statistical validation of the BMG factor

[sichen1234]

This is from pages 184 - 188 of the CARIMA paper, which shows these statistics to validate the BMG factor:

Please build scripts to calculate these statistcs for BMG and other factors in our data so we could see how good different ways of constructing BMG benchmarks are.

[sichen1234]

3 parts of validation:

1. Correlation with the other factors - Determines if the BMG factor is different or already described by other factors
2. Regression of stand error from 3-factor model (without BMG) against BMG factor - determines if the BMG factor has additional explanatory power on return residuals
3. Panel regression - Determines if adding the additional BMG factor improves the model.

[sichen1234]

Please look at

Why are the MSCI sector t-statistics significant but the overall market not?

[sichen1234]

Here are the S&P 500 sector and market t-statistics.

Here the overall market t-statistic is more significant but please check the numbers as well.

[sichen1234]

The correlations with other factors is calculated:

Here are the predictive power (change in R2 and adjusted R2) for MSCI World and S&P 500: MSCI Predictive Power Table by Sector.csv

SP500 Predictive Power Table by Sector.csv

SP500 Predictive Power Table by Sub Sector.csv

[sichen1234]

The key question now is whether the increase in R2 is significant. Are the standard errors of residuals smaller or more normal or in some ways "better"? The Barra MSCI E4 model showed an increase in R2 of 0.0066 vs E3 but did not go into any further analysis of it.