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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. The explanation for this is found in the provided content, which states that multicollinearity exists between the variables in the regression due to the high correlations between each pair of index returns. Specifically, the correlation coefficients between the Russell 1000, Russell 2000, and Russell 3000 are 0.937, 0.856, and 0.945 respectively, indicating a strong positive relationship between these indexes. Multicollinearity can distort the regression coefficients and make them less reliable, as it becomes difficult to isolate the individual effect of each regressor on the dependent variable. The presence of multicollinearity suggests that while the overall regression model may be useful for prediction, the individual coefficients may not be accurately reflecting the unique contribution of each index to the portfolio returns.
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A risk manager performed a regression analysis of a firm's monthly portfolio returns on three US domestic equity indices: the Russell 1000, Russell 2000, and Russell 3000. The results are presented below:
Regression Statistics Multiple R: 0.951 R-Squared: 0.905 Adjusted R-Squared: 0.903 Standard Error: 0.009 Observations: 192
Based on the regression results, which statement is correct?
Regression Statistics
Multiple R: 0.951
R-Squared: 0.905
Adjusted R-Squared: 0.903
Standard Error: 0.009
Observations: 192
| Regression Output | Coefficients | Standard Error | t-Stat | P-Value |
|---|---|---|---|---|
| Intercept | 0.0023 | 0.0006 | 3.5305 | 0.0005 |
| Russell 1000 | 0.1093 | 1.5895 | 0.0688 | 0.9452 |
| Russell 2000 | 0.1055 | 0.1384 | 0.7621 | 0.4470 |
| Russell 3000 | 0.3533 | 1.7274 | 0.2045 | 0.8382 |
| Correlation Matrix | Portfolio Returns | Russell 1000 | Russell 2000 | Russell 3000 |
|---|---|---|---|---|
| Portfolio Returns | 1.000 | |||
| Russell 1000 | 0.937 | 1.000 | ||
| Russell 2000 | 0.856 | 0.813 | 1.000 | |
| Russell 3000 | 0.945 | 0.998 | 0.845 | 1.000 |
A
The estimated coefficient of 0.3533 indicates that the returns of the Russell 3000 Index are more statistically significant in determining the portfolio returns than the other two indexes.
B
The high adjusted R2 indicates that the estimated coefficients on the Russell 1000, Russell 2000, and Russell 3000 Indexes are statistically significant.
C
The high p-value of 0.9452 indicates that the regression coefficient of the returns of the Russell 1000 Index is more statistically significant than the other two indexes.
D
The high correlations between each pair of index returns indicate that multicollinearity exists between the variables in this regression.