Question

The monthly returns of two portfolios are to be compared. The monthly returns are analyzed for each of 14 months, with the months being chosen at random and independently for the two portfolios. The following statistics for monthly returns are reported for portfolio1 and portfolio 2 Portfolio 1 x1-0.11 i 0.0025 Portfolio 2 x2=0.12 2-0.0016 (The first row gives the sample means, and the second row gives the sample variances.) Assume that the monthly returns of the two portfolios are each normally distributed. Construct a 99% confidence interval for the monthly returns for these two portfolios. Then complete the table below. Carry your intermediate computations to at least three decimal places. Write your final responses to at least two decimal places. (If necessary, consult a list of the ratio of the variances of formulas.) What is the lower limit of the 99% confidence interval? What is the upper limit of the 99% confidence interval?

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Answer #1

Here ni = n2 = 14. 1-α = 0.99 α = 0.01, a/2 = 0.005

The 99% confidence interval for the ratio of variances is

o/2.ni-ї,n2 0.0025 0.0025 0.0016 0.0016 4.5733 0.2187 - (0.342,7.146)

The lower limit of the 99% confidence interval is 0342

The upper limit of the 99% confidence interval is 7146

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