I am evaluating the performance of a sample of 1000 mutual funds over the period 2000 to 2017 using Carhart (1997) four factor model.

As a way to test for robustness, I use two benchmarks. The CRSP total market index (from Dr Kenneth French website) and Wilshire 5000.

I ran individual time series regressions for all 1000 funds. Then I cross-sectionally average the coefficients to get a sense of how my sample performs on aggregate.

When I use CRSP market index as a benchmark, I get a momentum coefficient of -0.06.

However, when I use Wilshire 5000 as a benchmark, I get a momentum coefficient of -0.01.

Both coefficients are statistically different from 0.

My question is, what could be a reason why momentum differs significantly when I change the benchmark?

Thank you.

  • $\begingroup$ I'm a little concerned about your regression specification, do you control for the fact that the individual fund coefficients are measured with error and possibly correlate with other fund coefficients before you take an average across funds? $\endgroup$
    – jd8
    Commented Aug 8, 2017 at 1:36
  • $\begingroup$ @jd8 yes I do adjust standard errors for possible cross sectional dependence and time series autocorrelation. $\endgroup$
    – user28909
    Commented Aug 8, 2017 at 3:04
  • $\begingroup$ Thanks, the setup sounded a little unfamiliar, but I don't do anything with mutual funds. Is the idea to make a statement like "on average funds do/do not earn alpha controlling for momentum"? $\endgroup$
    – jd8
    Commented Aug 9, 2017 at 12:37
  • $\begingroup$ @jd8 the idea is to test whether mutual funds are able to beat the market using the four factor model. I could set the data as a fixed effect panel, but then I'll be imposing the same beta for all funds, which is problematic. That's why I am taking the cross sectional average of all time series regressions. $\endgroup$
    – user28909
    Commented Aug 9, 2017 at 20:47

1 Answer 1


See this wiki Frisch-Waugh-Lovell Theorem

and it will explain how to interpret multiple regression coefficients from a regression of the form \begin{equation} Y = X_1 \beta_1 + X_2 \beta_2 + u \end{equation} as capturing the relationship between some variable $X_2$ and $Y$ after the relationship between $X_2$ and $X_1$ and the relationship between $Y$ and $X_1$ has been removed (we only consider residual correlation after controlling for other variables).

Imagine now that you have a regression where you change $X_1$ from your CRSP index to the Wilshire 5000 as you keep $X_2$ as your momentum index - the change must come from co-variation of these indices with returns or momentum.


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