It's often assumed that some value funds (e.g. from DFA) are more style consistent than other funds (e.g. those tracking the S&P, MSCI and Russell indexes).

I have tried to test whether this has been the case (using backtested index data). The methodology used was as follows:

- 1) Estimate the factor loadings of several value indexes (funds) over the period July 1995 to April 2007 (presented in this earlier post).

2) Calculate the monthly returns (R-Rf) implied by the factor loadings estimated over this period (as factor loads multiplied by the respective annual Mkt-Rf, SmB, HmL returns).

3) Calculate rolling 36 month correlations between the historical annual index (fund) returns (less the risk free rate) and those implied by the factor loads (calculated in 2).

The results below are listed from most style consistent to the least style consistent (as defined above) for a set of mid-cap indexes (tickers for funds currently tracking these are also listed) and for a set of small-cap indexes (including the DFA small value fund).

All the indexes were fairly style consistent. The DFA small value fund was the ‘most style consistent’. The Russell indexes also did fairly well. The least consistent was the S&P 600 pure value index. The S&P 600 value index came out slightly ahead of the MSCI small value index (the reverse was true for mid-cap value). One caveat - the numbers just tell us about correlations and not the absolute return differences with the FF factor load equivalent.

Code: Select all

```
Results for 36 month rolling correlations (107 in all) between 'actual' returns and
those implied by estimated factor loadings over July 1995 - April 2007
Correlations
Average Highest Lowest SD
MID-CAP VALUE
Russell Mid Cap Value [IWS] 0.96 0.97 0.90 0.017
MSCI US Mid Cap Value [VOE] 0.95 0.97 0.89 0.019
S&P 400 Value [IJJ] 0.94 0.96 0.88 0.022
SMALL-CAP VALUE
DFA Small Value 0.98 0.99 0.94 0.011
Russell 2000 Value [IWN] 0.96 0.98 0.89 0.017
S&P 600 Value [IJS] 0.95 0.98 0.89 0.020
MSCI US Small Value [VBR] 0.94 0.97 0.87 0.026
S&P 600 Pure Value [RZV] 0.92 0.97 0.80 0.039
Source of primary data: MSCI, S&P, Russell websites and M* Principia
```

Just one approach to try to answer the question.

Robert

Edit - after redoing the analysis the table and text above were changed to reflect the new results. Apologies for previous errors.

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