Alpha is a relative measure, that is not only not observable but is also highly model dependent. Thus, there are alphas, not an alpha.

Alpha can, in some contexts, help rank investors’ performances, but it tells you nothing about overall performance. It also tells you nothing about market efficiency.

The default approach of throwing a few years of returns of an investment and benchmark into a spreadsheet and doing a vanilla ordinary least squares linear regression isn’t going to give you a meaningful estimate of alpha. Perhaps the best you can hope for is some insight about relative volatility and covariance.

Doing alpha the right way is hard, really hard. It demands professional level statisitical modeling skills and tools.

In using alpha the model-dependence, the statistical uncertainty, the non-stationarity, and the need to shrink forecasts all must be kept in mind. Often when you do this and assess what you’re getting from alpha, then you realize it’s not going to be able to give you what you need.

It would be a good exercise to ask the students to prove the “zero mean alpha” result. That is, given a capital weighted benchmark and the set of frictionless investors which collectively equal that benchmark, then the mean capital-weighted alpha is zero. This doesn’t require much beyond high school algebra skills.

Hope that helps.

I should mention this to my MBAs this fall…

Great post, of course, but I do take issue with this one point:

Arguing that the investment management industry is not doing its job because of that fact is like arguing that American education is failing because half of the students are below average.

This doesn’t seem right to me, because not all investors are professional money managers. There are also individual investors. Thus, it is mathematically possible for the alpha of the investment management industry as a whole to be positive.

It seems to me that if the alpha of the money management industry as a whole is not positive after fees, then this has an important implication for individual investors. It means that if you don’t know how good an investor you are, you will be better off investing your money yourself than picking a third-party manager purely at random (well, “purely at random” = probabilities weighted by existing market capitalization).

That strikes me as a non-trivial, useful thing to know.

Small correction: all the “m(t)” terms should be “r_m(t)” instead