KELLY CRITERION | Ed Thorp | Optimal Position Sizing For Stock Trading

in this review we look at the kelly criterion strategy and how we can apply the principles to our trading or investing activities to maximize growth created by computer scientist john kelly

in a paper from 1956 often referred to as the fortunes formula and later popularized by edward thorpe when he applied the theory to beat the game of blackjack

another noteworthy investor to apply the theory is jim simons founder of the renaissance medallion hedge fund i also use a variation of the strategy and this 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 boxes 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 and as such the odds of 1.9 offered by the exchanges suggest a 52.6 chance of winning leaving boxer a with a 47.4 percent

chance of winning however through our own analysis we determined that boxer b not only has a weight advantage but is also much more experienced and therefore we suggest a more

realistic 55 chance of winning reflecting odds of 1.8 and leaving boxer a with a 45 percent chance of winning we decide to put money aside for the

whole tournament and start with a betting bank of one thousand dollars 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 analyzed true winning

probability of 55 percent and losing probability of 45 percent the equation is therefore as follows 0.9

multiplied by 0.55 minus 0.45 divided by naught point nine which finally provides the sum of naught point not five or five percent five percent multiplied

by our betting bank of one thousand dollars is fifty dollars 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 it is 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 percent 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 let's use a 20 000 equity balance

my long-term win rate or win probability of 59 percent leaving my losing probability of 41 my expected profit on risk for a winning trade is 4.04

therefore for every dollar i risked i get just over four dollars in profit using the same kelly calculation as before we can now determine the optimum position size for a trade

we have 4.04 multiplied by 0.59 minus 0.41 divided by 4.04 which provides the sum of 0.488

or rounded up 49 therefore the optimum position size recommended by the kelly formula would be the twenty thousand dollar equity multiplied by forty nine percent which equals nine thousand eight hundred

dollars i'm sure many of you are quite rightly thinking that this is a large amount of capital to have allocated to a position in comparison to the equity balance that's why many including myself use

what is called fractional kelly in essence this simply means a certain fraction of the recommended position size i personally use 33 percent of the recommended position

and therefore in this example my position size would be 3266.

remember this is position size not expected risk my risk based on a typical stop loss would be near 10 of this position size equating to 326

this 326 dollar positional risk equates to a risk on equity of 1.63 percent the difficulty however in applying the kelly criterion formula to the stock market

is the randomness of price movement and therefore the variability of these inputs the game of blackjack on the other hand has factors that are fixed for example the number of cards in a

deck is fixed at 52.

with this in mind it's important to keep track of your performance and adjust the inputs accordingly let's assume our strike rate reduces to 50 percent and we only profit two dollars for every

one dollar risked by applying the same formula kelly calculates a new position size of 25 percent of equity or 5 000 but again i prefer fractional

kelly equal to 33 of the suggested position size based on an average 10 stop loss position the expected risk on

equity would now be 165 or 0.83 per trade the theory is that the kelly score changes with the fluctuating performance

of the trading strategy if enough people show interest below i'll add the staking spreadsheet i use into the description for ease of use

to conclude we present the theory of kelly criterion in this diagram to better understand its concept this centre green line represents full kelly

as opposed to fractional kelly which could be at 33 percent here the blue line represents portfolio return the left side of the kelly line is

considered more conservative and the right side more aggressive the concept suggests that the higher the kelly or equity used the less return and more volatility is

experienced whereas a smaller position provides less return and less volatility the optimum position size is considered to be here

but remember this theory is ultimately based on events with fixed variables and true probabilities like a game of blackjack the stock market however has numerous variables

and as such fractional kelly would be the advised approach should you decide on using the concept it is my preferred position management tool due to its ability to reflect on my trading performance

and adjust the risk accordingly more often than not a trending market will improve my edge and the position size will increase as a result the opposite is also true for a ranging

market my edge will decrease as will my position size to compensate i hope you found this relatively short review of the kelly criterion formula useful

and as always please hit the like button and i look forward to seeing you in the next book review

thanks for listening you