Tuesday, January 12, 2010

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'.


  1. Stephen Campisi, Intuitive Performance SolutionsJanuary 12, 2010 at 10:51 AM

    Beta is perhaps the most misunderstood risk measure. And so, it's criticism is often more of a commentary on the lack of understanding of those making the criticisms. One shortcoming of many analysts is their failure to understand the basic assumptions of each model and of each resulting statistic. For beta, we start with the assumption that we are analyzing an investment within the context of a well diversified portfolio. We can relax this assumption somewhat so that we are at least comparing the investment with its appropriate benchmark (for example, a large cap stock relative to the S&P 500.) This way we have an "apples to apples" comparison.

    Here's a useful definition of beta: the ratio of the asset's relative volatility to the benchmark (AKA the ratio of the standard deviations) multiplied by the correlation of the asset to its benchmark. In this context, we see that beta is actually the joint occurrence of two relevant risks: volatility and tracking error. Unfortunately, this is also what makes beta so dangerous. You can have a more volatile asset (i.e. perhaps 50% riskier) and it may have a high degree of tracking error risk (evidenced by a correlation of only 0.75) and so using the simplistic approach to beta that has become customary, you get the "insight" that this security is of equal risk to the market since its beta is 1.0. Of course this security is much riskier and requires a higher return. Too bad that the typical approach to beta will assign this investment a positive alpha, and the resulting investment experience will probably be disappointing. Now enter the "beta naysayers" who use this as an example of the deficiencies of beta... all the while ignoring the fact that the only deficiency has come from their lack of understanding of a few basic ideas.

    It's easy to show that over the long term, beta does a good job of evaluating the amount of performance due to simple market exposure, leaving the residual performance to be the result of other active effects. This also shows that the majority of active return is due to "active beta" bets rather than the security selection process which dominates so much of everyone's time. However, none of this will become evident if the benchmark is wrong. We will get better performance results when we put more attention on understanding the investment process and on selecting/creating more appropriate benchmarks.

    Academic criticisms of beta have failed to displace it as a valid risk statistic because the logic behind beta is sound. It's the misuse of beta that has been the problem. As the Bard said: "The fault lies not in our stars but in ourselves."

  2. One of the challenges with beta is what IS the market. I agree that it makes sense to compare the security with the benchmark, which seems to have escaped most academic literature (at least what I've seen). From a practitioner perspective, this makes sense. As a component of CAPM, it's intent is to predict what the expected portfolio return will be. I haven't seen any empirical evidence that even when narrowed to the index that beta works well. Beta, like standard deviation, will have its critics. Interesting, though, that even Jack Treynor has criticized it.

  3. Another interpretation of Beta (from Fama & French): it measures the sensitivity of the asset's return to variation in the market return.

  4. Stephen Campisi, CFAJanuary 12, 2010 at 9:10 PM

    Aaarrggghhh! Pardon my math typo!! I should have said that the volatility ratio is 1.5 and the correlation is 0.67 so that the resulting beta is 1.0 (still the point is valid: the security is NOT equally risky as its market.)

    Regarding Dave's points: both are valid but neither is really a criticism of beta. "What is the market benchmark?" is a somewhat tired and impractical argument. We all recognize that the theoretical market portfolio contains assets that cannot be realistically owned and which lack liquidity. An example would be works of art: you can't own a piece of the Mona Lisa; we all get that. The more realistic argument is one of opportunity cost: each investor can buy a global basket of market exposures and this is an adequate representation of the investor's opportunity of a well diversified portfolio. In THIS context we find that beta works quite well. The other "market portfolio" is the opportunity set for an individual manager. So, if the manager is a large U.S. stock picker, then the passive opportunity of this manager's market exposure is a representative benchmark such as the S&P 500 or the Russell Top 200 index. Over the long term, there is plenty of empirical evidence (as Dave indicates) that the majority of the asset's return is explained by its market exposure, and that the remaining deviations in both return and the pattern of return are explained by the idiosyncratic process we call "issue selection."

    So, we see that beta is actually a very good long term risk statistic for evaluating performance. Better yet, it's a nice, linear factor that is intuitive and easily understood by clients. What's not to like?


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