The Cross-Section of Expected Stock Returns:
A Tenth Anniversary Reflection

Ten years ago this month, Eugene Fama and Kenneth French fired the shot heard ’round the world. Its echoes still plainly reverberate today in boardrooms and trading floors. And although most investors are unaware, these effects also appear regularly in their mailboxes under the guise of investment-account statements.

The projectile in question was a 39-page piece bearing the above title, published in the June 1992 edition of Journal of Finance. It was no walk in the park; even among the Journal’s rarefied readership, I doubt many grasped the full meaning without multiple readings and hours of peer discussion.

Its import lay on three levels:

• The month-to-month performance of a diversified portfolio of U.S. stocks can be explained by only three factors: the portfolio’s exposure to the market itself, to small-cap stocks, and to value orientation (the latter defined by price-to-book ratio). In plain English, "Show me the returns series of any U.S. diversified portfolio and, in almost every case, I can explain nearly all its performance based on these three factors; the precise securities are irrelevant." And, "Oh, by the way, without knowing exactly what’s in this portfolio, I can tell you the median market cap and price-to-book ratio just by looking at its returns."

• The corollary of their work was that once one considered the size and value factor "loadings" of a diversified U.S. all-stock portfolio, the market loading—Sharpe’s famous "beta"—did not explain return. In other words, portfolios of high-beta stocks did not have higher returns than portfolios of low-beta stocks. Beta was dead.

• Most importantly, the size and value factors, because they were surrogates for risk, had positive returns. Therefore, value stocks should have higher returns than growth stocks, and small stocks, higher returns than large stocks; small value stocks should have the highest returns of all. The one place where the model "didn’t work" was with small growth stocks, which empirically had much lower returns than expected, having the worst performance of the four "style corners" (large growth, large value, small value, and small growth).

Heeding these findings, investors (myself included) began to accumulate small- and value-weighted portfolios and promptly had their heads handed to them. Suppose it took several months to read the piece, confer with your savviest colleagues, and assemble a portfolio loaded down with small value stocks on January 1, 1993. Here’s how the "four corners" of the equity world, as defined by Fama and French, would have fared over the next seven years.

(But first, let me explain the Fama and French definition of the four corner portfolios. In the simplest case, stocks are split into two halves by size: "large" constitutes size deciles one through five of the CRSP (Center for Research in Security Prices) database, and "small," deciles six through ten. "Value" and "growth" are defined as the bottom and top 30% of stocks sorted by price/book.)

Annualized Returns, January 1993 to December 1999
Small Value: 13.90%
Small Growth: 16.92%
Large Value: 15.72%
Large Growth: 21.64%
Wilshire 5000: 20.47%

Mind you, you’d still have done fine, thank you. But not nearly as well as your uncouth, beer-swilling, Janus fund-buying neighbors. (And not as well, for that matter, as the folks at Vanguard, who have never bought into the model and still insist that the optimal core equity holding is their Total Stock Market Fund, which tracks the Wilshire 5000 and is heavily weighted towards large growth stocks.)

It didn’t help that the biggest proponent of the model was Dimensional Fund Advisors, an institutional fund company that eschews the mass market and does not go out of its way to cultivate journalists. The latter proceeded to have a field day at the expense of multifactor investing, turning back on its creators the old efficient-marketeer observation that market-beating strategies have a nasty habit of disappearing the moment they are described.

Academicians raised a more serious objection—Fama and French were guilty of data-mining; their results were an artifact of the U.S. market during the article’s study period from 1963 to 1990. And finally, practitioners raised the most serious objection of all: small- and value-oriented strategies could not be implemented. Yes, in a frictionless world, excess returns could be earned. But in the real world, you’d be eaten alive with commissions and transactional costs.

In their quiet way, Fama and French disposed of the data-mining  j’accuse. They examined stock markets abroad, then those in the U.S. before 1963. Value and size premia were found on every hill and under every rock.

Then at last, the markets themselves came to their rescue. In 2000, the tech-led large-growth dominance began to violently unwind. By early 2002, all the damage to a multifactor strategy was more than undone. So let’s extend the returns of the above hypothetical investor to April 30, 2002.

Annualized Returns, January 1993 to April 2002
Small Value: 15.23%
Small Growth: 8.20%
Large Value: 10.43%
Large Growth: 11.08%
Wilshire 5000: 11.69%

Suddenly, the world according to Fama and French is a much happier place, where savvy, patient investors favoring small value stocks reap their due rewards.

But what about the implementation objection: Can these factors be captured in real life? Yes, indeed. Looking back from the vantage point of April 30, 2002, there is no time period when the DFA U.S. Small Cap Value strategy has not been king of the hill. The below graph plots "backward-looking" returns from this date. The graph takes a bit of getting used to, but basically plots your return to April 30, 2002 from any given starting point. All of the four strategies listed (DFA does not run growth funds) are commercially available from them.

Extend the graph back before the fund inceptions in 1993 using theoretical data and the picture is even prettier:

For foreign stocks, things aren’t as agreeable. DFA has had all four international corners running since 1995. Value seems to hold up, but size does not:

If you use theoretical data and go back far enough, eventually small does provide a positive return, but you have to go back 15 years, to 1987, for this to occur.

Finally, in the emerging markets arena, with astronomical transactional costs, particularly for value and small stocks, the three-factor model seems to be defending its turf. DFA’s plain-vanilla Emerging Markets fund incepted in 1994, their Emerging Markets Value (large-cap) fund began as an institutional portfolio in 1995, and the Emerging Markets Small Cap started in 1998. Here’s how things look back to 1995 (with theoretical data used for the small-cap portfolio before 1998):

What’s a small investor without access to DFA to do? For U.S. small-cap value, Vanguard Small-Cap Value Index Fund, although it includes a fair slug of "blend" in addition to "value," seems to track the DFA fund nicely and has nearly identical small and value loadings.

The same cannot be said for the Vanguard Value Index Fund (for U.S. large-cap value), which does not seem to capture the value factor very well and whose median market size is considerably greater than that of the DFA U.S. Large Value fund, which, truth be told, is really a midcap value fund. The lack of a retail U.S. large-cap value index fund has a relatively quick fix: the iShares Midcap 400 Value offering (an ETF, so be careful about dollar-cost or value averaging with this one).

The Vanguard International Value Fund also does a pretty good job of capturing the value factor return, though it is not an index fund. Since the 1994 inception of DFA International Value, the Vanguard offering (which is far older) tracks the DFA fund very closely and lags it by only 0.4% per year.

But if you want international or emerging-markets small or value exposure, you’re out of luck. Fortunately, these make up a relatively small part of most investors’ portfolios. I’d stay away from active funds in these areas for the usual reasons—tracking error and very high expenses.

So, after ten years, the three-factor approach, which overweights small size and particularly value, seems to be alive, kicking, and eminently doable, even for the small Vanguard-only investor. But, as the 1990s demonstrated, no small amount of patience may be required, and many fools may have to be suffered.

Copyright © 2002, William J. Bernstein. All rights reserved.

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