Topic Test Quant: Hamilton’s conclusion that multicollinearity is not a problem, is most likely based on the observation that:

CFA Level II Quant
#1

Hi Forum,

I just came across this question in the quant section:

Hamilton’s conclusion that multicollinearity is not a problem, is most likely based on the observation that:

  1. model F-value is high and the p-values for the S&P 500 and SPREAD are low.
  2. correlation between the S&P 500 and SPREAD is low.
  3. model R2 is relatively low.

Correct answer would have been (2) because correlation b/w S&P and Spread is low (given in the question).

However I chose (3) because the question also shows a R2 of only 0.4. As far as I know, testing for multicollinearity is the following:

  • high R2 or high F-stat together with insignificant t-stat indicate multicollinearity.

So this would be the case here as well!?

Can someone please have a quick look? Many thanks and kind regards

Update: Basically, what is a “high” or “low” R2? Here the model explains 40% of the independent variables…

#2

Since there are only 2 independent variables, they want you to look at the pairwise correlation. The model R2 and F-stat are not impacted by multicollinearity-- the CFAI is just bad at explaining and teaching that (they even argued with me regarding that a while ago, until they ceded after the QM curriculum author reviewed and agreed with me). Sure, it may increase simply because you added another variable, but the fact of the variable being collinear is more or less irrelevant. A hint that MC may be present would be a case where the model seems to look good with high R2 and significant F-test, but the individual t-tests are nonsignificant. This isn’t a sure thing, though., and it needs to be looked at with other signs such as beta estimates with opposite signs or magnitudes than expected, for example. High R2 is relative, too, depends on what you’re doing.