Answer: The high correlations between each pair of index returns indicate that multicollinearity exists between the variables in this regression.

The correct answer is **D**. ### Explanation of Why D Is Correct The correlation matrix shows extremely high pairwise correlations among the three independent variables (the equity indexes): - Russell 1000 and Russell 3000: **0.998** - Russell 1000 and Russell 2000: **0.813** - Russell 2000 and Russell 3000: **0.845** These values (especially the near-perfect 0.998 between Russell 1000 and Russell 3000) indicate **multicollinearity**—a situation in multiple regression where the independent variables are highly linearly related to one another. Multicollinearity is a classic violation of OLS regression assumptions and leads to several issues visible here: - Inflated standard errors for the slope coefficients (notice how large they are relative to the coefficients themselves: 1.5895, 0.1384, and 1.7274). - Very low t-statistics and correspondingly high p-values for all three index coefficients (none are statistically significant at conventional levels like 5% or 10%). - Despite this, the model as a whole has an excellent fit: R² = 0.9 and Adjusted R² = 0.9, with a very low standard error of the regression (0.0, likely rounded). In FRM Part 1 (Quantitative Analysis section), multicollinearity is detected precisely by high correlations among regressors combined with a high overall R² but individually insignificant coefficients. This is an example of **imperfect multicollinearity** (not perfect, since correlations are not exactly 1.0). ### Why the Other Options Are Incorrect - **A**: The coefficient 0.3533 on Russell 3000 is the largest in magnitude, but statistical significance is determined by the **t-statistic** (or p-value), not the size of the coefficient. Here, its t-stat is only 0.204 with a p-value of 0.8382—**insignificant**, and actually less "significant" than the Russell 2000 coefficient (t-stat 0.762). The large coefficient size is likely an artifact of multicollinearity distorting the estimates. - **B**: A high Adjusted R² (0.9) shows that the model as a whole explains a large portion of the variation in portfolio returns. However, it **does not** imply that the individual coefficients are statistically significant. In fact, multicollinearity often produces exactly this pattern: strong overall fit but insignificant individual t-tests. - **C**: A **high** p-value (0.9452 for Russell 1000) indicates the coefficient is **less** statistically significant (we cannot reject the null hypothesis that the true coefficient is zero). Lower p-values mean higher significance. All three p-values are high, confirming insignificance across the board. ### Key FRM Takeaway on Multicollinearity - **Consequences**: Unreliable individual coefficient estimates and standard errors; difficult to interpret the marginal effect of each index. - **Detection**: High correlations between independent variables + high R² but low t-stats. - **Common in finance**: Equity indexes like Russell 1000/2000/3000 overlap heavily (large-cap, small-cap, and broad market), so they naturally move together. - **Remedies** (not asked here, but for context): Drop one or more highly correlated variables, combine them, or use techniques like ridge regression (though not emphasized in basic FRM Part 1). This question tests your ability to interpret regression diagnostics beyond just R² and to recognize multicollinearity from both the correlation matrix and the pattern of insignificant coefficients. Focus on similar examples in GARP practice exams, as this is a recurring topic.