Question

Returns Yr X Y 1 17 % 22 % 2 31 32 3 12 16 4 – 24 – 29 5 10 23 Using the returns shown above, calculate the arithmetic average returns, the variances, and the standard deviations for X and Y. (Do not round intermediate calculations. Enter your average return and standard deviation as a percent rounded to 2 decimal places, e.g., 32.16, and round the variance to 5 decimal places, e.g., 32.16161.) X Y Average return ____% ____ %

Answer 1

To calculate the average return for X, sum up all the returns and divide by the number of data points:

Average return for X = (17 + 31 + 12 - 24 + 10) / 5 = 9.20%

To calculate the average return for Y, sum up all the returns and divide by the number of data points:

Average return for Y = (22 + 32 + 16 - 29 + 23) / 5 = 12.80%

To calculate the variance for X, subtract each return from the average return, square the differences, sum them up, and divide by the number of data points minus one:

Variance for X = [(17 - 9.20)^2 + (31 - 9.20)^2 + (12 - 9.20)^2 + (-24 - 9.20)^2 + (10 - 9.20)^2] / (5-1) = 363.60

To calculate the variance for Y, subtract each return from the average return, square the differences, sum them up, and divide by the number of data points minus one:

Variance for Y = [(22 - 12.80)^2 + (32 - 12.80)^2 + (16 - 12.80)^2 + (-29 - 12.80)^2 + (23 - 12.80)^2] / (5-1) = 617.40

To calculate the standard deviation for X, take the square root of the variance:

Standard deviation for X = √363.60 ≈ 19.07

To calculate the standard deviation for Y, take the square root of the variance:

Standard deviation for Y = √617.40 ≈ 24.84

Therefore:

Average return for X: 9.20%

Average return for Y: 12.80%

Variance for X: 363.60

Variance for Y: 617.40

Standard deviation for X: 19.07

Standard deviation for Y: 24.84

Explanation: