# The Kelly Criterion – Maximise Your Capital Growth

How much trust should you put in an uncertain information? How much money should you risk with your next trade? The answer, essential to every trader, is hidden in John Kelly’s jr. famous paper “A New Interpretation of Information Rate“. This article will show some applications of his research in trading and give you the position sizing formula to archive the maximum possible capital growth.

## Noisy telephone lines and random markets

John Kelly has been a scientist at the AT&T Bell Laboratory in the fifties of the last century. His subject of research has been to find out how much useful information can be transmitted over a noisy telephone line.

Due to the noise level on an old phone line, a high frequency signal might get too distorted to carry any useful information. On the other side a low frequency signal might just be too slow to carry a useful amount of information over a specific time. The optimal signal rate, and that’s Kelly’s contribution, is set by the amount of noise vs. the amount of data correctly transmitted over the line.

## The Kelly Criterion – Learning from Information Theory

Kelly’s paper starts with an intellectual experiment: If you would have a secret telephone line which would tell you tomorrows close, how much should you risk on the information transmitted over this line? 100% would be the answer if the information transmitted over the line would always be true. But what if the prognosis is wrong in 5% of the time? What if a wrong reading has more severe consequences than a good signal?

In trading there are no such magic lines, but there are trading strategies. Like on a magic noisy telephone line not every signal of your trading strategy will be right…

To calculate the Kelly criterion you first will have to find out how accurate your strategy’s signal is. Second you need to how much you might win or lose on the next trade. Knowing these numbers the Kelly criterion defines the maximum amount of your equity that should be risked with the next trade. Doing so will lead to the highest possible equity growth over time.

## Kelly for Traders

Let’s put his formula to work with a simple example: If our trading strategy has 65% winning trades and you win 500$ or lose 550$ on average, the optimal risk per trade would be 65%-(1-65%)/(500$/550$)=26.5% of your equity.

This 26.5% is a theoretical risk percentage and usually way too high for non suicidal trades. The Kelly criterion is a barrier for equity growth. If you would invest more than the given number, you might not be able to recover from drawdowns within a long period of time, and therefore miss the maximal possible equity growth. If you would risk less than given by the Kelly criterion, you would not make full use of the edge your strategy offers, and therefore also miss the maximum capital growth.

**WARNING: ** Kelly optimises for capital growth, not volatility of returns. Also, in above’s example, we used the average loss for the calculation of the Kelly number. As you know the average loss will be way below the actual maximal loss. So in real world trading you most probably will use a fixed fraction like 1/10th of the theoretical Kelly barrier as a risk level for your trading.

Whatever fraction of the Kelly criterion you will use, the effect will stay the same: You will shift risk and exposure to the strategies and markets which offer the highest edge. Your investment grade will always reflect this edge. Winners get more, losers fade out.

## Comparing Markets using the Kelly Criterion

The above example was an example of how to apply the Kelly criterion to find the optimum rate of investment in a trading strategy. You had the historic wins and losses, and based on these numbers the Kelly formula returned the optimum risk level.

Another way to use the Kelly formula in trading is to use it to compare different markets against each other. For a long only investor the winning probability would be defined by the number of up days, and the ratio of average win vs. average loss by the average close to close swings.

The chart above shows the Kelly criterion programmed as an indicator. It uses the last 250 daily bars to calculate the shown results.

A value of zero suggest that the market is not fit for an investment on the long side. On the other side a rising indicator indicates that you should increase your exposure to this market. The suggested level of risk to be taken can be seen on the scale of the indicator.

As you can see above, the formula started to suggest an exposure in 20+ year treasury bonds in February 2019. Due to the strong trend in this market (ETF: TLT) the Kelly criterion suggests an increasing exposure in bonds.

Quite the contrary can be seen on the right side of the chart, showing the ETF: SPY. There the Kelly criterion shows a falling percentage reading. The golden times of stocks ended in 2018, and Kelly suggest that the logical answer to this is a decrease in exposure to this market.

## Kelly criterion in Tradesignal Equilla

The picture below gives you a sample version of the Kelly formula, using it as a trend following / risk grade indicator.

The coding uses the bar-to-bar absolute price swings and the probability of an up and down move to calculate the indicator. Adjust the look-back period to fit the indicator to your trading requirements. Feel free to adjust it to your own needs and contact us with questions and suggestions.

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