Financial Risk Manager Part 1

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Explanation:

Explanation

This is a chi-square test for variance. The test statistic is calculated as:

$\chi^2 = \frac{(n-1)s^2}{\sigma_0^2}$

Where:

n = 61 (sample size)
s = 21% (sample standard deviation)
σ₀ = 14% (hypothesized standard deviation)
df = n - 1 = 60

$\chi^2 = \frac{(61-1) \times (0.21)^2}{(0.14)^2} = \frac{60 \times 0.0441}{0.0196} = \frac{2.646}{0.0196} = 135$

The calculated test statistic (135) is greater than the critical value (79.08), so we reject the null hypothesis that the population standard deviation is ≤ 14%. Therefore, we can conclude that the standard deviation of returns is higher than 14%.

Explanation:

Explanation

This is a chi-square test for variance. The test statistic is calculated as:

$\chi^2 = \frac{(n-1)s^2}{\sigma_0^2}$

Where:

n = 61 (sample size)
s = 21% (sample standard deviation)
σ₀ = 14% (hypothesized standard deviation)
df = n - 1 = 60

$\chi^2 = \frac{(61-1) \times (0.21)^2}{(0.14)^2} = \frac{60 \times 0.0441}{0.0196} = \frac{2.646}{0.0196} = 135$

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Using a sample size of 61 observations, an analyst determines that the standard deviation of the returns from a stock is 21%. Using a 0.05 significance level, the analyst: (If df = 60 and p = 0.05, the critical value is 79.08)

Exam-Like

Can conclude that the standard deviation of returns is higher than 14%.

75.0%

Cannot conclude that the standard deviation of returns is higher than 14%.

25.0%

Can conclude that the standard deviation of returns is not higher than 14%.

None of the above.