Kelly Criterion Formula For Optimal Position Sizing
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In this review we look at the Kelly Criterion strategy and how we can apply the principles to our trading or investing activities to maximise growth. Created by computer scientist John Kelly in a paper from 1956, often referred to as the Fortune’s Formula, and later popularised by Edward Thorp when he applied the theory to beat the game of Blackjack.
Another note-worthy investor to apply the theory is Jim Simons founder of the Renaissance Medallion hedge fund. I also use a variation of the strategy and is the reason for our review.
Let’s take a look, and as always, please hit the like button and join our growing community below.
The Kelly Criterion calculation is used to calculate the optimum stake or position size for a given event, and is made up of four factors.
The equity balance.
The expected return from a winning outcome.
The probability of winning, and the probability of losing.
Ultimately, the Kelly Criterion formula calculates the perceived edge you have over an event and varies the stake accordingly, thereby determining the optimum stake size, or in trading terms, determining the optimum position size.
Contrary to the trading community, position size should not be a predetermined input to a strategy but rather an output depending on each of these four variables.
I’ll apply this concept to my personal trading stats shortly but first let’s look at how it applies to a sporting event.
In this example we have two boxers in a tournament. Boxer A from the red corner and boxer B from the blue corner.
Boxer B is seen to have a slight advantage due to the weight difference, as such the odds of 1.9 offered by the exchanges suggest a 52.6% of winning, leaving boxer A with a 47.4% chance of winning.
However, through our own analysis we determine that boxer B not only has a weight advantage but is also much more experienced, therefore we suggest a more realistic 55% chance of winning, reflecting odds of 1.8 and leaving boxer A with a 45% chance of winning.
We decide to put money aside for the whole tournament and start with a betting bank of $1000.
With all the metrics available we can now complete the Kelly Criterion calculation and therefore determine the optimum stake.
We have, an expected return offered by the exchanges of 1.9, which equates to a 90 cent profit for every dollar wagered, and our analysed ‘true’ winning probability of 55% and losing probability of 45%.
The equation is therefore; 0.9 multiplied by 0.55 minus 0.45, divided by 0.9, which provides the sum of 0.05 or 5%.
5% multiplied by our betting bank of $1000 is $50, therefore the optimum Kelly Criterion stake is $50.
Try not to be put off by all the numbers, there are calculators and spreadsheets available to calculate the figure automatically, but its important to understand the reasoning behind the number.
Had our probability been equal to the probability offered by the market, the calculation would have provided a negative figure implying there was no edge and therefore no reason to place a wager. Or, if our probability was even higher, perhaps 60%, the calculation would have suggested a higher wager to take advantage of the higher edge.
Next we will use my trading stats as an example to show how we can apply the same Kelly principle to a trading or investing strategy.
For simplicity l