In part 1 of this article, we set the scene of putting Dunn’s Law to the test. In part 2, we will look at the results.
The results of this analysis demonstrate that differences in investment style between U.S. active and index funds can help explain the variation in success rates. However, the data did not clearly follow all the predictions of Dunn's Law.
The nine U.S. equity categories offer a cleaner test of Dunn's Law than the two international-stock categories because the index funds in each category have specific style constraints and are likely more style pure than their active counterparts.
Exhibits 1-3 show the results of the regression analysis for the nine U.S. equity categories. The numbers in all but the last column are the regression coefficients. The bolded coefficients are statistically significant. The cells highlighted in dark green are statistically significant with the sign Dunn's Law predicts (that is, the direction of the relationship between the variable and success rates mirrors the prediction of Dunn's Law); those highlighted in light green have the right sign, but are not statistically significant. Cells highlighted in red have the wrong sign and are significant, while those highlighted in light red only have the wrong sign. There were no clear predictions from Dunn's Law for those cells that are not highlighted. The adjusted R-squared figures show the proportion of the variability in success rates that the regression explains.
Overall, the model did a decent job explaining the three- and five-year success rates in most categories. It isn't surprising that the regressions had less explanatory power for the one-year success rates because there is more noise over shorter periods. As expected, there was a negative relationship between the performance of the market and active managers' success rates in every category except small growth. And all categories exhibited the expected positive relationship between success rates and the performance of international stocks relative to U.S. stocks.
However, the relationships between success rates and the value and small size factors didn't clearly fit the predictions of Dunn's Law. It's possible that our assumptions about how active managers differ from their index peers could be wrong. For example, active managers in the large-growth category could have a larger-cap orientation than their index peers, explaining why they might benefit from weaker performance among small-cap stocks. The size and value factors in the regressions could also be picking up other risk exposures that active managers might have.
But the best explanation for why there isn't a clean inverse relationship between the returns to active managers' investment style and their success rates is that these success rates are noisy. Changes in success rates are partially random and influenced by many variables the model does not capture. While it's possible that some periods may be more conducive to stock-picking than others, stock-picking success across managers is not highly correlated, so success rates are partially driven by luck of the draw.
The regression results for the foreign large-blend and diversified emerging-markets categories are shown in Exhibits 4 and 5. They were less supportive of Dunn's Law than the results for the U.S. equity categories, but they demonstrate that style differences between active and passive funds influence success rates.
Exhibit 6 shows the regression results for the intermediate-term bond category, which offer strong support for Dunn's Law, particularly over the three- and five-year windows.
The results of this study suggest there is some truth to Dunn's Law, but it doesn't always hold. Even though they don't always conform to the predictions of Dunn's Law, differences in investment style between active and index funds can explain much of the variation in success rates over time. But just as it is difficult to predict when the market will do well, it is difficult to predict when certain investment styles will be in favor. So, it's best to accept that active managers' success rates will be volatile and not try to time exposure between active and passive funds.