GB792 Unit 4 Asset Pricing Memo Example

Risk or Mistake: A Unit 4 Asset Pricing Memo on What the Value Premium Pays For

[Student Name]

Purdue University Global

GB792: Advanced Topics in Finance

Unit 4 Asset Pricing Memo

[Instructor Name]

[Date]

The memo concerns real published research; its position is the candidate's.

Memo

To: GB792 seminar From: Doctoral candidate Re: What would distinguish a risk premium from a mispricing in value stocks

Summary

The two leading explanations of the value premium make different predictions about whether returns follow a stock's exposure to a risk factor or follow its book-to-market ratio itself. The most direct test of those predictions, by Daniel and Titman, favored mispricing in one period; the reply by Davis, Fama and French, using a much longer sample, favored risk. The memo's position is that the evidence has not separated the accounts, and it names what would.

What the Premium Is

The value premium is the return earned by stocks with high ratios of book value to market value, value stocks, over stocks with low ratios, growth stocks. Fama and French (1993) built a factor to capture it, called HML for high minus low. Within groups of small and large stocks, the factor holds stocks in the top 30 percent of book-to-market and sells those in the bottom 30 percent. The average return to that factor over long samples of American stocks has been positive and economically meaningful.

Two Explanations, Two Predictions

The risk explanation. Fama and French (1993) argued that high book-to-market firms are often in financial distress or have poor prospects, and that their returns move together in a way that represents a risk investors cannot diversify away. Investors who hold them bear that risk and are paid for it. If this is right, a stock's expected return should depend on how strongly its returns move with the HML factor, its loading or covariance, whatever its current book-to-market ratio happens to be.

The mispricing explanation. Lakonishok et al. (1994) argued that investors extrapolate past performance too far into the future. Growth stocks, which have done well, are bid up on expectations that their growth will continue, and value stocks, which have done poorly, are sold down on expectations that their troubles will last. When results revert toward the average, value stocks outperform. If this is right, expected returns should depend on the characteristic itself, the book-to-market ratio, whatever the stock's covariance with any factor.

The predictions separate only when the characteristic and the covariance are pulled apart. Most of the time, high book-to-market stocks also load heavily on HML, so both explanations predict the same thing.

The Test and the Reply

Daniel and Titman (1997) designed a test to pull them apart. They sorted stocks first on book-to-market and then, within each group, on their estimated loadings on the HML factor. If risk drives returns, stocks with high loadings should earn more than stocks with low loadings even when their book-to-market ratios are similar. They found that, in their sample from the 1970s through the early 1990s, returns followed the characteristic and not the loading: within a book-to-market group, stocks with high and low loadings earned similar returns. They interpreted this as evidence against the risk explanation.

Davis et al. (2000) replied with a sample running back to 1929. Over that longer period, they found that loadings did help explain returns, and that the characteristic did not dominate as it had in the shorter sample. They argued that the Daniel and Titman result was specific to its period. The disagreement therefore turns partly on which sample is more informative: a shorter, more recent one with more precise data, or a longer one with more history and more variation.

The decisive test asks whether returns follow the ratio or the risk, and the answer changed when the sample changed.

The Memo's Position

The evidence has not settled the question. The direct test produced opposite answers in different samples, and each side has a reasonable argument for preferring its sample. The case for mispricing gains some support from the finding that value stocks did not perform especially badly in recessions or falling markets, when a distress risk premium would predict they should (Lakonishok et al., 1994). The case for risk gains support from the consistency of the premium across countries and long periods, which is harder to attribute to one pattern of investor error.

What Would Reverse the Position

Two kinds of evidence would move the memo toward one side. If the characteristic-versus-covariance test, repeated on new samples from other countries, consistently found that returns followed the ratio rather than the loading, the mispricing account would gain decisively. If, instead, value stocks were shown to do particularly badly in states of the world that investors fear most, such as deep recessions or financial crises, in a way that matched the size of the premium, the risk account would gain. Either would be more persuasive than further averages of the premium itself, which both explanations already predict.

References

Daniel, K., & Titman, S. (1997). Evidence on the characteristics of cross sectional variation in stock returns. The Journal of Finance, 52(1), 1-33. https://doi.org/10.1111/j.1540-6261.1997.tb03806.x

Davis, J. L., Fama, E. F., & French, K. R. (2000). Characteristics, covariances, and average returns: 1929 to 1997. The Journal of Finance, 55(1), 389-406. https://doi.org/10.1111/0022-1082.00209

Fama, E. F., & French, K. R. (1993). Common risk factors in the returns on stocks and bonds. Journal of Financial Economics, 33(1), 3-56. https://doi.org/10.1016/0304-405X(93)90023-5

Lakonishok, J., Shleifer, A., & Vishny, R. W. (1994). Contrarian investment, extrapolation, and risk. The Journal of Finance, 49(5), 1541-1578. https://doi.org/10.1111/j.1540-6261.1994.tb04772.x