Use the following returns for X and Y. Returns Year X Y 1 21.7 % 26.1 % 2 – 16.7

Question

Use the following returns for X and Y. Returns Year

X Y

1 21.7 % 26.1 %

2 – 16.7 – 3.7

3 9.7 28.1

4 19.4 – 14.4

5 4.7 32.1

Requirement 1: Calculate the average returns for X and Y. (Do not round intermediate calculations. Enter your answers as a percentage rounded to 2 decimal places (e.g., 32.16).)

Requirement 2: Calculate the variances for X and Y. (Do not round intermediate calculations. Round your answers to 6 decimal places (e.g., 32.161616).)

Requirement 3: Calculate the standard deviations for X and Y. (Do not round intermediate calculations. Enter your answers as a percentage rounded to 2 decimal places (e.g., 32.16).)

Explanation / Answer

Ans) Returns of X and Y

Year X Y

1 21.7 % 26.1 %

2 – 16.7 – 3.7

3 9.7 28.1

4 19.4 – 14.4

5 4.7 32.1

1) Average return of X (Xavg) = Total of returns / no of years(n)

= (21.7 + (-16.7) + 9.7 + 19.4 + 4.7) / 5 = 7.76

Average return of Y(Yavg) = (26.1 + (-.3.7) + 28.1 + (-14.4) + 32.1) / 5 = 13.64

2) Variance of X = ((21.7 - 7.76)2 + (-16.7 - 7.76)2 + (9.7 - 7.76)2 + (19.4 - 7.76)2 + (4.7 - 7.76)2) / 5 - 1

= (194.32 + 598.29 + 3.76 + 135.48 + 9.36) / 4

= 235.30

Variance of Y = ((26.1 - 13.64)2 + (-3.7 - 13.64)2 + (28.1 - 13.64)2 + (-14.4 - 13.64)2 + (32.1 - 13.64)2) / 5 -1

= (155.25 + 300.67 + 209.09 + 786.24 + 340.77) / 4

= 448.00

3) Standard deviation of X = square root of variance of X

= square root of 235.30

= 15.33

Standard deviation of Y = square root of variance of Y

= square root of 448

= 21.16   

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