Monte Carlo Analysis of Major Berkshire Hathaway Holdings

Sep. 20, 2006 1:44 AM ETBRK.A, BRK.B10 Comments
Geoff Considine profile picture
Geoff Considine

In the process of analyzing a range of portfolios with Monte Carlo analysis using the Quantext Portfolio Planner [QPP], I decided to see how Berkshire Hathaway’s (BRKA) (BRKB) equity holdings would look. Quantext Portfolio Planner uses historical market data on a portfolio to generate forward-looking simulations of probable future risk and return on a portfolio. What I wanted to determine was whether a portfolio made up of the top 20 largest Berkshire Hathaway equity holdings would have any notable statistical properties in history and on a forward looking basis?

Having obtained the equity holdings of Berkshire Hathaway, I constructed a portfolio that used the relative size of each of the top twenty holdings to build a 20-component portfolio. Top holdings include Coke (KO), American Express (AXP), Wells Fargo (WFC), and Procter and Gamble (PG):


Rather than analyzing this portfolio in terms of its individual holdings, I am looking for distinguishing features that can be seen for the portfolio as a whole. To begin, let’s look at trailing performance of this portfolio over the past five years and the past three years:


Remember that these results are what the current allocation would have done if it were held over past years. There are several notable historical features of the current allocation. First, the Beta of this allocation is increasing—and quite a bit. Over the past three years, the Beta for this portfolio is 78% (above), whereas if we use five trailing years of data it is 55%. An increasing Beta means that this group of companies is increasingly tracking with the market as a whole.

Second, we notice that this portfolio has generated quite stable total returns over the period. The three-year average annual return is only different from the five year average annual return by about 0.6% per year (11.84% vs. 12.43%, shown above). This is in contrast to the S&P500, which has a trailing three-year average annual return of 9.6% but a trailing five-year average annual return of 5.4%. The Berkshire Top 20 portfolio has generated a stable average annual return over a period when the S&P500 has been far from stable.

The standard deviation in annual return [SD] for this portfolio has also been far more stable than the market as a whole (as shown in the chart above). The SD for the Top 20 portfolio drops by 2.1% when we go from the five year to the three year period, in contrast to a drop of 5.05% for the S&P500. What this suggests is that not only is the inherent volatility in this portfolio lower than the broader market, but the volatility is also more stable.

When we examine the projected future performance of this portfolio using Quantext Portfolio Planner, we obtain the following:


The projected future performance of this portfolio from the Monte Carlo simulation is greater when we select the trailing three years of data rather than the trailing five years of data. This suggests that more recent conditions favor higher future returns. Further, the projected returns using the trailing three years of history as input are greater than the average return over the trailing three years. This is not the case when we use the trailing five year data as input. QPP is forecasting increased potential for higher returns from this portfolio in time. This result is in contrast to the fact that the average return over the trailing three years is actually less than the average return over the trailing five years. In short, QPP suggests that this portfolio has under-performed over the past several years and has a good potential to generate higher returns in the future. It is notable that this portfolio has far out-performed on a risk adjusted basis over the past three- and five-year period. The ratio of average annual return to standard deviation in annual return realized over this period is very high by historical standards for an equity portfolio. These results stand in marked contrast to those when we analyze the recently out-performing sectors. QPP invariably will predict future average returns that are lower than recent years for the hot asset classes, whereas QPP is predicting future average returns higher than recent years for the Berkshire Hathaway Top 20 portfolio.

Another interesting feature of this portfolio is that it shows a very high level of diversification. Beta measure the degree to which the portfolio tends to respond to the broader market. If you mix high and low Beta stocks, you will get a higher level of return relative to total portfolio risk (as with mixing stock and bond funds). There is another component of diversification that is very important however and this is non-market diversification. QPP accounts for both market-driven and non-market diversification effects. QPP also produces an indicative measure of how well a portfolio exploits non-market diversification effects that is called the Diversification Metric [DM]. A portfolio with a high value of DM is doing a better job of strategic asset allocation to exploit offsetting risks between investments. The Berkshire Hathaway Top 20 portfolio yields DM=67% when we use the trailing five years to initialize the model and DM=66% when we use the trailing three years. These are very high values for the diversification metric and show that this portfolio is an effective mix and relative weighting of stocks to exploit non-market correlations between components to manage total portfolio risk levels.

What do these results tell us? Monte Carlo tools such as QPP can provide insight into the aggregate characteristics of a portfolio of assets. In the case of the portfolio profiled here, we see a fairly conservative equity portfolio that is projected to generate moderately higher returns in the future than we have seen over the past three to five years—even though this portfolio has been out-performing the S&P500 over this period on an absolute and risk-adjusted basis. Investing in a portfolio that is somewhat contrarian (i.e. that you project will generate higher future returns than in recent years) is a basic precept of Warren Buffett’s philosophy.

This portfolio has delivered a stable level of average returns and a stable level of risk over the past five years—encompassing substantially varying market conditions. From all of these measures generated by our portfolio planning tool, QPP, this portfolio can be seen to combine some substantial concentrations in individual equities in such a way as to yield a portfolio that effectively exploits diversification effects. This is the goal of strategic asset allocation: getting good diversification without simply buying some of everything. Warren Buffett summarizes this in his own words:

Wide diversification is only required when investors do not understand what they are doing.

Please note that I am not holding this portfolio up as an ideal for anyone. This portfolio mix may make sense for the domestic equity portion of your portfolio but that is not really the point. The main result from our analysis is that QPP’s measures of what makes a good conservative mix of stocks appears to be consistent with Berkshire Hathaway’s selection and weighting criteria. QPP tells us that this portfolio has performed quite consistently over varying markets and is predicted to deliver higher returns in the future than it has delivered over the past several years. The portfolio is also calculated to effectively exploit diversification effects across its holdings.

For users (and potential users) of Quantext Portfolio Planner (and its slightly more complex brother, Quantext Retirement Planner), these results should serve to build more confidence in the basic ‘reasonableness’ of a good Monte Carlo-based portfolio planning tool. I would be concerned if QPP suggested that Warren Buffett’s largest equity allocations were not very good. We would all like to have Mr. Buffett looking over our portfolios. Short of that, it is comforting to know that the performance metrics generated by a portfolio management tool (such as QPP) are broadly consistent with his investing choices.

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This article was written by

Geoff Considine profile picture
Geoff has worked in quantitative finance for more than twenty years. Before entering finance, Geoff was a research scientist for NASA. Geoff holds a PhD in Atmospheric Science from the University of Colorado - Boulder and a BS in Physics from Georgia Tech. Neither Geoff Considine nor Quantext (Geoff's company) are investment advisors. Nothing in any commentary here on Seeking Alpha or elsewhere shall be regarded as advice.

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