Recent empirical research provides useful insights into the factors managers consider. CRSP was the first to introduce investment rate ("INV") and return on assets ("ROA") as growth factors. Academic studies show that firms that invest more tend to grow faster, as do firms that are more profitable. Additionally, economic theory links both INV and ROA to expected stock returns.
CRSP studied its factors in typical empirical fashion: portfolio sorts along factor dimensions, cross-sectional Fama-MacBeth regressions, cross-sectional and predictive rank correlations, etc. We conducted individual and multifactor regression tests. Validation depended on achieving the behavior expected for the process: Value factors should explain variation in future returns, while growth factors should predict future growth.
However, CRSP also recognizes that investment managers possess information beyond that contained in scaled price ratios and growth statistics. The decisions these investors make are shaped by this unobservable information. We aim to capture that information by choosing an appropriate model—one that proxies for information managers know, but that we do not know. Naturally, the best proxies should be those that best emulate active managers.
CRSP's exercise was to find a set of weights for our factors that tracks the most widely used active manager indexes, Lipper and Morningstar, with limited error and low turnover. We ultimately evaluated more than 2,500 differently weighted candidate factor models before coming to our current design. Here there was a risk of over-fitting—selecting a model that was just representative of the world that did occur as opposed to one that is a better representation of all worlds that may have occurred. Simple rank tests helped stratify our models in sample. However, we also conducted a novel cluster analysis to understand broad functional classes of possible models. We were able to map the performance of these functional model classes back to the underlying factors to understand what factors managers used in their style appraisal and in what proportions these factors were likely considered. The cluster and ranking analysis agreed in a large number of cases, which gave us increased confidence in our ultimate index design.
CRSP arrived at a model that uses five value and six growth factors (Figures 4a and 4b). For value, our model groups forward and historical earnings to price ("FEP" and "HEP," respectively) into an EP factor and combines that with book to price ("BP"), creating a primary value superfactor ("V1"); sales to price ("SP") and dividend yield ("DP") create a secondary value superfactor ("V2"). The two value superfactors merge into a composite value score ("V"). Growth builds a future growth superfactor ("FG") from analyst-estimate future long-term growth in earnings ("FLGE"), analyst-estimate future short-term growth in earnings ("FSGE"), INV and ROA. A historical growth superfactor ("HG") comprises three-year historical growth in sales ("HGS") and three-year historical growth in earnings ("HGE"). The two growth superfactors combine to make a composite growth score ("G").
CRSP assigns each composite score a rank value ("RV" or "RG") as a percent of the cumulative market cap with lower scores. The growth score is inverted and the scores averaged to arrive at an average rank ("AR"). High ARs (those above 0.5) are value securities, low ARs are growth. As mentioned earlier, there is little agreement on what, specifically, value and growth are, or when, as often happens, a growth security becomes a value security (and vice versa). Therefore, we employ our threshold packeting mechanism here as well. As in the cap indexes, a security must pass a threshold beyond 0.5 AR before a 50 percent packet is moved to the adjacent style index (Figure 5). Again, this improves fit with manager behavior and dramatically decreases turnover.
