Quant Logic Tackles Sloppy Betas in Finance. (Part I)

I’ve been blogging a lot recently to the lay investing community.  I feel it is time to geek out a bit and exercise my inner quant (Quantitative analyst).  I was in the shower thinking about beta and expected return.  My mind came back to something that has bothered me for years… that beta is not rigorously defined.  It occurred to me, strikingly, that if beta is poorly defined then so is alpha!

Now this is somewhat unsettling since CAPM is highly wedded to the concept of beta, and alpha [which some scholars believe is approximately 0].  Let me be clear, the sampling frequency and sampling period of beta are not consistently defined!  One common definition of beta is based on monthly sampling over a period of one year.  Another definition I’ve seen is monthly sampling over a three year period.  I’ve also seen daily (trading days) sampling over periods of about 1-3 years.  Investments 6th Edition (Bodie, Kane, and Marcus)  even mentions the Merrill Lynch concept of adjusted beta (= 2/3 sample beta + 1/3).

These fast and loose definitions of beta are in sharp [no pun intended] contrast to the more rigorous definitions of maturity, duration, coupon rate, yield to maturity, etc. in the study of bonds.

The net effect of “beta sloppiness” is that a given given security, on the same day can get different betas from different investing houses even though they are all using the same data!  To put it mildly, I think this is kind of a big deal.   Beta, alpha, efficient frontiers, “risk free assets”, and CAPM are all interesting and useful concepts.   I think that after 50+ years, it is finally time to put a bit more rigor into the fundamental building blocks of modern portfolio theory.  I plan to crunch a few numbers and refine and test a few ideas, and I intent to help start doing just that (or at least help encourage others to) in the weeks ahead.

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