Professors Eugene Fama and Kenneth French have a new paper, “Incremental Variables and the Investment Opportunity Set,” that provides some important insights for investors considering funds designed to supply exposure to multiple factors, or styles, of investing.

In their study, they note: “Much asset pricing research is a search for variables that improve understanding of the cross section of expected returns. Researchers often claim success if a sort on their candidate produces a large spread in average returns. A better measure, however, is the variable’s incremental contribution to the return spread produced by a model that includes the variables already known to predict returns.”

The paper’s important message is that factors (systematic variables such as size, value, momentum and profitability) that possess strong marginal explanatory power in cross-section asset-pricing regressions and that exhibit large premiums typically show much less power to produce incremental improvements to average portfolio returns.

**Which Exhibits In The Factor Zoo Should You Visit?**

The factors to which investors should allocate assets, and the funds they should select to gain exposure to their choices, are important issues. Further complicating the problem is that, as professor John Cochrane has noted, the literature on factors now fills a veritable “factor zoo” of more than 300 options. How do investors select from this huge array of possibilities?

Following are the criteria I would recommend investors consider before allocating assets to a given factor.

- Strong evidence in the academic literature that premiums associated with the factor are persistent across both time and economic regimes as well as pervasive across geographic regions, countries, industries and sectors. The case for a factor can be made even more compelling when the evidence exists across asset classes (stocks, bonds, commodities, currencies). Examples where this is the case include value, momentum and carry.
- The factor has exhibited significant premiums that are expected to persist in the future. Not only should we understand why the premium exists, but there should be a strong basis for believing it will persist into the future. In other words, there needs to be an intellectual foundation with compelling logic (whether risk or behavioral).
- The factor must have returns history available for bad times. Factor risk premiums exist because they reward an investor’s willingness to endure losses during down times in the market.
- The factor’s results are not subsumed by already-known factors. The factor should have its own explanatory power when it comes to the cross section of returns.
- The factor should be implementable in liquid, traded investments. This is especially important for large investors where scale is required.

Additionally, inclusion of the factor among asset pricing models now in common use by academics would be a strong argument in support of an allocation to it. The most commonly included today are beta, size, value, momentum and profitability/quality.

**Combine Securities, Not Factors**

Once an investor has chosen the factors he or she wants exposure to, the next decision should involve whether to target the factors individually, separately or through a multistyle fund. For instance, an investor could decide to own three funds, each of which targets the size, value and momentum factors individually. Alternatively, the investor could choose to invest in one multistyle fund that targets all three.

As Roger Clarke, Harindra De Silva and Steven Thorley explain in their October 2015 paper, “Factor Portfolios and Efficient Factor Investing,” it is far better to combine individual securities to achieve optimal portfolios than to combine factors.

This is intuitive. For example, suppose one chooses to invest in both the size and value factors. Constructing a portfolio at the security level would mean buying small and value stocks. But combining them at the factor level would mean buying a bunch of small stocks and also a bunch of value stocks. The small stocks would include some with a lot of growth exposure (little value), while the value stocks would include some that are large (not small). This would be less optimal.

And it would be even less optimal if the strategy involved both long and short positions in the factors. The reason is that one factor could be long a security and the other factor could be short.

Thus, if the factors were targeted separately, the investor would not only be paying two fees for no net position, but would also be incurring unnecessary trading costs. (Note that there are funds, such as AQR’s Style Premia Alternative Fund, QSPIX, that avoid these problems. And in the interest of full disclosure, my firm, Buckingham, recommends AQR funds in constructing client portfolios.) Using multistyle funds is clearly optimal.

And that brings us back to the issue addressed by Fama and French: What’s the incremental impact of adding exposures to additional factors? Here again, intuition can help us.

**The Explanatory Power Of Asset Pricing Models**

The publication in 1992 of the paper “The Cross-Section of Expected Stock Returns” by Eugene Fama and Kenneth French, out of which came the Fama-French (FF) three-factor model, was a major advance from the original asset pricing model, the capital asset pricing model (CAPM).

The CAPM, while it did advance the science of investing and gave us the first formal definition of the relationship between risk and expected returns, was only able to explain about two-thirds of the difference in returns between diversified portfolios. Beta was the CAPM’s single factor.

As a simple example, if equity portfolio A returned 10 percent and equity portfolio B returned 13 percent, the two portfolios’ exposure to beta would be able to account for two-thirds (2 percent) of the 3 percent difference in returns. The FF three-factor model (adding size and value) increased the explanatory power of the model to more than 90 percent.

The annual average premiums for the three factors have been approximately 8 percent for beta, 3 percent for size and 5 percent for value. It’s important to note that the factor premiums are determined from long/short portfolios. A long-only fund will have exposure to just one side of the premium. For most factors other than beta, a reasonable estimate is to assume that approximately half the premium will come from the long holdings and half from the short holdings.

In our example, the FF three-factor model would now be able to explain more than 2.7 percent of that 3 percent difference in returns, leaving less than 0.3 percent that was unexplained. That remaining 0.3 percent could be a result of skill, luck or perhaps an as-of-yet undiscovered factor.

The important point is that, if we uncovered another factor, the incremental explanatory power wouldn’t be all that great because you could already explain more than 90 percent of the differences in returns (again, 2.7 percent of the 3 percent difference in the returns to portfolios A and B).

**Finding Factors**

In March 1997, Mark Carhart (in his study, “On Persistence in Mutual Fund Performance”) was the first to use momentum, together with the Fama-French factors, to explain mutual fund returns. And since 1998, the four-factor model basically has been the standard asset pricing (at least until recently, when profitability/quality has entered the debate).

This new momentum factor made a significant contribution to the explanatory power of the model. And the *annual* average return to the momentum factor has been roughly 8 percent. The explanatory power of the model improved by a few percentage points (into about the mid-90s range), which certainly doesn’t leave another factor the ability to add much more in the way of explanatory power, even if in isolation it produced a large premium.

The publication in 2012 of Robert Novy-Marx’s paper, “The Other Side of Value: The Gross Profitability Premium,” provided investors with new insights into the cross section of stock returns. Marx found that profitable firms generate significantly higher returns than unprofitable ones, despite having significantly higher valuation ratios.

Controlling for profitability—which Novy-Marx defined as revenue minus cost of goods sold divided by assets—increases the performance of value strategies, particularly when value is defined by book-to-market ratio. The most profitable firms earn average returns that are 3.7 percent per year higher than the least profitable firms.

This idea has been extended to a quality factor, which captures a broader set of quality characteristics. In particular, high-quality stocks that are profitable, stable, growing and have a high payout ratio outperform low-quality stocks with the opposite characteristics. And the explanatory power of the model was improved a bit further.

**Diminishing Returns**

And that brings us to the insight from the recent paper from Fama and French, which asserts: “Adding a variable with marginal explanatory power always shrinks the values of other explanatory variables.”

In other words, if a portfolio already has exposure to beta, size and value, adding exposure to momentum cannot add that much more in the way of incremental returns (certainly nothing anywhere close to the 8 percent annual premium momentum has provided, or even half that for a long-only portfolio). The reasons again are intuitive.

If you add exposure to a factor that has a positive correlation with the other factors already in the portfolio, then part of the explanatory power of the new factor is already accounted for by the exposure to the original factors. Fama and French explain: “Attenuation of variables already in the model almost always limits an incremental variable’s contribution to the expected return spread produced by a multivariate model.”

Thus, exposure to a new factor cannot add that factor’s full premium to the portfolio’s return. And if the factor being added is negatively correlated (as is the case with momentum and value) with existing factors, adding exposure to one factor (adding some expected return) will reduce the exposure to the other (subtracting some expected return).

This doesn’t mean, however, that there may not be an improvement in the efficiency of the portfolio. Adding factors that aren’t perfectly correlated can provide a diversification benefit. Another benefit is that adding negatively correlated factors can reduce the risk of catching the dreaded disease known as “tracking error regret.”

In fact, for many investors, once you get beyond the three factors of beta, size and value, this may be the biggest incremental benefit of adding exposure to additional factors.

Another issue to consider is that, when adding exposure to additional factors, you may also increase the turnover of the portfolio, increasing trading costs and reducing tax efficiency.

**Conclusion**

It’s highly likely that once investors have exposure to a few factors (four or five at most), adding exposure to others isn’t likely to produce much, if any, additional benefit in terms of incremental returns, especially when all implementation costs are considered. The takeaway for investors is to be cautious when looking at many of the new so-called smart-beta funds that provide exposure to many factors or styles.

*Larry Swedroe is the director of research for* The BAM Alliance*, a community of more than 140 independent registered investment advisors throughout the country.*