## Monday, February 16, 2009

### Is Warren Buffett’s Record a Fluke?

Warren Buffett’s investment record has been very impressive for decades. It seems a virtual certainty that his success is due to skill. However, there are some who say that it may be just luck. They argue that out of billions of people, you’d expect at least one investor to perform as well as Buffett. Let’s take a stab at figuring out which side is right.

From the first table in Buffett’s 2007 letter to shareholders we see that over the 43 years from 1965 to the end of 2007, the S&P 500 (including dividends) returned 6840% and Buffett’s Berkshire Hathaway returned 400,863%. An investment in Berkshire over this period would have made you 57.8 times richer.

This is an impressive record, but we want to know if it could have happened by chance. This depends greatly on how Buffett approached investing. To see this, consider the following scenario.

Suppose that in January of 1965, a few hundred people took \$1000 each to gamble on blackjack. They all used the same strategy. They bet everything on 6 consecutive hands hoping to double their money 6 times. Odds are that at least one of these people would succeed. Let’s call him lucky Eddy.

Eddy was lucky enough to turn his \$1000 into \$64,000 at the blackjack table. Suppose that Eddy then invested all this money in the S&P 500 and left it there until the end of 2007. With his factor of 64 head start, Eddy would have more money than someone who invested \$1000 in Berkshire starting in 1965. We see from this little thought experiment that it’s possible for an investor who takes wild chances to beat Buffett’s record.

But Buffett didn’t amass his wealth by taking wild chances. The question is whether a random stock picker who takes an approach superficially similar to Buffett’s could reasonably perform as well or better. To answer this question we’ll have to make several assumptions, any of which could be challenged.

For those not interested in the math, here is the spoiler on the math section below. I worked out that the odds of a random investor matching Buffett’s record by chance are about 0.00000000000000000000007. Even if every person alive right now were to choose stocks randomly in an effort to match Buffett, the odds of at least one of them succeeding are less than one in two trillion. However, let me stress that this is based on several assumptions (see below). Changing these assumptions would give a very different answer.

Based on this analysis, I conclude that it is very likely that Buffett has skill and isn’t just lucky. However, skill at picking stocks seems to be quite rare. Most investors would be better off to just own low-cost index funds rather than try to beat the index by picking individual stocks.

If any readers have others ideas about how to assess Buffett’s record, I’m interested in hearing them.

The Math

The variance of US stocks over the last century has been about 0.04 per year, which corresponds to a standard deviation of 20% per year. Roughly speaking, this means that about 70% of the time, the yearly return from the stock market is within plus or minus 20% of the average return.

Suppose that Buffett was choosing among stocks and whole businesses whose individual variance is about 0.12 (3 times that of the stock market as a whole). This means that each stock or whole business has a non-market specific variance of 0.08. This is consistent with some of the data shown in Table 6.2 of the book The Intelligent Portfolio by Christopher L. Jones.

Suppose further that, on average, Berkshire owned 20 businesses at a time. This cuts the non-market specific variance by a factor of 20 to 0.004 per year. Over 43 years, the total non-stock market specific variance is then 0.172, which corresponds to a standard deviation of 41.5% (square root of the variance).

To take us from the lognormal distribution of investment returns to the normal distribution we take the natural logarithm of Buffett’s outperformance factor of 57.8 to get 406%. Dividing the 41.5% standard deviation into Buffett’s 406% outperformance gives 9.8 standard deviations. This corresponds to an event probability of 0.00000000000000000000007.

If we multiply this probability by the number of people alive, we find that the odds of even one person matching Buffett’s performance by chance are less than one in two trillion. Although I find these assumptions reasonable, others may not, and changing them would give a very different answer.

1. What's your outlook for Buffett going forward, now that Berkshire is much more an operating company than an investment vehicle? With recent Berkshire prices, I've been a disappointed owner since I accumulated stock between 1998 and 2000.

Seems the best times to invest in Berkshire are well past. I'll continue to hold though, since Berkshire is likely to surprise on the upside.

2. Gene: According to Buffett and Munger, the years of significant outperformance are over because they are so big now. But that doesn't mean that Berkshire will be below average. Beyond this, I have little further insight into Berkshire's future.

3. I'm quite convinced that Mr. Buffett showed skill as a stock picker. However, there is no way for me to profit from this information. I'm not an above average stock picker and I have no reliable method of selecting above average stock pickers to pick stocks for me. By the time an above average stock picker is identified (e.g. Mr. Buffett), the opportunity has largely come and gone.

Oh well, at least there are some good low-cost stock indexes these days.

4. blitzer68,

Apparently someone did a study where a portfolio added Buffett's picks after they were publicly announced. That portfolio still outperformed the market.

I can't really advocate this strategy, since we can't be sure what Buffett was thinking when he bought something, nor that it was truly his decision. Also, we won't know exactly when he decides to sell it.

I still think such a strategy would likely outperform the major indexes, though.

5. I agree with Blizter. For the vast majority of investors, advice such as "be Warren Buffet" is useless.

They're much better off in index funds/ETFs. Of course, I'm not the only person who thinks that... :)

6. Maybe he was lucky in that his style of investments was in fashion for the earlier part of his investment cycle. From 1956-69 - the period of his partnership - the US stock market had a secular bull run. So with some leverage he could have gotten to the 64,000\$ you mentioned. And from there just ride the S&P!

7. @nobody: It certainly makes sense to examine Buffett's record in different ways, but I don't think what you described is what happened. If anything his investing approach was fairly conservative. He never seemed to take big chances. He definitely took chances, but they were always with an amount of money that, if lost, he could recover from.