Beta ... what is 1.0?

Beta is a risk statistic which tells us essentially how our portfolio behaves relative to the market. It is a derivative of Modern Portfolio Theory, and more specifically, the Capital Asset Pricing Model (CAPM). The purpose of this post isn't to address whether or not beta is dead; Fama & French can tackle that one. It's really a lot simpler than that.

The market gets 1.0; our portfolio's value is measured using the following formula:

We measure the covariance of the portfolio's return stream relative to the market's; that is, how they vary relative to one another. We then divide this value by the variance of the market.

One question that has held firm for CAPM is "what's the market?" Well, that's something that is taken up in the hallowed halls of academia; for our purposes, we have the same question, but not perhaps from such a purist perspective. We want to know what gets the "1.0."

Standard practice seems to be to assign the 1.0 to the portfolio's benchmark. In my opinion, to do anything but this can be of little value. For example, let's say that you use the S&P 500 to represent the broad market, and everything, including your portfolio's benchmark, relative to it. And let's say that as a U.S. small cap manager, your benchmark is the Russell 2000. And so, you first calculate the Russell 2000's beta, which you find to be (for exhibition purposes only; not in reality) 1.53. You next calculate your portfolio's beta relative to the S&P 500, and it turns out to be 1.61. This tells us that both the portfolio's index and the portfolio itself are more volatile than the S&P 500, meaning that they both exhibit more risk. So what? We're interested in the risk you've taken relative to the index your managing against, aren't we? And wouldn't it be more appropriate to set the Russell 2000 to 1.0, and measure the portfolio's beta in comparison to it? We should let the academics try to define "the market." But when we're measuring a portfolio's risk, its market is its benchmark, and risk should be compared against it. This holds for tracking error, information ratio, Jensen's alpha, Modigliani-Modigliani, and any other risk statistic that uses a benchmark in its formula.

p.s., There may be some value to measure a benchmark's beta relative to the S&P 500 (or some other "market"), to exhibit how each behaves relative to it, so I don't want to "pooh-pooh" the idea completely. But from a fundamental, foundational perspective, use the portfolio's benchmark when measuring risk. You're not managing against "the market," other than as represented by the associated benchmark.

Why are you still here?

Fama & French's famous paper, "The Cross Section of Expected Stock Returns" (The Journal of Finance, June 1972), is credited with the "Beta is Dead" suggestion, as a result of the empirical evidence to discredit the Capital Asset Pricing Model  (CAPM), which was developed independently by Sharpe ('64) and Lintner '65). Beta has been found to be a poor predictor of a portfolio's return, with Fama and French's 3-factor model ('73), augmented with a fourth factor by Carhart ('97), generally seen as better models. In only two years we will reach the 40th anniversary of the '72 F&F paper and yet beta remains a solid part of many firm's risk measures.

Extending this further, Jensen, in '68 recognized that CAPM needed an additional factor (alpha), which some consider the manager's skill in finding performance beyond beta, generally known as Jensen's alpha and one of the many risk-adjusted return measures that are available and often used by asset managers. But if CAPM is truly dead, shouldn't Jensen's alpha be, too?

The Journal of Performance Measurement® is scheduled to include an article by Fama and French in its summer issue which does an exceptional job of describing the CAPM and addressing many of the tests which have been performed. It provides a very concise and fairly intuitive discussion of the many issues surrounding this area of investments finance. Perhaps if more in the industry understand the model's failings its constituents will be dropped from common use... but perhaps not.

We are planning a webinar in the coming months as well to discuss the model in what we hope will be an easy to comprehend manner. More details to follow.

Beta, wanted dead or alive

A 1992 Journal of Finance article by Fama & French is often cited as the source for the line, "Beta is dead."

Recall that Beta is a measure of volatility; actually, a security's volatility vis-a-vis the market. It is used in the Capital Asset Pricing Model, for which William Sharpe received the 1990 Nobel Prize in Economics.

The formula is the covariance of security return with the market, divided by the market's variance. The market's beta equals 1.0; a higher beta means the security goes up faster than the market, and will also go down faster; a lower beta means the security moves won't be as great as the market's.Critics (and sufficient analysis) contends that beta fails as a predictor of security returns; that there are other attributes that play a bigger role. Most of the criticism has been somewhat respectful, though some, like Nassim Taleb (The Black Swan) have been a bit more forceful. Even Jack Treynor criticized its use in the aponymously named risk-adjusted measure which he disavows responsibility for.

Fama & French, as you may recall, introduced a three factor model, which includes beta, size (large cap vs. small cap) and style (growth, value). Other models have been suggested, as well.

In spite of the critics, beta remains a much calculated and reported risk measure. And why is this? Perhaps because "everyone does it." Or, "we've been doing it so long, why stop?" Or, "because it's easy to understand and interpret" (even though it's wrong?). Beta may be dead, but it's still around and kickin'.