Question

Suppose that the index model for stocks A and B is estimated from excess returns with the following results: RA = 2.50% + 0.95RM + eA RB = -1.80% + 1.10RM + eB σM = 27%; R-squareA = 0.23; R-squareB = 0.11 Assume you create portfolio P with investment proportions of 0.60 in A and 0.40 in B.

a. What is the standard deviation of the portfolio? (Do not round your intermediate calculations. Round your answer to 2 decimal places.)

b. What is the beta of your portfolio? (Do not round your intermediate calculations. Round your answer to 2 decimal places.)

c. What is the firm-specific variance of your portfolio? (Do not round your intermediate calculations. Round your answer to 4 decimal places.)

d. What is the covariance between the portfolio and the market index? (Do not round your intermediate calculations. Round your answer to 3 decimal places.)

Answer 1

A	B	C	D	E	F	G	H	I	J
2
3		RA = 2.50% + 0.95RM + eA
4		RB = -1.80% + 1.10RM + eB
5
6		R-square A	0.23
7		R-square B	0.11
8
9		σM	27%
10
11		Using the above equation,
12			A	B
13		Beta	0.95	1.1
14		Weight	0.6	0.4
15		For portfolio equation will be
16		Rp = E(rp)+βp*RM+ep
17
18		Where E(rp) = ∑wiE(ri), βp= ∑wiβi and ep = ∑wiei
19
20		R-square is coefficient of determination which shows fraction of total variance explained by market
21		R-square	=(β)2 (σM)2/(σ)2
22		or
23		(σ)2	=(β)2 (σM)2/R-square
24
25		(σA)2	0.286053	=((D13*D9)^2)/D6
26		(σB)2	0.8019	=((E13*D9)^2)/D7
27
28		Total variance (σ2) of the stock which is given by following formula:
29		(σ)2	=(β)2 (σM)2+σ2(e)
30
31		using the above equation
32		σ2(e)	=(σ)2-(β)2 (σM)2
33
34		σ2(eA)	0.220261	=D25-((D13*D9)^2)
35		σ2(eB)	0.713691	=D26-((E13*D9)^2)
36
37		σ2(ep)	=∑wi2σ2(ei)
38			0.193485	=(D14^2)*D34+(E14^2)*D35
39
40		βp	= ∑wiβi
41			1.01	=D14*D13+E14*E13
42
43		Total variance (σ2) of the portfolio is given by following formula:
44		(σp)2	=(βp)2 (σM)2+σ2(ep)
45			0.26785	=((D41*D9)^2)+D38
46
47		a)
48
49		Standard deviation of portfolio	51.75%	=SQRT(D45)
50
51		b)
52
53		Beta of the portfolio	1.01	=D41
54
55		c)
56
57		Firm specific variance of the portfolio	σ2(ep)
58			0.1935	=D38
59
60		d)
61
62		Covariance of the portfolio with market	= βp*(σM)2
63			=1.01*((27%)^2)
64			0.074	=D53*(D9^2)
65
66		Hence Covariance of the portfolio with market	0.074
67