Monday, May 21, 2012

Clothing & Beta: is there a connection?

The Spaulding Group held its Spring North American Performance Measurement Forum meeting earlier this month in Atlanta, and during the session I had a thought about how the subjects of beta and Jensen's alpha can be related to clothing (being one who is always on the lookout for metaphors and analogies, this seemed to be a good one to share).

Jensen's alpha, as you may recall, is a risk-adjusted measure, that can be viewed as excess return that takes beta into consideration. The typical way we view excess return is:

Jensen's alpha looks a bit like this expression, but with a twist:

First, we're dealing with equity risk premiums (portfolio return minus the risk free rate). But, basic knowledge of algebra would make it clear that if this was the only difference, it would match our excess return. What's really different is the use of beta. Jensen's alpha takes the portfolio's beta and applies it to the benchmark (or more precisely, the benchmark's equity risk premium), essentially saying that THIS is what the portfolio's return WOULD be (net the risk free rate), if beta captured everything for the portfolio; that is, if beta was a perfect predictor of portfolio return. But, Jensen's alpha is usually not zero, based on the portfolio's idiosyncrasies.

And so, where does clothing come in? Well, the benchmark could be looked upon as a school uniform, which everyone is required to wear. Assuming students are required to keep them clean and pressed, there would be no differences. However, if there was some leeway in terms of the shoes a student could wear, whether they could have their uniform custom made, if they could substitute fancy socks, or perhaps (as my friend Steve Campisi likes to do) include a pocket handkerchief, they would be different.

The military doesn't permit much in the way of variation. But, when I was on active duty (with the Field Artillery branch of the U.S. Army) we had the option of substituting "airborne boots" for our standard issue ones; they looked much sharper, and many of us did (even if we weren't airborne!). And, one could buy their "dress blues" off the rack, or get them custom made. And so, even here we had the ability for some degree of idiosyncratic adjustments.

This difference is like what we see with the result from Jensen's alpha. When one speaks of "portable alpha," THIS is the "alpha" they are speaking of: the part of excess return that is completely attributable to the idiosyncrasies of the portfolio, with no baggage from the benchmark.

By the way, you are probably also noticing that we use the term "alpha" here, but in the "Jensen's alpha" context. Whenever anyone simply says "alpha," you should ask "what alpha are you referring to?" This isn't an offensive question, but rather an insightful one, because it reflects your awareness that there are at least two versions of alpha: basic alpha, which is derived from excess return, and Jensen's alpha.


  1. Isn't R(p) - R(b) typically considered Active Return? I think of Excess Return as the return above R(f).

  2. Derek, thanks for your comment. You've identified yet another phenomenon: multiple terms for something. R(p) - (R(b) goes by multiple names, including alpha, excess return, AND active return. In Sharpe's paper he also uses the term "excess return" to represent what we also call the equity risk premium. I think MOST folks think of "excess return" to be the difference as I've identified hee.

  3. If most people call R(p)-R(b) excess return, what is the most common terminology for R(p)-R(f)?

  4. Derek, it's "equity risk premium." Or, simply "risk premium."


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