"The results show that, in the 1936-1975 period, the common stock of small firms had, on average, higher risk-adjusted returns than the common stock of larger firms." That one sentence, which appeared in a paper by Rolf Banz published in the Journal of Financial Economics in 1981, is the foundation for the investment truism, "Small stocks beat large stocks." As it turns out, Banz was wrong.

Banz's groundbreaking research appeared originally in his paper, "The Relationship Between Return and Market Value of Common Stocks." His conclusion was later substantiated by Eugene Fama and Kenneth French in one of the most famous of all investment research papers, "The Cross-Section of Expected Stock Returns," published in the Journal of Finance in 1992. It has been accepted as true ever since.

For three decades, this belief has had a profound impact on the way financial advisors build portfolios. It also led to the launch in December 1981 of the Dimensional Fund Advisors U.S. Micro Cap Portfolio. (It was originally called the DFA U.S. 9-10 Portfolio, but was recently renamed.) The fund was designed to allow advisors to efficiently take advantage of the "small-beats-large" anomaly. Today, many investment firms emphasize the advantage of "going small."

However, our research does not support the idea but instead shows it's easier to argue the opposite-that large beats small.

Our Discovery
We believe that often an anomaly disappears or is diminished once its existence is widely known. The original purpose of our research was to explore what happened to the small-beats-large anomaly after it was revealed by Banz in 1981.

We started looking for our answer in the "post-Banz" period from 1982 through 2010. We analyzed the performance of small stocks relative to large and also compared the performance of both to the performance of the DFA U.S. Micro Cap fund to see if it had successfully capitalized on the idea that small beats large.

What we found was consistent with our original hypothesis-that the anomalies fade after they are discovered. We found that, on a risk-adjusted basis, large stocks performed better than both small stocks and the DFA U.S. Micro Cap Portfolio. No surprises there.

Then we looked at two different periods-the 56 years before Banz's paper came out (from 1926 to 1981) and the 29 years afterward-and tried to decide which of those two time frames most influenced investment history. We discovered large stocks prevailed in the post-Banz time period and we assumed, based on the earlier research, that small stocks prevailed in the pre-Banz time period. But we wanted to see what happened when you looked at these periods together. So we analyzed what we call the "full historical period"-1926 through 2010.

What we found was puzzling. We found that large stocks beat small stocks on a risk-adjusted basis over the full historical period. Though that in itself did not baffle us, what did was the extent to which large stocks beat small. We did not expect them to so greatly outperform.
To solve this mystery, we revisited the conclusions of the earlier researchers whose findings had been viewed as hallowed truth for so long. We analyzed the pre-Banz period and, for good measure, the exact period examined by Banz himself: 1936 to 1975.

What we found shocked us. Large stocks beat small in both periods. The long-held belief that small stocks beat large on a risk-adjusted basis is simply not supported by the facts.

How We Reached Our Conclusion
We analyzed the returns of two well-established indexes. To represent small stocks, we used the Center for Research in Security Prices (CRSP) 9-10 index. To represent large stocks, we used the S&P 500 index.

We chose these indexes for good reason. The CRSP 9-10 index is the premier small stock index and goes back to 1926. The S&P 500 also goes back to 1926 and is commonly used to represent the large stock universe. Ibbotson's Stocks, Bonds, Bills and Inflation uses the same indexes for these universes.

For each time period, we calculated the monthly "excess returns" of the CRSP 9-10 index and the S&P 500 index. We defined "excess return" as the return in excess of the risk-free rate. We used three-month T-bills to represent the risk-free rate.

We determined risk-adjusted returns using two measures. First, we determined the "alpha" of small stocks relative to large. A positive alpha indicates a higher risk-adjusted return for small stocks. A negative alpha indicates a higher risk-adjusted return for large stocks.
We also determined the Sharpe ratios for both indexes. A higher Sharpe ratio for one index relative to the other would indicate a higher risk-adjusted return for that index.

We also compared the "lag-adjusted monthly returns" of the CRSP 9-10 index and the S&P 500 index. Fama and French identified a problem that arises when you analyze the monthly returns of small stocks: Their prices can be "stale" because of the lack of trading during the month. Even though the prices "catch up" in the following month, this "lag" understates their true volatility, and thus their risk.
Fama and French addressed that problem this way: They compared small stock prices for a given month to large stock prices for both the current and the previous month. We did the same thing.