Fama and French Factors

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The value and size effects were exquisitely documented by Eugene Fama and Kenneth French in their Journal of Finance masterpiece (1992). They found that, in addition to broad market exposure, exposure to value stocks and small-cap stocks increases a portfolio's expected

18.08%

17.50%

11.23%

Russell 1000

Russell 2000

Figure 10.5 Fundamental Index Performance in Large-Cap Cycle, 1984 through 1998

Source: Research Affiliates, LLC.

RAFI U.S. Large

Russell 1000

Russell 2000

Figure 10.5 Fundamental Index Performance in Large-Cap Cycle, 1984 through 1998

Source: Research Affiliates, LLC.

return. That is, diversified portfolios of value stocks and small-cap stocks can earn more than a large-cap portfolio of similar market beta! Fama and French subsequently posited that value and small-cap exposure must be substantially more risky than what is suggested by their market betas (as measured by the CAPM). After all, in a rational and efficient market, additional return can be had only through taking on more risk.

Critics of the Fundamental Index strategy argue that the RAFI concept does not create economically significant alpha; it just takes on more value and small- cap risk. If so, the Fundamental Index strategy is nothing new. It is just a way of embedding value and small-cap exposure into a portfolio in an intelligent and dynamic way (by contra-trading against the market's largest excesses). We agree. In fact, we pointed out this nuance in the article (Arnott, Hsu, and Moore, 2005) that introduced the Fundamental Index concept.

The Fama-French model is a long-short model. To mirror the behavior of a portfolio very different from the cap-weighted market while using the Fama-French factors, one must be prepared to have some short positions. For the RAFI U.S. Large at the peak of the bubble, the Fama-French mirroring portfolio (the Fama-French portfolio that precisely matched the beta and style tilts of the Fundamental Index portfolio) was approximately 115 percent long and 15 percent short. The investor willing to take long and short positions can replicate the characteristics of the Fundamental Index strategy by (1) complementing an S&P 500 or Russell 1000 core portfolio with an overlay of long-short satellite portfolios that are long in deep-value and small-cap names and short in high-growth and mega-cap names; (2) shifting the composition of these long-short portfolios as the constituent holdings change; (3) shifting the size of these long-short overlay portfolios monthly, to match the changing style tilts of the RAFI program over time; and (4) frequent rebalancing. That's a lot of work to match a dumb old index that just selects and weights companies by their fundamental footprint in the economy!

When applied to the Fundamental Index concept, not surprisingly the Fama-French model shows an exposure to the value effect and, to a modest extent, to the size factor. Surprisingly, even net of these factors, the Fundamental Index portfolio earned an estimated alpha of 30 basis points from 1979, when Russell style portfolios were first available, through 2006. In contrast, most indexes, particularly those with a value tilt, exhibited a negative Fama-French alpha in that period, as shown in Table 10.3. In fact, as far as we are aware, no other existing indexes offer a value tilt relative to the cap-weighted markets while avoiding large negative Fama-French alphas.

The Davis analysis (2007) for 1940 through 1962, which we covered in Chapter 7, had similar Fama-French results for the Fundamental Index strategy. He focused on the lack of a significant alpha, net of the Fama-French three factors, and the consistent value tilt of the Fundamental Index portfolios. Unlike Davis, we focus on the raw return difference of more than 200 basis points per year in his results, leading to 40 percent more wealth after just 22 years. After all, few investors would be happy with a poor rate

Table 10.3 Fama-French Alpha Comparison, 1979 through 2006

Portfolio

Annual Return

Fama-French Alpha

Adjusted R2

Small

Value

Beta

RAFI U.S. Large

15.8%

0.3%

0.97

-0.10

0.36

1.03

Russell 1000

13.5%

0.4%

1.00

-0.15

0.01

1.01

Russell 1000

Value

14.6%

-1.1%

0.96

-0.15

0.44

1.02

Source: Research Affiliates, LLC.

Source: Research Affiliates, LLC.

of return and a positive Fama-French alpha if the alternative is a higher rate of return with no Fama-French alpha!

Mark Carhart extended the Fama-French model by observing that price momentum also carries unexpected rewards. It's interesting to note that a Fundamental Index portfolio will sell winners if their economic success hasn't risen commensurate to the rise in share price. Because momentum strategies add value and because a Fundamental Index portfolio trades against momentum, we should have been hurt by the anti-momentum character of our portfolio. It's striking to note that the 0.3 percent Fama-French alpha on Table 10.3 soars to 1.1 percent in the Fama-French-Carhart analysis. This is 1.1 percent of return, which is utterly unexplained in a Fama-French-Carhart model!

We find the relatively neutral results for the Fundamental Index concept relative to the Fama-French factors not at all surprising. A well-specified risk model ought to be able to explain the differential returns of simple indexes constructed in a formulaic fashion with no overt stock selection. The Fundamental Index concept is nothing if not simple, and the Fama-French three-factor risk model is obviously a well-specified risk model. That being said, it's clear that the Fundamental Index portfolio captures these factors more efficiently than existing commercially available benchmarks and products. It is far simpler to implement than a core-satellite approach, in which we create a core of market- replicating equities plus Fama-French long-short factor portfolios. The complexity of the replication, the cost associated with managing the Fama-French factor portfolios, and the potential need to hold short positions that at times will be quite large make the Fundamental Index approach more attractive from an implementation perspective.

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