In: Finance

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 ?

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%**

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