View From a Height

RBSA

As part of my research, I've been looking at something called Returns Based Style Analysis. Reading through the papers and the technique, I can't believe anyone ever took this stuff seriously at the style-box level.

RBSA purports to be a way of determining if a Growth manager really is doing what he says he's doing. The idea is that you take a Growth Index and a Value Index, and then maybe a large-, a small-, and maybe a mid-cap index, and see how well the manager's returns correlate with each of them.

The actual equation is this:

R = a + b₁R₁ + b₂R₂ + ... + e

where R is the fund's return, a is the manager's alpha, e is an error term. Each R is the return for a given index, and each b is the fund's exposure to the style represented by that index. If you do this for a series of quarters or years, you can solve for the b's, and find out the manager's actual (as opposed to advertised) style.

Right.

This is like trying to figure out whether a pitcher is a power pitcher or not by looking at his ERA.

Now, RBSA was originally invented by the Nobel Prize Winner William Sharpe, a founder of modern portfolio theory, CAPM, and the Sharpe Ratio, so naturally I'm a little reluctant to call it bunk. Still, "Nobel Prize Winner" probably had a lot more heft to it before two of them almost crashed the world financial system in 1998. Secondly, it's far from clear that these relationships actually are linear.

One thing, though, that distinguishes Sharpe's idea from current usage is that he was using actual asset classes. We know what a stock is, and we know what gold is, and it's unlikely that someone's going to mix up the two. But there are at least five different indexing services out there (Wilshire, S&P, Morningstar, Russell, Morgan-Stanley), and they can't agree from quarter-to-quarter what's a growth stock and what's a value stock. Heck, they can't even agree what large, mid, and small mean, and some can't even agree that there is such a thing as mid-cap. The granddaddy of risk factor exposure, Barra, even admits that a firm definition is impossible.

So now, it's like trying to figure out whether a pitcher is a power pitcher or not by looking at his ERA, only the official scorer routinely tries a little too hard to support the sponsor (you know, Coors, Busch, Milwaukee), and can't figure out what an error is.

Finally, we have something better. We can actually look at mutual funds' holdings, and decide for ourselves what this manager is up to.

So really, what RBSA is trying to do is figure out a pitcher's style by using an inconsistent definition of an earned run, when two columns over, we can see his strikeouts and walks, fly-outs and ground-outs.

We can do better than this. Really, we can.