolio.

This strategy is considered the Holy Grail of the financial market, as it allows investors to outperform the market consistently.

The position size of an asset in your portfolio should not be predetermined, but rather defined by the outcome according to each of these factors.

What is the formula for Kelly rule?

Kelly's rule, or the Kelly criterion, is a money management strategy that aims to maximize the growth of capital over the long term.

It provides a formula to determine the optimal size of a series of bets or investments. The rule takes into account both the probability of winning and the potential return to calculate the optimal bet size.

What is the Kelly multiplier formula?

The Kelly Formula takes into account four key components:

Total Risk Capital: This is the total amount of money that you are willing to risk on a particular bet or investment.
Probability of Positive Results: This is the probability that the bet or investment will result in a positive outcome.
Probability of Negative Results: This is the probability that the bet or investment will result in a negative outcome.
Return/Risk Ratio: This is the ratio of the potential return on the bet or investment to the amount of money risked.

Kelly Formula (K)

Kelly Formula in Financial Markets

The Kelly Formula applied to the Betting Market has an advantage over the Financial Market, a finite number of possibilities.

In Blackjack the deck has 52 cards, the lottery numbers are limited.

Unlike the Financial Market, where there are an infinite numbers of variable.

And the way to reduce risk when the Formula is applied to the Financial Market is to apply a percentage factor to the result, the K% FACTOR.

For example 50%, which in the example above, we would arrive at a position of: The smaller the K% FACTOR, the more conservative is your position.

Within the Alfa Hedge Algorithm, the K% FACTOR is automatically calculated according to the statistical data of the Markets in which we have positions set up in the month.

This way, you know exactly the size of the positions optimized for your portfolio.

What is an example of Kelly formula?

Case Study on S&P 500 Leveraged ETF

Let's go to an example based on the Alfa Hedge Strategy Algorithm for the SPXL Asset (Direxion Daily S&P 500 Bull 3X Shares) extracted from the TrendSpider Platform on 02/10/2022 and a capital of US$ 50,000.00.

ETF SPXL Data extracted from the TrendSpider Platform on 2022/02/10

Total Risk Capital: US$ 50,000.00

Probability of Positive Results: 86%

Probability of Negative Results: 14%

Return/Risk Ratio: 7.12

Example K% FACTOR: 50%

K = (7.12 x 86% - 14%)/ 7.12 = 5.98/7.12 = 83.98%
Optimal Position Sizing = US$ 50.000 x 83.98% x 50% = US$ 20,995.00

The Kelly Formula is a powerful tool for managing risk and optimizing position sizing in the financial markets. By taking into account the total risk capital, the probabilities of positive and negative results, and the return/risk ratio, it provides a mathematical framework for making informed investment decisions.

Bottom Line

The Kelly Formula is a powerful tool for managing risk and optimizing position sizing in the financial markets.

By taking into account the total risk capital, the probabilities of positive and negative results, and the return/risk ratio, it provides a mathematical framework for making informed investment decisions and outperform the markets.

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