*Making it Real*

Warren Buffett is an investment legend and last week, he
released his 50^{th} annual investor newsletter in his role as lead at
Berkshire Hathaway, the company that he has used as the vehicle for his investment
exploits. The entire newsletter is part of the puzzle and is worth reading
because it lays out not only the history of the company but also Buffett's
investment philosophy, which is much misunderstood even by his followers.

*Measuring Performance*

While there are many corporate finance lessons about dividends, buybacks, investments and spin offs in the newsletter, the focus of this weekly challenge is a narrow one. It is to look at the performance of Berkshire Hathaway, relative to the market, over the last 50 years. I know that you already have a sense of what the answer is but I would like you to not only be specific but dig deeper into the numbers using the tools that we have developed in the class.

*Key Questions to
Answer*

You can start with these self-reported numbers from Buffett on the company's book value performance (Buffett is a great believer in increasing book value over time) and its market performance together with the S&P 500 each year. Since Berkshire Hathaway does not pay dividends, the price change is the return you would have made each year.

1. What was the average return and standard deviation in Berkshire's book value and market value returns over the entire 50-year period?

2. What was the average return and standard deviation in the S&P 500 returns over the period?

3. Compare the average returns on Berkshire Hathaway to the average returns on the S&P 500? What is your judgment on performance?

4. Break down the return comparison into five decades: 1965-74, 1975-84, 1985-94, 1995-2004 and 2005-2014. Are there any trends and what explanations can you offer for the change?

5. Finally try running a regression of annual returns on Berkshire Hathaway against the S&P 500, using all 50 years of returns? Using the same template that we used for Disney, read the output from the regression. In particular

- What beta would you estimate for Berkshire Hathaway? What cautionary notes would you have about using this beta?

- Based on the beta, what is your estimate of how much Berkshire Hathaway has beaten the market by, on average, over the entire period?

- How much of the risk in Berkshire Hathaway is market risk?

You can assume that the average annual risk free rate during the period was 4%.

(The average annual risk free rate over the entire 50 year period was about 4%)