Small differences in monthly returns could potentially add up to a meaningful shortfall over a long time period; similarly, two funds can have an identical cumulative return but vary quite a bit between start and endpoints. The correlation between two funds can be equal but not capture the exaggerated movements of one fund relative to another, because it’s only a measure of the sympathetic movement between two series. Correlation measures pattern similarity and direction, basically the average frequency with which the two returns move together; it doesn’t take into account the magnitude of how asset returns move together.
There is no one-size-fits-all calculation to assess the comparability between our proxy-DFA and the authentic DFA that it is designed to imitate. The challenge is to create an alternative return stream that has the same first moment (mean return) and is equal in return distribution to the DFA fund it replaces.
Looking at the results, our Frankenstein blend tracks DFA’s Small Cap Value offering very well for the eight years that all of these funds have been available. DFA and the clone return 47.6 percent and 45.7 percent, respectively, in the out-of-sample period. Annualized over the entire period, DFA returns 0.61 percent, while the clone returns 0.60 percent. Correlation in the out-of-sample period is 0.97; beta is 0.85 and the tracking error is 0.95 percent (Figure 11). Typical tracking error for an active equity mandate is usually 5-7 percent, while anything under 2 percent is considered good for a passive index, so we consider the clone to be a good one.