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	12 %	20 %
2	30	41
3	19	-7
4	-20	-21
5	21	49

   

Requirement 1:
(a)	Calculate the arithmetic average return for X.
	(Click to select)10.04%15.13%15.50%12.40%14.01%

   

(b)	Calculate the arithmetic average return for Y.
	(Click to select)13.28%16.40%20.50%20.01%18.53%

  

Requirement 2:
(a)	Calculate the variance for X. (Do not round intermediate calculations.)
	(Click to select)0.0369300.0368120.0299130.0461630.046014

   

(b)	Calculate the variance for Y. (Do not round intermediate calculations.)
	(Click to select)0.0852570.1065710.0906800.0734510.113350

  

Requirement 3:
(a)	Calculate the standard deviation for X. (Do not round intermediate calculations.)
	(Click to select)19.09%24.02%15.57%21.45%19.22%

   

(b)	Calculate the standard deviation for Y. (Do not round intermediate calculations.)
	(Click to select)30.11%24.39%37.64%29.20%32.65%

Answer 1

Requirement 1:

(a)

Arithmetic average return for X = (X₁ + X₂ + X₃+ X₄+ X₅)/5

                                                           = (12 % + 30 % + 19 % - 20 % + 21%)/5

                                            = 62 %/5 = 12.40 %

Hence option “12.40 %” is correct answer.

(b)

Arithmetic average return for Y = (Y₁ + Y₂ + Y₃+ Y₄+ Y₅)/5

                                                            = (20 % + 41 % -7 % - 21 % + 49%)/5

                                             = 82 %/5 = 16.40 %

Hence option “16.40 %” is correct answer.

Requirement 2:

(a)

	X	Mean X m	Xi – X m	(Xi – X m)2
X1	0.12		-0.004	0.000016
X2	0.30		0.176	0.030976
X3	0.19		0.066	0.004356
X4	-0.20		-0.324	0.104976
X5	0.21		0.086	0.007396
∑	0.62	0.1240		0.147720

Variance for X = ∑ (Xi – X _m) ²/ (n -1)

              (Xi – X _m) ² = 0.147720

              n = 5

Variance for X = 0.147720/ (5 - 1) = 0.147720/4 = 0.03693

Hence option “0.03693” is correct answer.

(b)

	Y	Mean Y m	Yi – Y m	(Yi – Y m)2
Y1	0.20		0.036	0.001296
Y2	0.41		0.246	0.060516
Y3	-0.07		-0.234	0.054756
Y4	-0.21		-0.374	0.139876
Y5	0.49		0.326	0.106276
∑	0.82	0.1640		0.362720

Variance for Y = ∑ (Yi – Y _m) ² / (n -1)

              (Yi – Y _m) ² = 0.362720

              n = 5

Variance for Y = 0.362720/ (5 - 1) = 0.362720/4 = 0.09068

Hence option “0.09068” is correct answer.

Requirement 3:

Standard deviation = √ Variance

(a)

Standard deviation for X = √0.03693 = 0.192171798 or 19.22 %

Hence option “19.22 %” is correct answer.

(b)

Standard deviation for Y = √0.09068 = 0.301131201 or 30.11 %

Hence option “30.11 %” is correct answer.