Warren Buffet on position sizing and probability/ expectation

Warren Buffett (Quotes from Buffett Partnership Letter, January 20,1966)

1. We might invest up to 40% of our net worth in a single security under conditions coupling an extremely high probability that our facts and reasoning are correct with a very low probability that anything could drastically change underlying value of the investment. We are obviously only going to go to 40% in very rare situations – this rarity, of course, is what makes it necessary that we concentrate so heavily when we see such an opportunity.
2. Frankly there is nothing I would like better than to have 50 different investment opportunities, all of which have a mathematical expectation (this term reflects the range of all possible relative performances, including negative ones, adjusted for the probability of each – no yawning, please) of achieving performance surpassing the Dow by, say, fifteen percentage points per annum. If the fifty individual expectations were not intercorrelated (what happens to one is associated with what happens to the other) I could put 2% of our capital into each one and sit back with a very high degree of certainty that our overall results would be very close to such a fifteen percentage point advantage. It doesn’t work that way.
3. We have to work extremely hard to find just a very few attractive investment situations. Such a situation by definition is one where my expectation (defined as above) of performance is at least ten percentage points per annum superior to the Dow. Among the few we do find, the expectations vary substantially.
4. The question always is, ‘How much do I put in number one (ranked by expectation of relative performance) and how much do I put in number eight?’
   1. This depends to a great degree on the wideness of the spread between the mathematical expectation of number one versus number eight.
   2. It also depends upon the probability that number one could turn in a really poor relative performance. Two securities could have equal mathematical expectations, but one might have .05 chance of performing fifteen percentage points or more worse than the Dow, and the second might have only .01 chance of such performance. The wider range of expectation in the first case reduces the desirability of heavy concentration in it.
5. The optimum portfolio depends on the various expectations of choices available and the degree of variance in performance which is tolerable.
6. We probably have had only five or six situations in the nine-year history of the Partnership where we have exceeded 25%. Any such situations are going to have to promise very significantly superior performance relative to the Dow compared to other opportunities available at the time. They are also going to have to possess such superior qualitative and/ or quantitative factors that the chance of serious permanent loss is minimal (anything can happen on a short-term quotational basis …).
7. In selecting the limit to which I will go in any one investment, I attempt to reduce to a tiny figure the probability that the single investment (or group, if there is intercorrelation) can produce a result for our total portfolio that would be more than ten percentage points poorer than the Dow.
8. We presently have two situations in the over 25% category – one a controlled company, and the other a large company where we will never take an active part. It is worth pointing out that our performance in 1965 was overwhelmingly the product of five investment situations.
9. A quote not in the 1966 letter: “With each investment you make, you should have the courage and the conviction to place at least 10 per cent of your net worth in that stock”

Note that those are Buffett’s thoughts in 1966. We know from the more recent comments by Buffett/Munger that the variance of the portfolio is no longer a concern once they have moved to the Berkshire Hathaway holding company structure as opposed to a hedge fund / partnership structure. Hence adding in a large number of stocks to lower the variance, and incurring a performance hit in the returns, does not make sense any more.

Another thing to note is the explicit use of calculating mathematical expectations for the potential returns of each investment, and also looking that the probability of a really poor performance despite having a high expectation.

One thing that I thought should not be done is to try to calculate the outperformance relative to the Dow. To do that will require you to project how the Dow will do, and that is difficult. It also does not serve the point as it is the absolute return that matters. There might be some debate here as many value mangers (including Buffett in his letter) that if the index went down 30% but your portfolio went down 15%, then it is a good year. I would say that what needs to be evaluated is the execution, whether or not you monitored closely and moved swiftly to protect capital, as opposed to saying that the timing is too hard so ignore it. Firstly you need to determine whether the event would lead to a market-wide downturn (e.g. the credit crisis yes, but not the dot-com boom-bust where staple stocks like JNJ maintained their value) If there is an event that will lead to a market-wide downturn, I would say that a good manager would have known of that possibility early on, just that the timing of which is hard to predict. The manager should be watching the appropriate indicators and to get the hell out when the crumbling starts (e.g. for the housing crisis, when the delinquencies hits, margin calls start, etc., and for trading exuberance like the dot-com boom, and you are in tech stocks, could be if a stock dropped under its 20-day MA for 4 days, etc.)