Second, DFA's effort to capitalize on the small-beats-large anomaly was not successful. The DFA fund outperformed the CRSP 9-10, but did not outperform the S&P 500 on a risk-adjusted basis.
Finally, even DFA's original success in implementing its small-cap strategy faded in recent years. For the 20 years ending 2010, the DFA fund returned 13.48% annualized, while the CRSP 9-10 returned 14.52%. The gap was even wider for the ten years ending 2010. The fund returned 9.63% and the index 12.58%.
Next let's look at the full historical period (1926 to 2010). The results are shown in Figure 2.
The pattern is similar to the pattern for the post-Banz period. The CRSP 9-10 has an absolute return advantage over the S&P 500.
On a risk-adjusted basis, the monthly returns show the CRSP 9-10 has an advantage over the S&P 500 if you use alpha as the measuring stick, but gives the advantage to the S&P 500 if you use the Sharpe ratio. With lag-adjusted monthly returns, the alpha advantage for the CRSP 9-10 gets smaller and the Sharpe ratio advantage for the S&P 500 gets larger. With annualized returns, the advantage goes to the S&P 500 whether you use alpha or the Sharpe ratio as a measure of risk-adjusted return.
Now let's examine the pre-Banz period (1926 to 1981). The results are shown in Figure 3.
Again, we find the CRSP 9-10 index has higher absolute returns than the S&P 500 index regardless of how you look at the data-monthly, lag-adjusted monthly or annualized.
Looking at monthly returns, the CRSP 9-10 also has a higher risk-adjusted return than the S&P 500 when using either alpha or the Sharpe ratio as the measure. When looking at lag-adjusted monthly returns, the alpha advantage for small stocks is reduced and the Sharpe ratio advantage shifts to large stocks. Looking at the annualized data, the alpha advantage for small stocks almost disappears and large stocks continue to hold a slight advantage in the Sharpe ratio analysis.
Finally, let's examine the period from 1936 through 1975. This is the time period originally analyzed by Rolf Banz. The results are set forth in Figure 4.
Once again, we find the absolute returns for the CRSP 9-10 are higher than for the S&P 500, reflecting the greater risk of small stocks. When Banz originally examined this period, he concluded that investors were more than fairly compensated for this additional risk.
That conclusion appears questionable. Looking at monthly returns, the CRSP 9-10 shows a positive alpha relative to the S&P 500, giving small stocks the edge in risk-adjusted return. But the Sharpe ratio analysis suggests that large stocks may actually hold the advantage.
Looking at lag-adjusted monthly returns, the alpha advantage for small stocks drops dramatically and the Sharpe ratio advantage for large stocks increases. Looking at the annualized data, large stocks are superior on a risk-adjusted basis whether you use alpha or the Sharpe ratio as your measuring stick.