Final answer:
To test for a difference in variances between two portfolios, we can perform a hypothesis test using the F-test. If the p-value is less than the significance level (α = 0.05), we reject the null hypothesis and conclude a difference in variances. The coefficient of variation can be calculated by dividing the standard deviation of a portfolio by its mean and multiplying by 100.
Step-by-step explanation:
To test whether there is a difference in variances of the two portfolios, we can perform a hypothesis test using the F-test. The null hypothesis, H0, is that the variances are equal, while the alternative hypothesis, Ha, is that the variances are different.
- H0: The variances of the two portfolios are equal.
- Ha: The variances of the two portfolios are different.
We can calculate the p-value using the F-test statistic and compare it to the significance level, α = 0.05, to make a decision. If the p-value is less than α, we reject the null hypothesis and conclude that there is a difference in variances. If the p-value is greater than or equal to α, we fail to reject the null hypothesis and do not have enough evidence to conclude a difference in variances.
After finding the p-value, we can find the coefficient of variation by dividing the standard deviation of the portfolio by its mean and multiplying by 100. The coefficient of variation is a measure of relative variability and helps compare the variation between two or more sets of data.
The coefficient of variation can be calculated as:
CV = (standard deviation / mean) x 100