Combining equity risk factors: Implementation matters

In the financial literature, considerable evidence shows that equity tilts toward risk factors such as small size, high value or low volatility can, over time, earn excess returns above capitalization-weighted benchmarks. However, the bulk of this research addresses only the existence of individual factors, and relatively little attention has been paid to how factor-based strategies are best implemented.

The genesis of equity style factors can be traced to the seminal work in 1992 of Eugene Fama and Kenneth French, who proposed that size and value factors are indeed compensated. While the investment community has clearly come to understand the main message of Messrs. Fama and French — that excess returns can be generated from size and value factor tilts — what remains somewhat less understood is the secondary message of this research: that size and value are, in fact, independent sources of excess return.

Recognizing factor independence is critical, for it makes possible the efficacy of multifactor strategies. If returns to small size and high value are indeed independent and uncorrelated, investors can benefit from factor diversification by combining size and value tilts into a single multifactor strategy. In the past two decades other credible risk factors — such as momentum, dividend yield, quality and low volatility — have emerged. Research suggests these style factors are likewise compensated and potentially uncorrelated.

While the benefits of multifactor strategies are uncontroversial, there is little agreement within the industry as to the best approach for implementing multifactor exposure. To date, two primary avenues have emerged:

• Blending of single-factor portfolios. In this approach individual portfolios targeting single style factors are formed and discrete allocations are made to each portfolio. For example, an investor might choose to put 50% of assets in a portfolio targeting high-quality stocks and 50% in a portfolio targeting high-value stocks in order to obtain a multifactor quality/value tilt.


• Multifactor intersection portfolio: In this approach a single portfolio is constructed that targets stocks at the intersection of two or more style factors. For example, an investor might choose to put 100% into a portfolio buying stocks that are simultaneously high quality and high value to obtain a multifactor quality/value tilt.

Which approach is better? In this article we provide a conceptual model and empirical evidence that the blending of single-factor portfolios, although ubiquitous, is suboptimal and multifactor intersection portfolios produce superior results.

Figure 1A depicts a hypothetical universe of stocks such as the MSCI World or Russell 3000 as a square arrayed along two dimensions: quality and value. In a blended implementation of quality and value factors, we would buy a quality index consisting of, say, 50% of the names in the universe with the highest quality ranking. The holdings of this index are depicted as the blue shaded region. Likewise we would also buy a value index that consists of 50% of the names in the universe with the highest value ranking. These holdings are depicted as the yellow shaded region.

Importantly, note that because quality and value factors are known to be independent, the overlap between the holdings of these indexes will be approximately 50%. Thus, Figure 1A is an accurate depiction of reality, despite its simplicity. Therefore, in our example, blending quality and value indices will force the investor to hold upward of 75% of the names in the universe. Independence guarantees high-quality companies are a mix of high and low value and, conversely, high-value companies are a mix of high and low qualities. Thus, a blended strategy aimed at a quality/value tilt will hold many low-quality and low-value names, in this case up to half of the total portfolio. This suggests a possible and potentially significant dilution effect to blended strategies.

In contrast, a multifactor intersection portfolio targets just those names that are simultaneously high quality and high value. This is depicted in Figure 1B as the green shaded box. The intersection allows the investor to hold a smaller subset of names and not force them to buy low-quality and low-value stocks as in the blended approach. As a result, we would expect the performance of the multifactor intersection portfolio to exceed that of the blended approach.

Note the dilution problems of the blended approach are exacerbated as you increase the number of factors. Assuming each style factor index holds 50% of universe names and all factors are independent, then a three-factor tilt would require the investor to hold 87.5% of the names in the universe while a four-factor tilt requires nearly 93.8%. At these levels the actual factor exposures are largely muted, and returns to the multifactor strategy converge to the simple beta return of the universe. Hence, there are fleeting benefits to a blended multifactor tilt.

To provide empirical support for our conceptual model we created single-factor portfolios for size, value, volatility, dividend yield using the MSCI Barra definition of the factors and quality using the Northern Trust Quality Score. Within the Russell 3000 universe, we ranked stocks each month from January 1979 to June 2013 based on these factors and placed stocks into five quintiles. Individual-factor portfolios represent the equally weighted performance of the most advantageous two quintiles, namely, highest quality, highest value, smallest size, lowest volatility and highest dividend yield. The returns and volatilities of these portfolios as well as 50/50 blends of individual factors with quality are charted in Figure 2.

We also created intersection portfolios using the same rankings and quintiles by selecting only those stocks that were jointly within the top two advantageous quintiles of factor pairs. For example, for a quality/value intersection portfolio we would include only those names that were simultaneously in both the top two quintiles of quality and the top two quintiles of value. Return and volatility characteristics of these intersection portfolios are also shown in Figure 2.

Note that all of the individual factor portfolios outperformed the Russell 3000 benchmark. This is expected, as substantial evidence demonstrates that these style factors earn excess returns over time. However, for all factor pairs the return of the intersection portfolio significantly exceeded that of the blend and the standard deviation was roughly equal to or less than that of the blend portfolio. All of these differences in performance are significant at the 95% confidence level indicating that intersection portfolios do indeed earn higher returns than the blended counterparts as predicted by our conceptual model. The dilution effect inherent in the pervasive blended approach is very real and can significantly impair performance.

Michael Hunstad is director of quantitative research at Northern Trust Asset Management in Chicago.