On Wisdom, Wealth and…Berkshire Hathaway

Berkshire Hathaway is known today as one of the most successful and consistently performing companies in the world. From 1965–2016, a single dollar invested in BH would have yielded a gain of more than 884,000 percent compared with just under 13,000 percent for the S&P 500. BH is also synonymous with its CEO, Warren Buffett, and perhaps more so with its annual meetings where Buffett, along with Charlie Munger, would dispel wisdom and answer questions on all kinds of issues. Early meetings in the mid-1980s were cozy affairs with only about 300 attendees. Almost 30 years later, more than 44,000 people were in attendance. Omaha itself completely transforms leading up to, and during, this event.

Recently, I read a book called the ‘University of Berkshire Hathaway’ written by two Buffett ‘fans’ (and investors) that summarized key elements of those annual meetings, while providing (approximate) data on how attendance at these meetings has changed (and dramatically increased) over the years, along with other publicly available information such as BH’s stock price and its Fortune 500 rank. As a data geek, I found myself asking a question as I read the book: did the attendance numbers (as approximate as they may have been reported in the book) follow BH’s meteoric stock price rise over the years or vice versa? Or did they grow together without noticeable lag? Or is the data just all over the place, and we can’t conclude anything?

The interesting thing is that, depending on who you ask, several causal stories can be framed around a lag in either direction. I had a bias toward wisdom i.e., my view was that the growth in the attendance numbers would outstrip growth in the stock price, not least because of Buffett’s cultural significance and respect in the business community (everyone wants to hear what he has to say on any number of economic and extra-economic issues), but also because of the volatility and cyclical movements of stocks. In fact, if this was any other company that had existed for 30 years or more, I would have surmised the opposite, namely that ‘wealth follows wisdom, if at all’. The story in that case would be simple. If a company’s stock price (‘wealth’) went up, people may be more interested subsequently to hear what its leaders have to say, but in the other direction, it would probably just be interpreted cynically as the usual show of CEO confidence. With BH, however, the situation is exceptional both because of Buffett and (related to it) BH’s consistent success over the decades.

Nevertheless, it’s just a hypothesis. There’s no iron-clad reason why attendance at the annual meetings would have a close relationship with, or track, the stock price. I was curious to crunch some numbers (or perhaps I just needed an excuse) to find out. So I went through the book, and created three annual series over the period 1986–2017:

1. The approximate known attendance at BH’s annual Omaha meeting: Astoundingly, it grew from less than 20 in the late 1970s, to hundreds in the mid 1980s, to tens of thousands leading up to 2017. Live-streaming of the event started in 2017, and I don’t have numbers after that, so I stop the series at 2017. It’s just as well, since with live-streaming, the notion of attendance numbers (do we only count physical attendees? Physical attendees + live-streaming attendees? Views on YouTube?) becomes ill-defined.
2. BH’s stock price, as reported by Daniel Pecaut and Corey Wrenn (the authors of ‘University of Berkshire Hathaway’) in their book: A single number per year is reported, so some kind of aggregation must be happening. The most important thing to keep in mind is that we used a single consistent source, so however it was calculated (and it could always be replicated by consulting historical stock data on the Web), it is certainly systematic.
3. BH’s Fortune 500 rank over the years: This is fairly self-explanatory. I could have used the S&P 500 as a proxy (for evaluating BH against the market) but I thought that it would be interesting to use the F500 rank. Note that companies are ranked by total revenue, so it offers a different twist than the S&P 500. Furthermore, using the rank directly allows me the chance to flex my data crunching skills slightly, which is (sort of) the real reason I engaged in this evening exercise.

BH has done (extremely) well on all three metrics over the years. I could add a fourth series (the S&P 500) but my view is that the Fortune 500 rank adequately captures how the company is doing relative to other companies for our purposes. As I also noted at the opening of this article, BH has consistently and significantly outperformed index funds like the S&P 500 over three decades.

What can we do with the data? First, I want to see how the three series compare to one another. Specifically, do they grow together, or do peaks in one distribution lag peaks in the other, as I originally hypothesized they would? However, comparing these distributions is non-trivial from a data standpoint because of the different scales of (1) and (2), which are both numerical variables measuring completely different things (people and money), and also the fact that (3) is a ranking. Even if we could just plot all of them together, (3) moves in the opposite direction as (1) and (2): a numerically smaller ranking (such as 2 or 3) is better than a numerically greater ranking (such as 400), whereas the opposite is true for (1) and (2), since higher numerical values are better.

While there are a number of ways one could try to make these series more comparable, I took a simple, established route (those interested in my conclusions rather than my methodology should skip to the next section). For (1) and (2), the most obvious way to compress the scale (without losing the qualitative gaps between years) is to transform the series using the natural logarithm. For (3) a slightly more sophisticated approach is required because of the ‘inversion’ property, as well as the difference in scaling, since (3) is already compressed between 1–500 (not including the problem that BH is not in the Fortune 500 for some of the years in our study). Therefore, after taking the natural log, I reciprocated it (to account for inversion), and then multiplied by 10, to bring it into line with the logarithms of (1) and (2), which are 1–2 orders of magnitude higher at the upper end.

As a scientist, I would be amiss if I didn’t state the usual methodological caveats. This is a purely observational data, and has approximations in it. So take everything with a grain of salt. As I hope my description above has already made clear, I am relying on secondary data, not primary. However, I do not see any reason to doubt the numbers reported in the book. Still, one can never completely discount the possibility of an inaccuracy or typo somewhere. I believe this is unlikely. I should also note that, at the end of the day, we are still only dealing with 30 data points. In all likelihood (although I have not verified this explicitly), strong statistical significance is out of the question, but anyone who is that nit-picky has probably given up on this article already.

Now we’re ready to show what we find in the data. Here is where the advantage of putting in effort into understanding and appropriately transforming the data comes in, since I’m able to show what I want to show in just one plot.

Note that the y-axis is the transformed version of the variables that I described earlier. Now, higher is better for all curves, although the large differences that would be observed in the raw numbers across the years have been compressed by the logarithm. We see very close uniformity of movement between the stock price and attendance at the annual meetings. The F500 is a more interesting case, one that I will get into shortly. For now, all that we can say is that there is a relationship, but most likely not a causal relationship, between any of these variables. Probably, the single (difficult to quantify) variable that resulted in such a rise on all three fronts is the wisdom and strategic consistency with which Buffett and Munger ran the company.

What I found was that the correlation between the (logs of the) stock price and the attendance is 98.63%. That’s astounding, but it shows that wisdom is not completely divorced from wealth. Although we will not know the answer to this, it is worth wondering whether, if the stock price had not gone up or had had a long period of decline, the annual meetings would have grown as much as they did. It is also important to remember that the logarithm leads to a compression of large gaps, so the magnitude of the correlation can be amplified.

One of the other ways that we can test if one series lags the other is to compute a lagged correlation. I did this in two different ways. First, I computed the correlation of the attendance from 1986–2016 and the stock price from 1987–2017. No, that’s not a typo. Basically, we correlate the series that are out of sync by one year. If the correlation is found to increase, then it shows that the attendance in a given year was more correlated with the next year’s stock price. In fact, we find that the correlation decreases when we do this (to 98.2%). That’s not a huge drop, and it’s still high. Rather than lag by one time step, I can also lag by 2, 3 and 4 time-steps. I found that the correlations decline further (to 97.53%, 97.19% and 97.39%).

What happens when we do the same exercise but in reverse i.e., compute the correlation of the stock price from 1986–2016 and the attendance from 1987–2017? This time, the correlations for time lags of 1, 2, 3 and 4 are 98.42%, 98.18%, 98.11% and 97.84%. These look higher than the ones we found earlier. While preliminary, might these results be suggesting that higher stock prices in a given year begat greater attendance in the next year, rather than the other way around? If yes, a cynic could point to this to suggest that wealth takes precedence over wisdom. People may not show up to listen to you if they lost money on your stock, and vice versa. The differences are very small however.

The Fortune 500 rank is actually more unstable, and has interesting stories behind it, if we look carefully. BH seems to have entered the F500 in 1989 (since we set the value to 0 if it was not ranked) and over time, has climbed up. It has not been a completely smooth ride, and like all good things, took time to achieve. During much of the 1990s, BH stayed in the 100–300 range (the range is extremely compressed in the figure due to our transformation, which penalizes numerically higher rankings very significantly) and there were some wild ups and downs. For example, in 1995–1996, it was almost out of the top 300, but by 1997, it had become a fixture in the top 150. Recall that these were the wild years of Internet stocks, in which BH did not (wisely, as it turns out) get involved. In the early 2000s, BH was able to climb even quicker up the rankings. By 2005, it was no. 12 on the F500 list.

It may have taken a decade for BH to go from no. 170 (in 1991) to cracking the top 50 (no. 40 in 2001), but it would take roughly another decade before BH would crack the top 5. This shows just how hard it can be to not only stay in the tippy-tops of the big leagues but to keep climbing. BH was no. 12 in 2005, but it would take another 8 years before it cracked the top 5 in 2013. Buffett and Munger clearly put their money where their mouth is, and as disciples of the value-investor Benjamin Graham, bought/invested when ‘there was blood on the streets’. BH famously did well in the aftermath of the Great Recession. By 2017, BH was no. 2. It has managed to stay in the top 10 (no. 6 in 2020), despite the continued and phenomenal rise of companies like Apple and Amazon.

So what does it all really mean? Simply put, the evidence shows that, far from attendance numbers at Berkshire’s annual meetings predicting future stock prices, both variables either (i) move together, or (ii) rising stock prices may be (very weakly) associated with increased attendance at future annual meetings. However, the difference in lagged correlations is so small (and all correlations are very high) that (i) is most likely the case, statistically speaking.

To me, personally, it is amazing when I see two series move in sync in the way that the attendance and stock price did in the plot above. The logarithmic transformation compresses differences, for sure, but it can’t create a trend of its own where none exists (to begin with). BH’s stock price and attendance numbers have both also stood the test of time, and survived multiple booms and busts.

So it seems like going to those annual meetings was completely worth it, although if all you wanted was wealth, you could/should have just invested some stock in BH as early as possible. On a less elevated note, I hope that this article demonstrated that it can be fun and instructive to sometimes work with ‘small data’ (that you transcribe yourself from a book) and simple programs like spreadsheets to learn something about a complex entity such as Berkshire Hathaway. You don’t need a large computer or big datasets to do data science!