Eugene Fama

Professor Fama Answers the Critics

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Eugene Fama


The earliest Fama-French research into the sources of stock returns generated controversy among academics. Many disputed the research and published their own findings. This is normal scientific procedure and leads to a more robust hypothesis. The ideas that withstand scrutiny are the strongest, and today the Fama-French model is broadly accepted among academics and investment professionals alike.Gene_Jr

In the following interview, Professor Gene Fama Sr. takes on familiar challenges to the study one-by-one.

Fischer Black, “Beta and Return,” The Journal of Portfolio Management, Fall 1993.

Soon after the initial findings in Fama-French, the late Fischer Black criticized the research. Black thought the findings were the result of data mining, and claimed beta was still the sole theoretical factor in returns. “We have literally thousands of researchers looking for profit opportunities in securities,” Black wrote. “They are all looking at roughly the same data. Once in a while, just by chance, a strategy will seem to have worked in the past. The researcher who finds it writes it up, and we have a new anomaly.” Black criticized that the model used factors to test a sample comprised of the same data in the same period.

GFJ: Since that time we have a lot of out of sample evidence. U.S. returns prior to the original period (1927-1963) confirm the original study, as do international returns in nearly every country where accounting and returns data are available.

Fama: You should keep in mind that Fischer was one of the inventors of the Capital Asset Pricing Model, so he had a bias towards a one-factor model. He had a kind of a vested interest. It was an understandable hypothesis, but it got tested.

There’s a long discussion of that in “Multifactor Explanations of Asset Pricing Anomalies” (Fama and French, Journal of Finance, 1996), then another in “Value vs. Growth: The International Evidence” (Fama and French, Journal of Finance, 1998), which extends it to International stocks, and then the “Characteristics, Covariances, and Average Returns” (Davis, Fama, and French, forthcoming) extends it back to 1927. So it’s been tested completely out of sample.

Tim Loughran, “Book-to-Market across Firm Size, Exchange, and Seasonality: Is There an Effect?,” Journal of Financial and Quantitative Analysis, Vol. 32, No. 3, September 1997.

GFJ: Loughran asserts that Fama and French’s empirical findings are driven primarily by two features in the data: a January seasonal in the book-to-market effect, and exceptionally low returns on small, young, growth stocks. He claims book-to-market has no explanatory power among large cap stocks, which makes it unimportant as a factor.

Fama: His thesis is that the value effect is much stronger in small stocks than in big stocks. And we tested that in “Characteristics, Covariances, and Average Returns”. What we find is

“He’s slicing and dicing in every possible way. When you do that you’re going to observe things, but it’s not clear they’re going to mean anything.”


that the value effect is bigger for small stocks in the second half of the sample period and it’s smaller in the first half of the sample period. In the overall period [1927-1998] it’s just about the same for big and small firms.

If you believe in the January Effect [that stocks have higher average returns in the month of January], there’s a big January seasonal in the book-to-market effect. It’s bigger in small value stocks than in small growth stocks, and it’s bigger in large value stocks than in large growth stocks.

We know there’s a big January seasonal in these stocks, and if you take that out, the rest of the return is smaller, obviously. But you can’t capture it. Trying to trade on the January effect is risky because there’s a huge variance.

He’s slicing and dicing in every possible way. When you do that you’re going to observe things, but it’s not clear they’re going to mean anything. His hypothesis was that it’s mostly underpricing of small value stocks and overpricing of small growth stocks, so value isn’t as important in big stocks because big stocks are priced better.

But then we tested that out of sample and it reverses. The larger firms had a bigger value effect from 1927-1962. In the overall period the effect was about the same for both large and small firms.

Peter J. Knez and Mark J. Ready, “On the Robustness of Size and Book-to-Market in Cross-Sectional Regressions,” The Journal of Finance, September 1997.

GFJ: Knez and Ready say that the risk premium on size disappears when the
one percent most extreme observations are trimmed each month. They also claim that the negative average of the monthly size coefficients are entirely explained by the 16 months with the most extreme coefficients.

Fama: What they’re doing is taking out the biggest manifestations of the effect, and it goes away. If you take out the biggest manifestations of the market return the market premium pretty much goes away as well. You can do that for anything and it’s going to go away.

That’s not the way you trim. When you trim, you have to trim on both ends. And there’s no way to implement a trimming strategy. If you knew in advance what were going to be the biggest months you could capitalize on that. David Booth did those calculations. All stock returns occur in spurts. The distributions are fat-tailed.

If you think the distribution is symmetric you can trim and it won’t effect the mean. But the distribution of annual returns is not symmetric, so when you trim, it effects the mean. For returns, the positive values are more positive than the negative values are negative. The distribution of daily returns are approximately symmetric, but the distribution of monthly, annual, or multi-year returns are highly skewed to the right, so trimming is not a good procedure.

Josef Lakonishok, Andrei Shleifer, and Robert W. Vishny, “Contrarian Investment, Extrapolation, and Risk,” Journal of Finance, December 1994.

GFJ: Lakonishok, Shleifer, and Vishny postulate that value strategies outperform because the strategies exploit the suboptimal behavior of the typical investor and not because the strategies are fundamentally riskier.

Fama: That’s just the contrary view – the view that book-to-market isn’t risk. We wrote a paper that addresses that one. They never even referenced the paper that shows it’s a risk factor (Fama and French, “Common Risk Factors in Bonds and Stocks,” Journal of Financial Economics, 1993). They ignored that evidence. We answered their paper in “Size and Book to Market Factors in Earnings and Returns,” Journal of Finance, 1996, and the paper after, “Multifactor Explanations of Asset Pricing Anomalies,” Journal of Finance, 1996.

GFJ: Is it enough that their portfolios are explained by your factors? Does that invalidate their perspective?

Fama: Ultimately, if you say the premiums are irrational I don’t know how to deal with that. They don’t address that the effects are explained in an asset pricing framework [evidence they are risk factors]. We tested some of their more detailed hypotheses about the behavior of earnings and things like that and didn’t find anything.

Keep in mind that they’re not quarreling with the value effect, they’re quarreling with the explanation for it.

GFJ: I think investors should care about that distinction because if it’s an underpricing, you might not expect it to repeat in the future. It’s important to have a market equilibrium case.

Fama: Right.

A. Craig Mackinlay, “Multifactor Models Do Not Explain Deviations From the CAPM,” Journal of Financial Economics, 1995.

GFJ: Mackinlay claims that returns the CAPM fails to explain are harder to measure and that multifactor models don’t capture these returns properly. Therefore, multifactor models do not improve on CAPM for cost-of-capital analysis.

“It’s just a religious claim that you can’t get a premium this big for the level of risk taken. But there are many economists who say the same thing about the market premium.”




Fama: He’s one of my students, actually. All he’s saying is that the 5% value premium in the model is too big. He thinks cost-of-capital estimates based on the model are too big because the historical premium is too big. So if you say it’s too big to explain by risk, part of it must be irrational, or chance.

We tested this out of sample. It’s just a religious claim that you can’t get a premium this big for the level of risk taken. But there are many economists who say the same thing about the market premium. The market premium is the same size as the value premium.

F. Douglas Foster, Tom Smith, and Robert Whaley, “Assessing Goodness-of-Fit of Asset Pricing Models: The Distribution of the Maximal R2,” Journal of Finance, June 1997.

GFJ: This study claims that R2 is not an appropriate measure of goodness-of-fit in regression functions like the three-factor model, where factors are supposedly not independent of the returns being analyzed. It proposes a simple procedure to adjust R2 values.

Fama: That’s a purely statistical study. All they’re saying is if you start with a set of variables and you search for the ones that have the most explanatory power, the R2 that you get is biased upward, because you searched the data for the one that had the most power. We never did that, we never searched over factors.

GFJ: What does it mean to “search over factors”?

Fama: It means that you’ve got a more general case, like you’ve got fourteen factors and you throw out the ones that don’t work.

GFJ: You guys looked at a lot of factors and consolidated them, right? You found book-to-market subsumed the effect of the other factors.

Fama: It subsumed the effect of price ratio factors. But it didn’t pick up the bond effect, it didn’t pick up the size effect. We’ve always said it doesn’t matter which price variable you use, book-to-market works, but earnings-to-price and cashflow-to-price work too.

This paper has nothing to do with that. “It’s irrelevant” is the answer to that one.