Question

You have the following information on return on the stocks of Target (T), Macy's (M),and Best Buy (B)

Target (T) Macy's (M) Best Buy (B)

$6 $3 $11

$7 $8 $5

$3 $5 $8

$4 $8 $4

What are the variances and standard deviations of the returns on the three stocks?

	a.	V[T] = 4.5  V[M] = 8   V[B]  = 8.3333 S[T] = 2.121 S[M] = 2.828   V[B] =2.886
	b.	V[T] = 6 V[M]  =9.3333 V[B] = 10 S[T] = 2.449   S[M] = 3.055   S[B] =  3.162
	c.	V[T]= 3.3333    V[M] =   6   V[B] = 10 S[T] = 1.8257      S[M] =  2.449 S[B]  =  3.162
	d.	None of these

What is the covariance of the returns on T and M?

	a.	2.566
	b.	3.162
	c.	.333
	d.	None of the above

What is the covariance of M and B?

	a.	-3.163
	b.	-5.666
	c.	- 7.666
	d.	none of these

Answer 1

Calculation of Expected return:

Expected return Target (T) = 6+7+3+4/4 = 20/4 = 5

Expected return Macy's (M) = 3+8+5+8/4 = 24/4 = 6

Expected return Best Buy(B) = 11+5+8+4/4 = 28/4 = 7

Calculation of Variance and standard deviation of Target(T):

Return	Return-Expected return	Square of return-Expeced return
6	6-5 = 1	(1)^2 = 1
7	7-5 = 2	(2)^2 = 4
3	3-5 = -2	(-2)^2 = 4
4	4-5 = -1	(-1)^2 = 1
	Total	10

Varinace = 10/n-1 = 10/4-1 = 10/3 = 3.3333

n = 4

Std deviation = square root of varinace

= square root of 3.3333

= 1.8257

Varinace and standard deviation of Macy's

Return	Return - Expected return	Square of Return- Expected return
3	3-6 = -3	(-3)^2=9
8	8-6 = 2	(2)^2 = 4
5	5-6 = -1	(-1)^2 = 1
8	8-6 = 2	(2)^2 = 4
	Total	18

Variance = 18/n-1 =18/4-1 = 18/3 = 6

Std deviation = square root of 6 = 2.449

Calculation of Variance and standard deviation of Best Buy:

Return	Return-expected return	Square of Return-Expected return
11	11-7 = 4	(4)^2 = 16
5	5-7 = -2	(-2)^2 = 4
8	8-7 = 1	(1)^2 = 1
4	4-7 = -3	(-3)^2 = 9
	Total	30

Varinace = 30/n-1 = 30/4-1= 30/3 = 10

Std deviation = 3.162

Answer : C

2) Covarinace of T and M:

Return- Expected return of T (1)	Return- expected return of M (2)	Product (3) (1*2)
1	-3	1*-3 = -3
2	2	2*2 = 4
-2	-1	-2*-1 = 2
-1	2	-1*2 = -2
	Total	1

Covarinace = 1/n-1 = 1/4-1 = 1/3 = 0.333

Answer : C

3) Calculation of covarinace of M and B:

Return- Expected return of M (1)	Return-Expected return of B (2)	Product (3) (1*2)
-3	4	-3*4 = -12
2	-2	2*-2 = -4
-1	1	-1*1 = -1
2	-3	2*-3= -6
	Total	-23

Covarinace = -23/n-1

= -23/4-1

= -23/3

= -7.666

Answer : C