# How to Size Individual Positions Using Kellyesk Formula

It’s over a year since I read any of the articles I linked in yesterday piece on the Kelly formula and portfolio management. After reading the brilliant article by Michael Mauboussin Size Matters – The Kelly Criterion and the Importance of Money Management I realised that both he and I did not explain how to actually use the Kelly formula in sizing individual positions. So let’s try to fix that glearing omission.

I’ve now copied a few more columns from my portfolio spreadsheet to yesterday’s Kelly Spreadsheet. As I stupidly never documented my reasons for using these formulas, the following is my best guess and why I choose them.

**Geometric Mean**: As I am in the market for the long term, have no intention of withdrawing funds and will compound my investment I choose geometric mean instead of the average (also known as mean or arithmetic mean). For a discussion on this read the Mauboussin article.

Percent of Portfolio: This calculates what percent of my portfolio I should invest in one position. Based on dividing the geometric mean by the sum of the geomeans.

**Actual Percent of Portfolio**: Let me stress again all the figures in my example are made up. However, I do hold positions in all of the stocks except Microsoft. This column is exactly what it says on the can. The actual percent of my portfolio that I have invested in that stock.

**Adjust Actual**: This is the amount I need to change my investment to align my actual with my calculated amount.

Hopefully that makes it clearer how I use a Kellyesk Formula to determine my individual position sizing in my portfolio. If not please feel free to ask questions. Also, please note that I do not solely rely on the expected return, reward/risk, geomean or percent of portfolio to determine my actual investment. I consider them all and then use my gut for a final decision. Perhaps as time goes on I’ll get more comfortable relying solely on one or a combination of those calculations, but I’m not there yet. However, I have found these calcuations incredibly helpful for both my buying and selling of indivudal stocks. I hope you also do.

I started playing with the spreadsheet and noticed something – when I changed my probabilities, the outcome didn’t change at all!

Started digging in and saw that you are using GEOMEAN, which assumes all outcomes are equally probable. What needs to be used is weighted geometric mean, which respects the weights given by the probabilities. (Mauboussin uses the word “geometric mean”, but it’s not clear from the article whether he means a regular or weighted one – the only numeric example in the article with non-equal weights has one zero outcome, so weighted or not, in this case the geometric mean comes as 0).

To adjust the spreadsheet, I changed the formula from GEOMEAN function to multiply the low-med-high returns taken to the power of their respective probabilities (this is a bit simpler than the regular weighted geometric mean formula — it works as long as your probabilities always add up to 1). Since you seem to always use the 0.3,0.4,0.3 your results wouldn’t materially change from just using GEOMEAN, but if you start inputting probabilities like 0.1, 0.5, 0.4 you will see the difference.

Sergey

Thanks Sergey