The Paper that Formalized the Size Premium


At Index Fund Advisors, we implement portfolios for our clients that are tilted towards the compensated risk and return factors of small cap, value, and profitability. In this article, we will review the paper1 published in 1981 that formally identified the size premium, The Relationship between Return and Market Value of Common Stocks by Rolf W. Banz of Northwestern University.

Utilizing finance-specific multiple regression techniques developed2 by Fama and Macbeth (see here for a summary), Banz established the following:

"It is found that smaller firms have had higher risk adjusted returns, on average, than larger firms. This ‘size effect’ has been in existence for at least forty years and is evidence that the capital asset pricing model is misspecified."

Banz utilized individual stock data from the Center for Research in Security Prices which at that time only had NYSE listings. The forty-year period that he references above ranged from 1/1/1936 to 12/31/1975. It is interesting to note that his article was not actually published until more than five years after the data ending date. This is an indication of how long it took to analyze a large amount of data (the paper was submitted in 1979) as well as the couple of years required for peer review.

Banz makes an interesting observation about the size premium when he says, “The size effect is not linear in the market value; the main effect occurs for very small firms while there is little difference in return between average sized and large firms." The bar chart below illustrates this point.

Banz’s paper was historically significant in practical finance, as 1981 marked the founding of Dimensional Fund Advisors by David Booth and Rex Sinquefield. Its flagship offering was the DFA U.S. Micro Cap Portfolio whose purpose was to capture the size premium by staying in the lowest two size deciles while trading in a patient and opportunistic manner. As the table below shows, it has done an excellent job in delivering those returns.

Banz makes a very interesting comment at the end of the abstract and raises a question that remains unanswered to this day:

"It is not known whether size per se is responsible for the effect or whether size is just a proxy for one or more true unknown factors correlated with size."

At Index Fund Advisors, we consider smaller firms to be riskier and risk and return are inseparable. Here is how we explained it in a prior articleThe relationship between risk and company size is apparent in the credit ratings assigned to bonds issued by different companies, according to this research report in which the author explains the relationship: “Larger companies tend to have higher credit ratings. Empirically, size metrics offer the strongest statistical correlation with credit ratings—reflecting important qualitative factors such as geographic and product market diversification, competitive position, bargaining power, market share and brand stature.” If smaller companies have a higher cost of capital for their debt, then it stands to reason that they would have it for their equity as well. Recall that a company’s cost of capital is paid to its investors as returns.

If you would like to learn more about how IFA builds portfolios to capture the small premium as well as other risk premiums around the world, please call us at 888-643-3133.

1Banz, Rolf W. 1981. “The Relationship Between Return and Market Value of Common Stocks." Journal of Financial Economics, vol. 9, no. 1(March):3-18.

2Fama, Eugene F., and James D. Macbeth. 1973. “Risk, Return, and Equilibrium: Empirical Tests.” Journal of Political Economy, vol. 81, no. 3 (May-June):607-636.