# Kelly’s F

Kelly’s F is a monetary management technique applied to investments in financial markets. It indicates the maximum percentage that we must risk in each operation to maximize our results. It is applicable to both intraday trading and long-term investment.

Kelly’s F values ​​loss streaks and profit streaks positively. Kelly’s F has its origin in the book “A new interpreton of information rate” written by JL Kelly in 1956.

Kelly’s F calculation

To calculate this monetary management indicator we need certain data that we must extract from our history of stock market operations. The data are as follows:

• Percentage of operations in profits.
• Profit / Loss Ratiocalculated as the ratio between the average profit in our successes and the average loss in our operations in losses.

Kelly’s formula F is such that:

The percentage is calculated in the formula as per one. In addition the result is usually diluted. For this, the result is divided by 10 to avoid excessively high results.

One of the great advantages of Kelly’s F is that it maximizes the results mathematically. It allows more risk if the percentage of successes increases and recommends less risk if the percentage of successes decreases. Even so, it also has drawbacks.

Its main disadvantage lies in the fact that it assumes that the profit and loss results are constant. In financial markets, dominated by randomness, ensuring constant results is bold. If the results of a portfolio are not constant, applying Kelly’s F involves large fluctuations in the value of capital.

Thus, this problem would not be solved until 1990. Date on which Ralph Vince published “Portfolio Management Formulas”, where he presented his vision on Kelly’s F and then offer his own “optimal F”.

Kelly’s F example

Suppose that after collecting the necessary information from our history of operations our variables have the following values.

• Success rate:55%
• Total profit:€ 3,000
• Total loss:€ 2,000
• Total operations:50

With this information we calculate the data we need about the profit / loss ratio. We divide the profits by the total of operations and, subsequently, we do the same with the losses.

Average profit per operation = € 60

Average loss per operation = € 40

By dividing the average profit per operation and the average loss operation, we obtain the profit loss ratio. Which is equal to 1.5. We would get the same result if we divide the total earnings by the total losses. The reason why it has been calculated in this way, step by step, is to understand the concept more simply.

According to Kelly’s F formula in our next operation we must risk 25% of our capital. Since this is considered in terms of monetary management an aberration, what is done is to dilute the final result to 10%. So what we must risk according to diluted Kelly’s F is 2.5%.

Suppose now, that after 10 operations, our results get worse and remain as follows:

• Percentage of hits:50%
• G / P Ratio:2

We can confirm the above. If we have a losing streak of operations, our calculation is significantly reduced. Now we must risk, according to Kelly’s F 8.3% that diluted to 10% becomes 0.83% per operation. After 10 operations, five losing operations and lowering the profit / loss ratio by 0.3 points, our risk ends up being three times lower.