Swedroe: Book To Market & Size Premium

Looking at the value premium relative to book-to-market valuations tells us many things, but don’t try timing the size factor.e

Reviewed by: Larry Swedroe
Edited by: Larry Swedroe

Looking at the value premium relative to book-to-market valuations tells us many things, but don’t try timing the size factor.e

Since the 1992 publication of “The Cross-Section of Expected Stock Returns” by Eugene Fama and Ken French, the size factor has been among those used in asset pricing models that attempt to explain the differences in returns of diversified portfolios.

While Fama and French limited their model to three factors (beta, size and value), asset pricing models since 1998 typically have included momentum as a fourth factor. In the last few years, we have seen profitability (or quality or investment) added as a fifth factor.

Recently, the size premium has been called into question, because during the last 30 years (1984-2013), the annual size premium has been just 0.9 percent. In the 57 years prior to that (1927-1983), it had been 4.2 percent.

While the existence of a size premium is supported by a wide body of literature that provides a risk-based explanation for it, one explanation offered for the premium’s decline is the publication in 1981 of Ralph Banz’s paper, “The Relationship Between Return and Market Value of Common Stocks.”

This paper made the investing public aware of the outperformance attributed to the factor. And the publication of such findings can often lead to the shrinkage, or even elimination, of a premium. Elimination can occur if there is no risk-based explanation for the premium (only a behavioral one). Shrinkage, though not elimination, may occur if a risk-based explanation remains.

Trading Costs Add Up

A further explanation for the shrinking size premium could be that trading costs for small stocks, and trading costs in general, have declined as bid-offer spreads have narrowed dramatically.

One might argue that a belief among investors in the Federal Reserve’s ability to effectively dampen the risks of economic cycles (and thus the risks of small stocks) may help account for the declining size premium, as well as a falling equity risk premium.

Yet another explanation might be that stronger and improved government regulations, such as those included in the Sarbanes-Oxley Act of 2002, have reduced risks, and thus the required premium.

A September 2014 paper, “Discount Rates, Market Frictions, and the Mystery of the Size Premium,” provided a new and interesting insight into the size premium. The study, by Thiago De Oliveira Souza, covered the period 1927-2012 for the U.S. and 1980-2011 for the

U.K. The following is a summary of his findings:

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  • The average year-end size premium is significant (two standard errors above zero, 5 percent level of confidence) only when the beginning-of-year aggregate (median) book-to-market (BtM) ratio was historically high (in the top 10 percent).
  • The size premium tends to be insignificant (less than two standard errors above zero) or have the opposite sign in low or medium BtM years.
  • The findings held for both the U.S. and the


  • Changing the confidence level to one standard deviation leaves us with a significant size premium in only about one-third of the years (with a 10 percent level of confidence).

Souza’s Conclusion

Souza concluded that there’s a relationship between the time series variation in the discount rates (considering the aggregate BtM ratio as a proxy) and the cross-section effect known as the size premium. So it shouldn’t come as a surprise that the size premium is largest when the discount rate is high. Souza found the market premium is also highest when the BtM is high.

In other words, valuations matter. There’s nothing new there. But Souza did show that the size premium is not statistically significant in the other years, which make up the vast majority of the sample.

Souza’s findings raise the question of whether one should try to time the size premium. Before jumping to that conclusion, we should first consider the difference between economic and statistical significance.

In addition, there’s the matter of frictions (trading costs and taxes). While Souza found no evidence of a statistically significant size premium in the non-high BtM years, he did find that there was, in fact, a size premium of 0.9 percent in the low BtM years. But the t-stat was just 0.4, not even close to statistically significance.

More Interpretation

That’s not the same as economically insignificant, however. In the medium BtM years, there was virtually no premium (-0.1 percent). But in the high BtM years, the premium was 10.1 percent and the t-stat was almost 4, indicating a high level of statistical significance.

It’s also worth looking at the subperiod from 1963 through 2012. Here, Souza found that in low BtM years, the size premium was slightly negative at -0.4 percent with a t-stat of 0.1.


However, he found that in medium BtM years, the size premium was 3.9 percent, which certainly is economically significant, with a t-stat of 1.0. For the high BtM years, the premium was 7.5 percent with a t-stat of 2.5.

Looking at this subperiod, we now find an economically significant size premium in all but the low BtM years.

More Data To Consider

Here’s some additional data you should consider. The size premium has been persistent, and the longer the investment horizon, the more persistent it has become. For example, at the one-year horizon, there’s been a size premium almost 60 percent of the time.

At the five-year horizon, that figure increases to 65 percent. At 10 years, it’s at about 70 percent, and at 20 years, it’s more than 80 percent.

It’s also important to consider that, while the size premium has been less persistent than the value premium, this is explained, at least to some degree, by how the premiums are measured. Value stocks are considered the top 30 percent of equities when ranked by BtM (or other value metrics).

On the other hand, small stocks are considered the bottom 50 percent when ranked by market cap. If they were considered just the bottom 30 percent, not only would the premium have been larger, it would have been more persistent as well. Thus, if you own stocks in the bottom 30 percent of equities, instead of the bottom half, Souza’s evidence would likely have looked somewhat different for your portfolio.

Don’t Time The Size Premium

While it’s true that the size premium has been much larger in high BtM years, Souza’s findings shouldn’t tempt you into trying to time the size premium. Doing so would be tantamount to adopting a “tactical asset allocation” approach—and there’s insufficient evidence to warrant such a strategy. First, as we discussed, there’s generally been a size premium in most periods.


Even if it’s not statistically significant, it’s been economically significant. In other words, being out of small stocks except in the high BtM periods means you will likely miss out on a size premium in the other years. And costs, especially taxes, do matter.

Secondly, following such a strategy is what tactical asset allocation (TAA) funds have been doing for decades. And the evidence on their performance is pretty abysmal. For example, Morningstar recently reported that over the three years ending July 2014, TAA funds gained an annual average of 7.8 percent, or 3.8 percentage points per year behind their benchmarks.

Nothing New Here

And these findings are nothing new. My 2002 book, “Rational Investing in Irrational Times,” cited a study that found for the 12 years ending 1997, the S&P 500 rose 734 percent on a total return basis. The average return for 186 TAA funds was a mere 384 percent.

Finally, remember that disciplined rebalancing will likely require you to sell small stocks in periods of low BtM (because the low BtM was likely caused by strong performance) and to buy small stocks in periods of high BtM (because the high BtM was likely caused by periods of poor performance).

Thus, rebalancing will tend to reduce your exposure to small stocks when they’re expensive, but because you’re maintaining your portfolio’s asset allocation profile rather than trying to time the market.

Larry Swedroe is the director of research for the BAM Alliance, a community of more than 140 independent registered investment advisors throughout the country.

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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.