Question

an investor is evaluating the common shares od the three firms A,B and C. Expected returns, standard deviation of returns , and betas are :

stock    expected return    standard deviation    beta weight

A 10% 8% 1.4 20%

B 15% 12% 1.2 50%

C 20% 13% 1.8 30%

a) What is the expected return of the portfolio ?

b) What is Beta of the portfolio ?

c) Assume the risk free rate of interest is 6% and the required on the market portfolio is 13%. Using the capital asset pricing model, what is the required return on stock A ?

Answer 1

Stock	Expected return	Standard deviation	Beta	Weight
A	10%	8%	1.4	20%
B	15%	12%	1.2	50%
C	20%	13%	1.8	30%

Weight of stock A = WA = 20%, Expected return on stock A = E[RA] = 10%, Beta of stock A = βA = 1.4

Weight of stock B = WB = 50%, Expected return on stock B = E[RB] = 15%, Beta of stock B = βB = 1.2

Weight of stock C = WC = 30%, Expected return on stock C = E[RC] = 20%, Beta of stock C = βC​​​​​​​ = 1.8

Part a

Expected return of the portfolio is calculated using the formula:

Expected return of portfolio = E[RP] = WA*E[RA] + WB*E[RB] + WC*E[RC] = 20%*10% + 50%*15% + 30%*20% = 15.5%

Answer a -> 15.5%

Part b

Beta of the portfolio is calculated using the formula:

Portfolio beta = βP = WA*βA + WB*βB + WC*βC = 20%*1.4 + 50%*12 + 30%*1.8 = 1.42

Answer b -> 1.42

Part c

Risk- free rate = RF = 6%

Return on market portfolio = RM = 13%

The required return on stock A (RA) can be computed using CAPM,

RA = RF + βA*(RM - RF) = 6% + 1.4*(13% - 6%) = 15.8%

Answer c -> 15.8%