Financial Risk Manager Part 1
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A portfolio manager observes that the weekly return generated by a portfolio of high-beta stocks stood at 5%. The standard deviation of the portfolio return stood at 1.50%. However, the manager observes that the standard deviation of the portfolio return for the past 15 weeks stood at 2.00%. The portfolio manager wants to determine whether the standard deviation of the portfolio return has increased from 1.50% to 2.00%. What is the test statistic to test the above hypothesis?
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Community
NNikitesh
A
34.89
B
25.89
C
31.55
D
24.89
Explanation:
The chi-square test is used for hypothesis tests regarding population variance.
Test statistic = [(n-1) * s²] / σ²
= [(15-1) * 0.02²] / 0.015² = 24.89
Calculation details:
- n = 15 (number of weeks)
- s = 2.00% = 0.02 (sample standard deviation)
- σ = 1.50% = 0.015 (hypothesized population standard deviation)
Test statistic = [(15-1) * (0.02)²] / (0.015)² = [14 * 0.0004] / 0.000225 = 0.0056 / 0.000225 = 24.888... ≈ 24.89
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