Sunday, July 09, 2006

Kelly Criterion Limitations

I've recently written about a way to base asset allocation decisions - the Kelly Criterion. This suggest a way to maximize your returns while still positioning your portfolio for relative safety.

Another link also shows a way to apply the same criterion in more complex situations, that also offers some utility in business situations, or asymmetrical investing situations. However, it can be a time-consuming effort to apply this to every investing situation. Probably a better way to do it is to calculate the Kelly Criterion for your own portfolio and then use that as a baseline guide for your own investing behaviour.

However, using it in this simpler way requires some thinking about it's limitations. For example, calculating my own Kelly, suggests that based on my historical purchases, and assuming equal weightings, I should purchase about 11% of my portfolio into each position. Approximating my actual historical purchase amounts, suggests my Kelly in that instance is about 14.5%, indicating I was successful in properly overweighting more promising positions.

However, these Kelly calculations presume - to some extent - that our investment opportunities are symmetrical (as shown in the Mauboussin example), whereas most investors begin to recognize that investment opportunities are asymmetrical. In other words, sometimes you'll spot opportunities that you clearly feel are much better than some others.

For instance, in analyzing most of the trades I made to calculate my own Kelly, I had bit of a mixed bag in terms of wins and loses. Excluding my five largest purchases (of an initial 37 or so), I had 18 wins out of 32 purchases (37-5), which is a 56% win/loss ratio.

However, adding those five large purchases I made into the mix significantly changed both the absolute and relative results on the entire portfolio, and so are worth considering on their own.

On four of the five, I made significantly outsized gains, something I believed was possible ex ante. This expectation was clearly achieved. I also believed, ex ante, that my inherent risk in those five investments was much lower than my portfolio average. Even the one investment that wasn't quite as good as I thought, still turned out to be a break-even proposition.

So, while the Kelly Criterion would have maximized my gains if all the opportunities were highly similar, it couldn't quite close the gap here. Using your common sense in this instance would have helped you take advantage of this situation, just as I did, and just as I intend to do so in the future.

A couple of quick other limitations I can think of with the Kelly, when you analyze your portfolio trades the way I did:
  1. A rising tide lifts all boats; it's only when the tide goes out that you get to see who has been swimming naked - in other words - be careful to think about whether your Kelly covers a bear portion of the market as well as a bull portion - otherwise it may cause you to under or over state your Kelly.
  2. Analyzing the Kelly considers your history over the time considered - if you are getting to be a better investor (as shown by your more recent investments), then you might want consider upping your Kelly to properly reflect that. Of course, the opposite applies too ...
  3. Finally, you could consider segregating your portfolio analysis, so that - for instance - if you allow yourself 1/3 of your portfolio to be invested in small caps, 1/3 in mega caps, and 1/3 in ETFs, you could consider your Kelly on each of those segments. This might help you with portfolio risk and returns into the future.
The Kelly Criterion - not the be all and end all - but a useful tool ...


The Confused Capitalist

No comments: