Financial Risk Manager Part 1
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The following table represents the return of a portfolio over the return of its benchmark.
| Portfolio parameter | Value |
|---|---|
| Alpha | 0.25 |
| Coefficient of determination | 0.77 |
| Standard deviation of error | 2.40 |
| Beta | 1.2 |
Which of the following statements are correct?
I. The correlation is 0.69
II. The dependent variable is the portfolio
III. About 23% of the variation noted in the portfolio return is explained by variation in benchmark return
IV. For an estimated portfolio return of 10%, the 95% confidence interval is (5.296, 14.704)
Other
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NNikitesh
A
I and II
B
II and III
C
II only
D
II and IV
Explanation:
Explanation:
-
Statement I: The correlation is 0.69 - This is incorrect. The correlation coefficient (r) is the square root of the coefficient of determination (R²). Since R² = 0.77, correlation = √0.77 ≈ 0.8775, not 0.69.
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Statement II: The dependent variable is the portfolio - This is correct. In regression analysis where portfolio return is regressed on benchmark return, the portfolio return is the dependent variable (Y) and the benchmark return is the independent variable (X).
-
Statement III: About 23% of the variation noted in the portfolio return is explained by variation in benchmark return - This is incorrect. The coefficient of determination (R²) = 0.77 means that 77% of the variation in portfolio return is explained by variation in benchmark return, not 23%.
-
Statement IV: For an estimated portfolio return of 10%, the 95% confidence interval is (5.296, 14.704) - This is correct. The 95% confidence interval is calculated as:
- Estimated return ± Zα/2 × Standard deviation of error
- 10 ± 1.96 × 2.40 = 10 ± 4.704 = (5.296, 14.704)
Therefore, only statements II and IV are correct, making option D the correct answer.
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