### Adequate Diversification

A few words on “adequate diversification” from a legendary hedge fund manager. Emphasis is our own . . .

**Last year in commenting on the inability of the overwhelming majority of investment managers to achieve performance superior to that of pure chance, I ascribed it primarily to the product of: “(1)** group decisions – my perhaps jaundiced view is that it is close to impossible for outstanding investment management to come from a group of any size with all parties really participating in decisions; **(2)** a desire to conform to the policies and (to an extent) the portfolios of other large well-regarded organizations; **(3)** an institutional framework whereby average is “safe” and the personal rewards for independent action are in no way commensurate with the general risk attached to such action; **(4) **an adherence to certain diversification practices which are irrational; and finally and importantly, **(5) **inertia.”

*This year in the material which went out in November, I specifically called your attention to a new Ground Rule reading, “We diversify substantially less than most investment operations. 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 the underlying value of the investment.”*

*We are obviously following a policy regarding diversification which differs markedly from that of practically all public investment operations. 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 intercorelated (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.**

**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.** 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?” **This depends to a great degree on the wideness of the spread between the mathematical expectation of number one versus number eight.” 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.**

**The above may make the whole operation sound very precise. It isn’t. Nevertheless, our business is that of ascertaining facts and then applying experience and reason to such facts to reach expectations. Imprecise and emotionally influenced as our attempts may be, that is what the business is all about. The results of many years of decision-making in securities will demonstrate how well you are doing on making such calculations – whether you consciously realize you are making the calculations or not. I believe the investor operates at a distinct advantage when he is aware of what path his thought process is following.**

**There is one thing of which I can assure you. If good performance of the fund is even a minor objective, any portfolio encompassing one hundred stocks (whether the manager is handling one thousand dollars or one billion dollars) is not being operated logically. The addition of the one hundredth stock simply can’t reduce the potential variance in portfolio performance sufficiently to compensate for the negative effect its inclusion has on the overall portfolio expectation.**

*Anyone owning such numbers of securities after presumably studying their investment merit (and I don’t care how prestigious their labels) is following what I call the Noah School of Investing – two of everything. Such investors should be piloting arks. While Noah may have been acting in accord with certain time-tested biological principles, the investors have left the track regarding mathematical principles. (I only made it through plane geometry, but with one exception, I have carefully screened out the mathematicians from our Partnership.) Of course, the fact that someone else is behaving illogically in owning one hundred securities doesn’t prove our case. While they may be wrong in overdiversifying, we have to affirmatively reason through a proper diversification policy in terms of our objectives.*

**The optimum portfolio depends on the various expectations of choices available and the degree of variance in performance which is tolerable. The greater the number of selections, the less will be the average year-to-year variation in actual versus expected results. Also, the lower will be the expected results, assuming different choices have different expectations of performance.**

**I am willing to give up quite a bit in terms of leveling of year-to-year results** (remember when I talk of “results,” I am talking of performance relative to the Dow)** in order to achieve better overall long-term performance. Simply stated, this means I am willing to concentrate quite heavily in what I believe to be the best investment opportunities recognizing very well that this may cause an occasional very sour year – one somewhat more sour, probably, than if I had diversified more. While this means our results will bounce around more, I think it also means that our long-term margin of superiority should be greater.**

*You have already seen some examples of this. Our margin versus the Dow has ranged from 2.4 percentage points in 1958 to 33.0 points in 1965. If you check this against the deviations of the funds listed on page three, you will find our variations have a much wider amplitude. I could have operated in such a manner as to reduce our amplitude, but I would also have reduced our overall performance somewhat although it still would have substantially exceeded that of the investment companies. Looking back, and continuing to think this problem through, I feel that if anything, I should have concentrated slightly more than I have in the past. Hence, the new Ground Rule and this long-winded explanation.*

*Again let me state that this is somewhat unconventional reasoning (this doesn’t make it right or wrong – it does mean you have to do your own thinking on it), and you may well have a different opinion – if you do, the Partnership is not the place for you. 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. 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 which partially explains the greater risk of widened year-to-year variation in results). In selecting the limit to which I will go in anyone 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.*

*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. The 1965 gains (in some cases there were also gains applicable to the same holding in prior years) from these situations ranged from about $800,000 to about $3 1/2 million. If you should take the overall performance of our five smallest general investments in 1965, the results are lackluster (I chose a very charitable adjective).*

**Interestingly enough, the literature of investment management is virtually devoid of material relative to deductive calculation of optimal diversification. All texts counsel “adequate” diversification, but the ones who quantify “adequate” virtually never explain how they arrive at their conclusion. Hence, for our summation on overdiversification, we turn to that eminent academician Billy Rose, who says, “You’ve got a harem of seventy girls; you don’t get to know any of them very well.”**

*Warren E. Buffett, 1966 Annual Letter to Limited Partners*