Mauboussin on Strategy: Size Matters
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Submitted by Nick on Sat, 2007-04-14 20:32.
(via www.capatcolumbia.com)
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I just finished reading Mohnish Pabria's excellent new book, "The Dhandho Investor." In it Pabrai mentions this paper on the Kelly Formula; it is a must read for value investors interested the optimal sizing of investment decisions. Unfortunately, there are severe limitation to its application. Enjoy.
Applying the Kelly Formula
That was an interesting read. Now how does one actually apply these theories? How can we estimate the odds? I already understand the common sense that you should bet a larger portion of your funds when you think you have an outsized advantage in the odds. The question comes down to measuring the odds advantage.
This is nice theory however
This is nice theory however in my mind sizing portfolio positions is more art than science.
I agree with you that it is
I agree with you that it is more art than science. This is where your gut comes into play.
Figuring the odds with Kelly
Predicting the odds with Kelly is of course just a guess. But what it does is to make one think about the probabilty of a likely outcome. Robert Rubin talks about this in his book "In an uncertain world".
I think Kelly makes one think in a probabilistic context.
Kelly formula
I have done a good deal of research on the Kelly Criterion in the past. Anyone who is interested should read the papers by John Kelly and Ed Thorp (In Thorp's paper he talks about applying the model to Berkshire Hathaway stock), and the books "Fortune's Formula" and "In An Uncertain World". This is the Robert Rubin book mentioned above, which is great for thinking about probabilities.
Using the formula Mauboussin states(Edge/Odds)only works if you are making one investment at a time, and if you lose - it is a total 100% loss. In reality, when you have multiple investment options with multiple different outcomes, you can create a computer model that will give you the various bet sizes for each investment. This is much more complex than it needs to be but it is a good exercise in capital allocation.
Pabrai's method in the book (obtaining the single bet sizes and averaging them out over 8 investments) is not the way it is actually done, but again it can be a useful exercise. I think the best advice Pabrai gives is to always bet below the Kelly percentage, not only because it lowers volatility (like other authors have stated) but because no one knows the what the exact probabilities are and it's better to be conservative.
If you think about it, the probabilities of different outcomes are really the entire basis for making an investment in the first place. "Valuation" is simple and almost anyone can do it. This is why Buffett and Munger are so good - using their mental models, they are extremely good at estimating odds in various scenarios.
Here is a link to Ed Thorp's
Here is a link to Ed Thorp's paper that Max refers to:
THE KELLY CRITERION IN BLACKJACK, SPORTS
BETTING, AND THE STOCK MARKET