The Kelly Criterion

While reading an article over the internet, a certain line caught my attention - "while most of the investment world talks about what stock to buy, no one tells us how much of it should be bought."

I investigated further to find a paper written way back in 1956 by J. L. Kelly Jr. which evaluates "how much" a gambler needs to bet on a table such that he can maximize the growth of capital at a rate which is equal to his information rate over the channel. In other words, how can one achieve the maximum growth in capital for the amount of risk one is taking.

There has been a lot of work around this and is today called the Kelly Criterion. The question that the criterion seeks to answer is : how much of my capital should I allocate towards a trade?

Assume your research has indicated that there is 70% chance that the price of Ranbaxy is going to drop in the next 2 days. Further, you feel that the drop will be a good 12% from it's current price. Just to be on the safer side, you assume that even if the price of Ranbaxy rises, it wont go over 8%.

In other words, your probability of winning is 70%; your probability of losing is 30% and the win/loss ratio is 1.5 (12% divided by 8%).

Kelly % = Prob (winning) - [Prob (losing) / win-loss ratio]

In this case, Kelly % comes to 50% ... i.e. 70% - [30%/1.5]. Thus Kelly's % says that you must not invest more than 50% of your capital towards this trade i.e. shorting Ranbaxy.

Over time, the Kelly % has come under criticism for being too heavy (as in this case, 50%) to allow for easy diversification of portfolio. Most people who use Kellys' have settled for a half-Kelly i.e. 25% as in this case. However, I found the Kelly % quite simple and useful in ensuring that an investor is not putting too much capital into a single trade. So, the next time you run a buy or sell decision, try to measure it's effects using the Kelly criterion.