# Is Beta a Factor?

Many factor investors consider beta to be one among many factors.  If Einstein were to inspect CAPM and study the equations that produce beta, I think he would be offended by the lack of elegance.  If we assume that beta is a valid unidimensional construct as I suspect Markowitz did, then it is elegant.  Beginning with the work of Fama and French, this supposition was “blown out of the water.”  A multifactor model is necessary, and even William of Occam would disapprove of such an oversimplification.

Model complexity is to be avoided when a simpler model has the same predictive validity, but we cannot throw away factors that have explanatory power.  While I am decidedly not an econometrician, it seems to me that beta itself is not a factor, but rather a correlated error term.  In most regression models based on sample data, we simply delete the error term from the end of our prediction equations.  This is what differentiates our mere models from a formal mathematical expression of reality (such as Einstein’s elegant and precise expression of relativity).

When we consider what beta actually is in statistical terms, there isn’t much complication.  It is simply the correlation between the return of a particular asset or basket of assets with the return of a benchmark that is purported to represent the “market” (most often, the S&P 500 is used, or a proxy such as Vanguard’s mutual fund).  In the world of scientific research, it is customary to formulate prediction equations based on variables and to give those variables logical names.

These variables, taken one at a time or in clusters, are used to form linear models that predict the outcome variable.  If the model specification is based on theory (as I argue it should be), then each predictor is assumed to have an effect on the predicted value, which is the current case is the return of a particular investment.

Value, for example, is a variable in this traditional sense; we can observe it and record those observations as measurements (quantification), which means that we can subject value to prediction models.  There are many ways to operationalize the value construct, and there is a vigorous debate as to which is best.  We could, for example, adopt the method Morningstar uses to construct style boxes.  My basic point is that value meets the classical definition of what a factor is; it is a theoretically salient variable that can be quantified and subjected to empirical validation.  Beta, on the other hand, is a different beast entirely.

Beta is the leftover covariance that we cannot explain with other factors, which statisticians would call an error term.  If we recall what the acronym CAPM stands for, we are reminded that we are about the business of pricing assets.  In the world of ETFs and mutual funds, the S&P 500 may be an asset, but we obviously cannot determine a fair price for it based on its current price.  That is unless we blindly invoke the efficient market hypothesis and state that it is fairly priced because the market said so.  To do so would invalidate the entire endeavor of pricing assets in the first place.

Beta, then, is not what I would consider a factor.  I look forward to a day when the next generation of great economic thinkers shrinks beta to near zero by identifying the salient factors that actually compose it, moving if from the territory unexplained error to rigorous theory.  For econometricians, the size of beta (or the R2 of beta when all other factors are controlled for) dictates how bad the state of the art is.  Despite these limitations, in many ways, beta is still the best metric we have for certain purposes.  We know, for example, that beta is positive and we will make money over the long haul if we “buy the market.”

The question becomes more about tenacity than probability when we span decades.  This gives rise to the fact that market beta serves as the best available benchmark for other assets and portfolios.  Since our understanding of why assets keep growing in value over time is so limited (at least as far as empirical prediction models are concerned) we are left with a strategy that is inelegant and intuitively suboptimal:  We start with a market portfolio and add tilts, analyze the impact of those tilts, and retain the ones that increase return or decrease risk (or establish some sort of equilibrium between the two).

An important myth to dispel is that the beta of an individual security is a measure of risk.  Individual betas are measures of correlation between an investment and moves in the overall market (they are what those familiar with regression analysis will recognize unstandardized regression coefficients).  A beta of 1.0, then, means that we can expect an investment to move precisely in tandem with the market.  Note that these moves can be up or down or sideways.  Beta does not provide a measure of risk as we usually think of it.  It is merely a measure of probable movements under historical conditions without regard to direction.

It is important to realize that historical conditions under which these models are derived do not reflect panic selloff conditions.  If you are long equity and the market starts to sell off under high volume, go for a walk.  There is nothing sensible that you can do.  That being said, larger than market returns require larger than market moves.  Also, note that if a security is prone to make huge moves down, but those moves do not correlate with market moves, then beta will not capture that risk.  As a measure of risk, beta only informs us about a single source of risk, and it does a poor job of that when conditions are not similar to the ones under which beta was calculated.

With all of those caveats in place, let us not examine beta as if it were a factor (as indeed many factor-based investors do).  If beta is a factor, it should provide a return.  This should be intuitive since we are obviously taking on market risk by investing in the market.  The standard practice for assessing such returns is to compare them to a benchmark that represents the “riskless asset,” which is most often represented by the one-month US Treasury bill.  If you want to model this using a mutual fund in a particular software package, you can use any money market fund because such funds usually hold mostly these securities.

Despite the problems associated with the practice we discussed earlier, the standard practice when making these comparisons is to use the average annual return (as opposed to an inflation-adjusted compounded return, which would be my preference).  There are differences in the precise value of the return of beta over time because of the differences between data sets.  The consensus is that beta returns premiums (gains attributable to that factor alone) of around 8.3% per year.  Note that this would not be your total return; the cash premium has been subtracted.

Note that even with an investment horizon as long as 20 years, there is still about a 4% chance that you will lose money.  We can minimize risk, but we can never eliminate it.  If there were a way to reduce risk of any investment to zero, then it would reward us with the cash rate and no more.  Note that this is true for each particular investment, but may not be true for a well-diversified portfolio.  When we plot efficient frontiers, the absolute highest returns are always for equity only strategies and the riskier the strategy, the higher the return.

Considered as a factor, market beta is not to be missed.  The risk-reward ratios are such that satisfactory returns can only come with equities included in your portfolio.  As an element of a diversified portfolio, the total risk can be controlled such that beta risk is acceptable to even the most conservative investors.  As other factors will suggest, “buying the market” may not be the best approach to controlling beta risk.

The most efficient way to expose your portfolio to unadulterated beta is to buy an extremely low-cost mutual fund or ETF that goes a good job of tracking its index.  There are total market indices, but the most common method is to track the S&P 500.  Mr. Buffett and I strongly recommend the Vanguard 500 Index Investor Shares (\$VFINX) for this purpose.  From the fund’s inception in 1976 to 2015, the fund returned 10.8% annually to investors.

The S&P 500 returned a hypothetical 11.1%, but mutual funds cannot match the index return perfectly since trading fees need to be paid and Mr. Boggle needs to pay his bills.  Note that the costs of the fund have fallen over time as new capital has come under management.  Because fees and expenses are somewhat fixed, the more money a fund has, the smaller the percentage gets.  \$VFINX has a staggering sum of money under management at present, and the fees are extremely low.

In a vacuum, it is difficult to assess the goodness of a 10% return.  Overall, that is an excellent return that little else can match.  Equities, in general, pay a very high premium to investors.  The reason for this is that the short-term risks can be extraordinary.  For example, the worst year for US equity investors in recorded history was 1931.  That infamous year, the return on equities was -43.5%.  That does not tell the whole story.  From the beginning of the parabolic downturn in September of 1929 until a bottom was reached in June of 1932, the total loss was more than 83%.

As you probably guessed, this period was known as the Great Depression.  The stock market was only a part of the worst economic disaster in recorded global history.  It is also worthy of note that one-month Treasury bills returned a handsome 6% during that period.  This means that the stock market underperformance was over 90%, which by all definitions constitutes high risk.  It also shows that a diversified portfolio that held bonds during that period would have been spared much (but not all) of the downturn.

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`Last Updated: 6/25/2018`

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