February 6, 2006

Kelly’s betting system and portfolio configuration

Michael J. Mauboussin recently published a paper on the legg mason website called ‘size matters’ on the Kelly criterion and importance of money management.

The paper is slightly technical on probability and an extremely good read. The key point of the paper is that investors should use the kelly criteria of defining the optimum bet size based on the edge or information advantage one has over the market. The formulae is very simple, namely

F = edge/odds

Where F is the percentage of portfolio one should bet. Edge being the expected value of the opportunity and odds being gain expected from the opportunity.

So if one has a meaningful variant perception or edge over the market (translating into a positive expected value) and expects to win big, then the above formulae helps in deciding the size of the bet as a percentage of the portfolio.

In simple terms, if one’s expected value (probability of gain*gain+probability of loss*loss) is high and the gain is also high, then one should bet heavily.

Conceptually I find the above approach very compelling. My own approach has been the similar. For example, if I am confident of a stock (after all the necessary analysis), I tend to allocate a higher amount of money. My definition of low, medium and high is around 2 % , 5% and 10 % of portfolio for a single stock.

Ofcourse the above approach is sub-optimal and would not lead to highest returns over a long period of time. It is not that I have a problem with the formulae. My problem is how do I know that my ‘edge’ is really an edge. Ofcourse whenever I have put money into a stock, the unstated assumption is that I have an edge. but then i invested in tech stocks in 2000 thinking i had an edge. Although I have a quantitative approach of going for a high expected value with a 3:1 odd, I cannot be sure.
So to safeguard myself (against my own ignorance, risk aversion or stupidity or whatever you can call it), I tend to adopt a suboptimal approach which gives me lower returns, but lets me have sound sleep (I have sleep test for risk, if I lose sleep on something, then it is too risky)

But irrespective of how one executes the above concept, it is a very sound one and should be followed to manage risk prudently

1 comment:

abhi said...

Excellent read. I came across this formula somewhere in my reading. Don't you think the forumla is just mathematical way of putting what Buffet has been preaching against over diversification. If you feel you have edge (which is born out of circle of competence) allocate maximum capital towards that edge.
And I agree with you, the botton line is or rather main question is can you find the edge.