A stock has an expected return of 15 percent, its beta is 0.45, and the risk-fre
ID: 2715705 • Letter: A
Question
A stock has an expected return of 15 percent, its beta is 0.45, and the risk-free rate is 7.5 percent. What must the expected return on the market be?
rev: 09_20_2012
25.38%
16.67%
22.96%
25.13%
24.17%
Your portfolio is invested 30 percent each in stocks A and C, and 40 percent in stock B. What is the standard deviation of your portfolio given the following information?
A stock has an expected return of 15 percent, its beta is 0.45, and the risk-free rate is 7.5 percent. What must the expected return on the market be?
Explanation / Answer
First part
ER = Rf + beta(Rm-Rf)
15% = 7.5% + 0.45(Rm - 7.5%)
Rm = 24.17
Therefore answer to first part of the above question is 24.17%
Second part
R(A) = 0.25*0.25 + 0.10*0.25 + 0.03*0.25 + (0.04)*0.25
= 0.085 0r 8.50%
S.D (A) = {(0.25-0.085)2 *0.25+ (0.10-0.085)2*0.25 + (0.03-0.085)2*0.25 +(-0.04-0.085)2*0.25}1/2
=10.74%
R(B) = 0.25*0.25 + 0.13*0.25 + 0.05*0.25 + (0.09)*0.25
= 0.085 or 8.50%
S.D (B) = {(0.25-0.085)2 *0.25+ (0.13-0.085)2*0.25 + (0.05-0.085)2*0.25 +(-0.09-0.085)2*0.25}1/2
= 12.26%
R(C) = 0.25*0.45 + 0.11*0.25 + 0.05*0.25 + (0.09)*0.25
= 0.13 or 13%
S.D (C) = {(0.45-0.13)2 *0.25+ (0.11-0.13)2*0.25 + (0.05-0.13)2*0.25 +(-0.09-0.13)2*0.25}1/2
= 19.85%
CovA&B = (0.25-0.085)(0.25-0.085)0.25 + (0.10-0.085)(0.13-0.085)0.25 + (0.03-0.085)(0.05-0.085)0.25 + (-0.04- 0.085)(-0.09-0.085)0.25
= 129.25(%)2
rA&B = CovA&B/(S.DA*S.DB)
= 129.25(%)2/(10.74%*12.26%)
= 0.98
CovA&C = (0.25-0.085)(0.45-0.13)0.25 + (0.10-0.085)(0.11-0.13)0.25 + (0.03-0.085)(0.05-0.13)0.25 + (-0.04- 0.085)(-0.09-0.13)0.25
= 211(%)2
rA&C = CovA&C/(S.DA*S.DC)
= 211(%)2/10.74%*19.85
= 0.99
CovB&C = (0.25-0.085)(0.45-0.13)0.25 + (0.13-0.085)(0.11-0.13)0.25 + (0.05-0.085)(0.05-0.13)0.25 + (-0.09- 0.085)(-0.09-0.13)0.25
= 233(%)2
rB&C = CovB&C/(S.DB*S.DC)
= 233(%)2/(12.26%*19.85%)
= 0.96
SDABC = {(S.D.A*WA)2 +(S.D.B*WB)2 + (S.D.C*WC)2 +(2*S.D.A*WA*S.D.B*WB*rA&B) + (2*S.D.A*WA*S.D.C*WC*rA&C) + (2*S.D.B*WB*S.D.C*WC*rB&C)}1/2
= {(10.74*0.30)2 + (12.26*0.30)2 + (19.85*0.40)2 +(2*10.74*0.30*12.26*0.30*0.98) + (2*10.74*0.30*19.85*0.40*0.99) + (2*12.36*0.30*19.85*0.40*0.96)}1/2
= 12.89%
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