Has The Small-Cap Premium Disappeared?

October 07, 2013

A three-part column examines the much-talked-about small-cap premium.

[Editor's Note: This blog is the first of a three-part series IndexUniverse is publishing this week. Today's installment will be followed by columns on Wednesday and Friday.]

There has been some recent discussion calling into question the existence of the size premium. With that in mind, I thought it worth taking an in-depth look at the issue. The first of my three installments will start with the beginning of the small-cap premium research. Before we start, I ask that you keep the following quote from Mark Twain in mind: "The rumors of my death have been greatly exaggerated." Its relevance will become apparent as the data are explored.

The original research on the small-cap premium was done by Rolf Banz. Banz's paper was published in 1981. Among his findings was: "The results show that, in the 1936-1975 period, the common stock of small firms had, on average, higher risk-adjusted [emphasis mine] returns than the common stock of larger firms."

Professors Eugene Fama and Kenneth French looked at the evidence in their famous 1992 paper, "The Cross-Section of Expected Stock Returns." Their study covered the period 1963-1990. Their findings were different from Banz's. While they did find that small stocks had higher average returns, they believed the higher returns were compensation for risk, citing several papers that provided risk-based explanations. They certainly didn't state and—to my knowledge, have never stated—that small stocks provided higher risk-adjusted returns.

A close look at the data provides us with some interesting insights. The table below presents the data for the period covered by the Fama-French study (1963-1990), as well as the prior and succeeding periods, and the full period 1927-2012. Large stocks are represented by the Center for Research in Security Prices at the University of Chicago (CRSP) 1-5 Index (deciles 1-5); small stocks are represented by the CRSP 6-10 Index. The table presents the annualized returns.

Annualized Returns (%)

1927-1962 1963-1990 1991-2012 1927-2012
CRSP 1-5 (A) 9.22 10.15 9.33 9.55
CRSP 6-10 (B) 10.41 12.30 12.43 11.54
A-B 1.19 2.15 3.10 1.99


As you can see, small stocks outperformed large stocks over the full period, as well as each of the subperiods. In fact, not only hasn't the outperformance of small stocks disappeared, the greatest outperformance has been in the period following the publication of the Fama-French paper. There are several more important points to cover.

Defining Factors
In academic research, the returns to factors (such as size and value) are calculated in terms of average annual returns, not compound returns. In addition, factor (or risk factor) premiums are calculated in a different, more complex, manner. You don't simply subtract the annual average return to large stocks from the annual average return to small stocks. Instead, large and small stocks are first split into three categories: growth, neutral (or core) and value.

The calculation of the premiums is then done in the following way. You take the annual average returns of large growth, large neutral and large value, and divide the total by three. You then subtract the result from the same procedure for the three small-stock categories. This is done to try to isolate the small effect.

The table below shows the annual average returns for the same four periods we looked at earlier, as well as what is called the research premium (in this case, what is called SmB, or small minus big).


Annual Average Returns (%)

1927-1962 1963-1990 1991-2012 1927-2012
CRSP 1-5 (A) 11.86 11.34 11.08 11.49
CRSP 6-10 (B) 16.42 15.58 14.88 15.75
SmB Research Factor 2.93 3.37 2.95 3.08


You'll note that small stocks outperformed in all four periods. For information purposes, the table below shows the Sharpe ratio (a measure of risk-adjusted returns). The Sharpe ratio is calculated by taking the average annual return of the asset class and subtracting from it the annual average return on one-month Treasury bills (the riskless instrument) and dividing the result by the annual standard deviation of the asset class.

Sharpe Ratio

1927-1962 1963-1990 1991-2012 1927-2012
CRSP 1-5 (A) .448 .281 .419 .396
CRSP 6-10 (B) .407 .318 .505 .396


For the full 86-year period, small and large stocks provided identical risk-adjusted returns. However, you'll note that even though Fama and French never claimed that small stocks provided higher risk-adjusted returns—yet they did clearly state that they believe the higher returns are compensation for risk—in fact, small stocks did provide higher risk-adjusted returns during the period they looked at, and have also done so in the post-study period.

No matter how we have looked at it, the data clearly show that small stocks have provided higher returns over the long term, as well as in the post-1990 era. In other words, there has been a size premium.

By looking at the data from international markets, we can see out-of-sample evidence on the size factor.

The International Evidence

Dimensional Fund Advisors created an international small-stock index with data beginning in 1970. For the period 1970-2012, international small stocks outperformed international large stocks by 4.66 percent per year, returning 14.40 percent per year versus 9.74 percent per year for the MSCI EAFE Index.

Fama and French also provide us with another out-of-sample test with evidence from the emerging markets. For the period 1989-2012, the Fama-French Emerging Market Small Cap Index returned 13.44 percent per year, outperforming the 12.29 percent per year return of the large-cap Fama-French Emerging Markets Index by 1.15 percentage points per year.

In the next installment, we'll turn to the issue of whether the publication of the findings or outperformance automatically leads to the disappearance of a premium.

Larry Swedroe is director of Research for the BAM Alliance, which is part of St. Louis-based Buckingham Asset Management.


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