A Little Back-of-the-Napkin
Let’s take a look at BRK.A as compared to the S&P 500. While the S&P returned -3.3% over the past 10 years, Berkshire Hathaway returned 48.3%. Let’s annualize these to -0.3% for the S&P 500 and 4.8% for Berkshire.
I wanted to do a quick study on what all this means to the world. Using Jensen’s alpha, I’m going to calculate the “abnormal return” (alpha) of Berkshire over these ten years relative to the return of the larger market, the relative risk of Berkshire’s stock relative to that of the market (beta), and the “risk-free” 10-year treasury bond yield at the time (roughly 4.8% in 2001).
Before we get there: the way Jensen’s alpha works, you are essentially comparing your subject’s returns to what you would expect anybody to get out of the market at a certain level of risk. The expected return, as shown in the Wikipedia entry, is the risk-free (called Rf) rate plus the portfolio’s beta times the difference between the market’s return and the risk-free return.
In my experience, the best way to understand equations is to play with the coefficients at zero, one, and extremes.
With no risk (beta = 0), you’re just holding the bonds:
Rf + 0 * (Market - Rf) = Rf
At the same risk as the market (beta = 1, index fund), it’s reasonable you should expect the market’s return:
Rf + 1 * (Market - Rf) = Market
At double the risk of the market (beta = 2, invest in riskier things or take out a loan to double your capital) it’s no great achievement to return more than the market:
Rf + 2 * (Market - Rf) > Market (for decently good values of Market!)
In other words, the guy who bets against the odds and returns with a fistful of money should not be applauded until you figure out that he wins a lot, enough to compensate him for his huge risk, not just enough to show up every now and then and flaunt his fluke luck.
These numbers ended up really looking interesting for this calculation, because Berkshire’s annual return and the risk-free rate ended up being the same thing, 4.8%.
But, if you check the Google Finance page, Berkshire’s beta is around 0.5. Meaning, Berkshire is actually generally less risky (ups and downs) than the broader market. I read that Google Finance probably uses 5-year data for its beta calculation (that can matter quite a bit), and since Berkshire’s last five years have been pretty volatile that seems like a fair measure to use.
What return would we expect Buffett to achieve with his wimpy 0.5 beta, in a sucky market?
4.8% + 0.5 * (-0.3% - 4.8%) = 2.3%
What this is saying, and these numbers make it so illustrative and important, is that a less risky investment should be expected to have taken less punishment from the bad market than a straight index fund investor would.
What were Buffett’s abnormal returns (alpha) over that period of time, then?
4.8% - 2.3% = 2.5%
That’s 25% over ten years. Berkshire’s market cap right now is about $170 billion. If you reverse it back 48%, that’s about $115 billion ten years ago.
What this is saying is, we would expect Buffett to have returned 23% over ten years just doing a standard stock pick at half the market’s volatility (he could also have put half of his capital into the T-bonds and invested the other half in an index fund; interestingly enough, he does hold a lot of cash). He instead returned 48%, meaning the magic that is Buffett is a 25% return over ten years.
Meaning, of that $55 billion he has returned over this period of time, he is pretty much uniquely responsible for about $29 billion of it, which is money now sitting in the hands of pensioners, charities, and investors, not to mention the government in the form of the capital gains tax. Pretty good fruits for ten years’ efforts. Buffett is worth $50 billion as of this year’s measure.
He’s done enough.