Swedroe: Looking At Value Premiums

The size factor is a risk premium, but what about the value factor?

Reviewed by: Larry Swedroe
Edited by: Larry Swedroe

The size factor is a risk premium, but what about the value factor?

Today’s post will begin a two-part series that explores the research examining risk-based explanations for the value premium, which, unlike the risk-based explanations of the size premium, have been a bit controversial.

In June 1992, the paper “The Cross-Section of Expected Stock Returns” was published in the Journal of Finance. The authors, Professors Eugene F. Fama and Kenneth R. French, demonstrated that size (market capitalization) and the book-to-market ratio (BtM) had more explanatory power for stock returns than did market beta (exposure to stock market risk)—the traditional measure of risk.

While Fama and French didn’t attempt to identify the source of the incremental returns (premiums) provided by exposure to size and value (high BtM) stocks, they did posit that size and BtM are proxies for risk. The premiums, therefore, are compensation for risk-taking. Thus, the size and value premiums have often been called risk premiums.

While there has been little controversy over the source of the size premium—it’s accepted that small stocks are riskier than large stocks—there has been a great debate as to the source of the value premium.

There is a belief among many academics that the value premium is actually an anomaly, meaning they believe it may contradict the efficient markets hypothesis—the result of persistent pricing errors made by investors. For example, those from the “behavioral school” of finance believe that investors naively extrapolate past growth when evaluating a company, and thus overreact to that information.

In other words, growth companies are persistently overpriced and value companies underpriced. Behaviorists also find that investors confuse familiarity with safety. Since they tend to be more familiar with popular growth stocks, those stocks tend to be overvalued.

The debate—is it a risk premium or an anomaly?—among financial economists rages on, with supporting evidence on both sides. Today we take a look at the evidence from some of the papers that support the risk explanation for the value premium.

We begin with the 1998 paper “Risk and Return of Value Stocks, by Nai-fu Cheng and Feng Zhang. Their work makes the case that value stocks do contain a distress (risk) factor. The authors make their case by examining three factors of distress present in value companies:

  • DIV: Firms cutting dividends by at least 25 percent
  • LEV: A high ratio of debt to equity
  • SEP: A high standard deviation of earnings

The authors found that the three factors all captured the returns information contained in portfolios as ranked by BtM; that is, produced high correlations. When these three factors were present, the returns were greater.

Since all three factors have simple intuitive risk interpretations—that is, are associated with firms in distress—they stated that it isn’t surprising that the risk factors they studied were highly correlated and were also highly correlated with BtM rankings.

Their conclusion was that value stocks are cheap because they tend to be firms in distress, with high leverage that face substantial earnings risk and, therefore, provide higher returns due to the greater risks facing value investors.


Our second paper is the 2005 study “Is the Book-to-Market Ratio a Measure of Risk?” The authors developed a leverage-based approach to investigate the BtM effect. Since leverage is risky, it isn’t surprising that they found there is a positive relationship between higher stock returns and market leverage.

Their regression results also found that when compared with market leverage, the BtM ratio added a small amount of explanatory power for stock returns. They stated that they believe the incremental power of the BtM ratio is due to additional information about the riskiness of the firm’s assets.

Thus, they concluded that BtM effect is mostly a leverage—or risk—effect.The authors had another interesting find. When they considered only companies that they called “all-equity” firms—that is, firms with nominal amounts of debt, mostly current liabilities—there was no BtM effect at all.

In other words, if the value premium is an anomaly, the mispricing should show up in all high BtM firms, not just those with high leverage.

The third paper is the 2004 study “Default Risk in Equity Prices.This was the first paper to use an option-pricing model to compute the risk of default for individual firms. Unlike prior studies on default risk that used accounting information, this study used market valuations for debt and equity.

The rationale for using market information is that accounting information is backward-looking, while market information is forward-looking. In other words, market information contains information about investor expectations, and thus is better suited for calculating the risk of a future default.

Another benefit of this approach is that accounting data doesn’t consider the volatility of a firm’s assets. Intuitively, the volatility of a firm’s assets should be positively correlated with the likelihood of default. The authors used the market-based data and the option-pricing model to assess the effect of default risk on equity prices.

They concluded that the size effect results from default risk, and that this is also largely true for the BtM effect. They found that both premiums exist only in the segments of the market with high default risk.

Also of interest is that they found that high-default-risk firms provide higher returns only if they are small or have high BtM. Finally, they also concluded that the BtM ratio contains additional information about stock returns that is unrelated to default risk.

Next time, we’ll explore more research as well as the implications these findings have on investors.



Larry Swedroe is director of Research for the BAM Alliance, a community of more than 130 independent registered investment advisors throughout the country.


Larry Swedroe is a principal and the director of research for Buckingham Strategic Wealth, an independent member of the BAM Alliance. Previously, he was vice chairman of Prudential Home Mortgage.