A couple of things:
1. Formula - (Betting-Against-Beta and Quality-Minus-Junk)
The formula on page 30 doesn't have 7 components, and neither is it the grand formula that the authors use to explain Buffett's alpha. That formula actually just says:
excess return = (weight of private holdings X excess returns of private holdings + weight of public holdings X excess returns of public holdings) X leverage
which is basic arithmetic that any Singaporean primary school kid can do.
The real formula that the authors use to explain Buffett's alpha is on page 17 and has six main components. The first component was derived from standard CAPM* theory and says stocks' risks comes mainly from their correlation to market returns. The second and third component were found by Fama and French and explained through their Fama-French 3 Factor model. The fourth component on momentum was found by another academic Jegadeesh. The fifth and sixth components are the interesting ones because they were "discovered" by two of the paper's three authors in their previous research.
The reason why there are so many components to this linear regression model is because after standard CAPM was founded in the 1950s, the next few decades of stock market performance provided a rich database for people to test the theory. When some academics found out that CAPM cannot provide a good answer to stock market returns, i.e. one beta is not enough and there were significant values for the alpha and error terms in the linear regressions, they sought more and more parameters to try and explain away the alpha and error terms. This led to the proliferation of parameters and beta terms.
As you can see, these are clear examples of the dangers of
data-mining, and indeed data-mining was one of the earliest criticisms of the Fama-French model and the lesser discussed arbitrage pricing theory. I can imagine academic statisticians smirking at their finance colleagues.
2. Leverage
(i) Their calculation of leverage is clearly overly simplistic. It does not make any accounting adjustments to get a more realistic representation of BRK's book value. For example, it doesn't take into account the many spurious charges that BRK has had to take on its book value in the past due to accounting regulations. (See page 15 of its 2011 annual shareholder letter for an example using the Marmon acquisition)
(ii) Furthermore, it agrees that BRK was able to secure cheap leverage through its insurance float but says that it had an average cost of 2.2%. Table 3 on page 39 shows how they calculated this 2.2%. I quote "in years when cost of funds is reported as less than zero and no numerical value is available we set cost of funds to zero". BRK does not reveal the numerical values of costs of funds when they are negative because they don't want their competitors to know how much they are making. But Buffett has said before, at least in the early stages of his BRK career that the float they generate has a negative cost of fund in general. So the actual figure is likely to be much lower than 2.2%.
Anyway that's besides the point. While I agree that the float is a form of leverage, it is not your typical form of financial leverage where you simply borrow money to invest in something else. This leverage was formed from the operations of profitable insurance companies. Just like how Walmart, Costco and Japanese MNCs can extract operating leverage from their customers and suppliers, BRK is extracting leverage from its prudent insurance operations. Walmart etc. does it through their buying power, BRK does it through their prudent underwriting and their call brokers. It is not strictly financial leverage of the type with your typical interest rate and term risks etc.
(iii) This paper also only studies Buffett's BRK record. If you go back further, Buffett was achieving even better performance without leverage during his Partnership years.
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*Side note:
The CAPM model was introduced in the 1960s. Buffett's investment career started at least a decade before that and it makes you wonder what discount rate he used. I remember reading somewhere where he referenced John Burr Williams and the best source I have found on what John Burr Williams' ideas on discounting were is on page 75 of this book:
http://www.worlduc.com/UploadFiles/BlogF...nstein.pdf
Seems like he just used the risk-free discount rate.
And then I came across this (page xxii):
https://www.platinum.com.au/Documents/Sh...cl_601.pdf
The relevant line is: "Buffett stated at the meeting two years ago, 'We discount at the long-term treasury rate, but this is only appropriate for businesses with highly predictable earnings streams. If we can't determine the future earnings of the business we don't even bother to work out its net present value."
Remember also that Munger once said that he has never seen Buffett do a discounted cash flow calculation and that for himself, he never saw the use of any computing tools beyond a counting machine (calculator) and a dog-eared present value table. I think this sums up a large part of their attitude towards investing - focus on understanding the business.
