Question

Using the following returns, calculate the arithmetic average returns, the variances, and the standard deviations for X and Y.

  

	Returns
Year	X	Y
1	6 %	19 %
2	24	40
3	13	-13
4	-14	-27
5	15	48

   

Requirement 1:
(a)	Calculate the arithmetic average return for X.
	a.9.94% b.11.00% c.7.13% d.10.74 e.%8.80%

   

(b)	Calculate the arithmetic average return for Y.
	a.13.40% b. 10.85% c.15.14% d.16.35% e.16.75%

  

Requirement 2:
(a)	Calculate the variance for X. (Do not round intermediate calculations.)
	a.0.020370 b.0.019956 c.0.025462 d.0.016500 e.0.024945

   

(b)	Calculate the variance for Y. (Do not round intermediate calculations.)
	a.0.093791 b.0.086370 c.0.117239 d.0.133287 e.0.106630

  

Requirement 3:
(a)	Calculate the standard deviation for X. (Do not round intermediate calculations.)
	a.11.56% b.15.79 c.%14.03 d.%14.27 e.%17.84%

   

(b)	Calculate the standard deviation for Y.

Answer 1

Stock X:

Average Return = (0.06 + 0.24 + 0.13 + (-0.14) + 0.15) / 5
Average Return = 0.088
Average Return = 8.80%

Variance = [(0.06-0.088)^2 + (0.24-0.088)^2 + (0.13-0.088)^2 + (-0.14-0.088)^2 + (0.15-0.088)^2] / 4
Variance = 0.08148 / 4
Variance = 0.020370

Standard Deviation = (0.020370)^(1/2)
Standard Deviation = 0.1427
Standard Deviation = 14.27%

Stock Y:

Average Return = (0.19 + 0.40 + (-0.13) + (-0.27) + 0.48) / 5
Average Return = 0.134
Average Return = 13.40%

Variance = [(0.19-0.1340)^2 + (0.40-0.1340)^2 + (-0.13-0.1340)^2 + (-0.27-0.1340)^2 + (0.48-0.1340)^2] / 4
Variance = 0.42652 / 4
Variance = 0.106630

Standard Deviation = (0.106630)^(1/2)
Standard Deviation = 0.3265
Standard Deviation = 32.65%