Sunday, August 28, 2011

Beta Adored Before Data

There's a cover story from the September 1971 Institutional Investor entitled 'The Beta Revolution', which mentions 'portfolio managers and security analysts who mathematical backgrounds extend only slightly beyond long division are tossing betas around with the abandon of Ph.D.'s in statistical theory.'

They write the 'beta theory' started with Markowitz in 1952, and later papers by William Sharpe and Jack Treynor in 1963 and 65. By 1968, they note 253 articles and 89 books written about 'beta' (really, the Capital Asset Pricing Theory).

What's conspicuously absent is any mention of empirical corroboration. A simple scatter plot, with beta on the x-axis, returns on the y-axis, would have been nice. In fact, the first empirical support wasn't even until a couple years later, meaning, there was no data supporting the theory at this time, but the experts all believed the theory anyway. The subsequent supporting data was weak and contained a serious omitted variables bias, namely, that size explained any correlation between beta and average returns. All the hubbub was purely from theorists, without even any flawed empirical support. One can see why the initial flawed empirical research got through, because all the experts knew the right answer, and so didn't think to test the theory with appropriate skepticism.

Yet even then, the article notes that 'very low beta stocks, in fact, tend to have higher alphas and high beta stocks tend to have low alphas.' That is, the beta-return relationship, to the extent it did exist in unpublished studies, was pretty flat. A fund manager back in 1971 could have jumped on that small insight and blown away everyone over the next generation, but that little nugget was ignored.

The description of beta is distressingly vague, but the intuition they mention is based, in their words, on two 'widely accepted ideas.' First, that to obtain higher rewards, one must take higher risks. Secondly, that individual stock returns are correlated with the market as a whole. Interestingly, it is true that given standard utility functions (eg, u(x)=-exp(-ax), these do lead to beta-type risk premiums. Something's clearly wrong, and while most researchers seem to think it's schizophrenic risk-loving (within asset classes, not between them), I think it has to be we are more envious than greedy.


Anonymous said...

it took me about 30 minutes this morning to pull monthly prices on 8 major stocks and the S&P, run regressions to get betas and alphas, build some plots, compute some correlations to find evidence supporting what you're saying and against CAPM.

Alpha appears correlated with higher returns, negatively correlated with volatility, and beta appears negatively correlated with returns and highly correlated with volatility. Volatility meanwhile is negatively correlated with returns.

Anonymous said...

I will first laugh for a moment at anyone who did empirical analysis on 8 stocks and thinks he has anything to say.

Now I'll take on Eric. You HATE the CAPM, but LOVE low beta investing. Do you see the irony? Loving low beta investing is in many ways a belief that the CAPM should hold but doesn't. You LOVE the CAPM if you like low beta. That's not precise, but if no CAPM like logic, why is low beta investing exciting? If you aren't supposed to get lower returns on low beta, why would not getting them be interesting?

What you are saying is you believe the CAPM is a great model, and it should hold, but the market is too inefficient to get us there, creating an opportunity. That is very different from making fun of the CAPM as a model.

Pat Burns said...

I just happened to have such a plot waiting in the wings in a blog post wondering about the properties of portfolios with beta = 1. It is now posted at The effect of beta equal 1.

jsalvati said...

What would you suggest small investors wanting to invest low-vol look at? The people at ROBECO didn't seem very interested.

Eric Falkenstein said...

The CAPM is a good normative model, but a bad descriptive one. I think it was Steve Ross who said the CAPM is more important if it doesn't work, and I agree. That's not a paradox, and I've said this before. Also, I generally believe in efficient markets, and consider this unrelated to why the CAPM does not hold, having to do with utility functions instead.

Robeco has some very successful low volatility funds it sells to institutions.

Anonymous said...

Wow. I didn't realize that commenting on a blog post required the same rigor as a refereed paper. Next time, I'll be sure to include a complete literature review and suggestions for further research when I do a fun data exercise for a 30-minute diversion at work.

Dave Pinsen said...


I sent you an e-mail related to this post a few days ago. Could you please check your bulk folder for it?

Thanks a lot.

Anonymous said...

In a world where some are envious and some are greedy, what does the equibrium look like? It seems to me that part of the attraction of beta is that the equilibrium is stable and should obtain so long as some people are greedy even if many are envious.

I'm not disputing the empirical evidence here.