Question

Suppose that the index model for stocks A and B is estimated from excess returns with the following results: RA = 3.5% + 0.65RM + eA RB = –1.6% + 0.80RM + eB σM = 21%; R-squareA = 0.22; R-squareB = 0.14 Assume you create a portfolio Q, with investment proportions of 0.50 in a risky portfolio P, 0.30 in the market index, and 0.20 in T-bill. Portfolio P is composed of 60% Stock A and 40% Stock B. a. What is the standard deviation of portfolio Q? (Calculate using numbers in decimal form, not percentages. Do not round intermediate calculations. Round your answer to 2 decimal places.) b. What is the beta of portfolio Q? (Do not round intermediate calculations. Round your answer to 2 decimal places.) c. What is the "firm-specific" risk of portfolio Q? (Calculate using numbers in decimal form, not percentages. Do not round intermediate calculations. Round your answer to 4 decimal places.) d. What is the covariance between the portfolio and the market index? (Calculate using numbers in decimal form, not percentages. Do not round intermediate calculations. Round your answer to 2 decimal places.)

Answer 1

A	B	C	D	E	F	G	H	I	J
2
3		RA = 3.5% + 0.65RM + eA
4		RB = -1.6% + 0.80RM + eB
5
6		R-square A	0.22
7		R-square B	0.14
8
9		σM	21%
10		σ(T-bill)	0%
11
12
13			Portfolio P	Market Index	T-bill
14		Weight in portfolio Q	50%	30%	20%
15
16		Using the above equation,
17			A	B
18		Beta	0.65	0.8
19		Weight	60%	40%
20		For portfolio equation will be
21		Rp = E(rp)+βp*RM+ep
22
23		Where E(rp) = ∑wiE(ri), βp= ∑wiβi and ep = ∑wiei
24
25		R-square is coefficient of determination which shows fraction of total variance explained by market
26		R-square	=(β)2 (σM)2/(σ)2
27		or
28		(σ)2	=(β)2 (σM)2/R-square
29
30		(σA)2	0.0847	=((D18*D9)^2)/D6
31		(σB)2	0.2016	=((E18*D9)^2)/D7
32
33		Total variance (σ2) of the stock which is given by following formula:
34		(σ)2	=(β)2 (σM)2+σ2(e)
35
36		using the above equation
37		σ2(e)	=(σ)2-(β)2 (σM)2
38
39		σ2(eA)	0.066059795	=D30-((D18*D9)^2)
40		σ2(eB)	0.173376	=D31-((E18*D9)^2)
41
42		σ2(ep)	=∑wi2σ2(ei)
43			0.052	=(D19^2)*D39+(E19^2)*D40
44
45		βp	= ∑wiβi
46			0.71	=D19*D18+E19*E18
47
48		Total variance (σ2) of the portfolio P is given by following formula:
49		(σp)2	=(βp)2 (σM)2+σ2(ep)
50			0.0738	=((D46*D9)^2)+D43
51
52		Cov(P,M)	= βp*(σM)2
53			=0.71*((21%)^2)
54			0.031	=D46*(D9^2)
55
56		Since the t-bill has variance of zero, therefore
57		the variance of portfolio Q can be calculated as follows:
58		Var(Q)	= w2P*σ2(RP) + w2M*σ2(RM) + 2*(wP)*(wM)*Cov(P, M)
59			=(0.50^2)*0.0738+(0.30^2)*(0.21^2)+2*0.50*0.30*0.031
60			0.0318	=(D14^2)*D50+(E14^2)*(D9^2)+2*D14*E14*D54
61
62		Hence Standard deviation of portfolio Q	0.18	=SQRT(D60)
63