Problem 6. [10 pts]. Suppose Bank Y stock has a beta of 1.42, whereas XX stock h

Question

Problem 6. [10 pts]. Suppose Bank Y stock has a beta of 1.42, whereas XX stock has a beta of -0.80. If the risk-free interest rate is 2.25% and the expected return of the market portfolio is 15%, according to the CAPM, (Show your calculations) a- What is the expected return of Bank Y stock? b- What is the expected return of XX stock? c-What is the beta of a portfolio that consists of 35% Bank Y stock and 65% XX stock? d-What is the expected return of a portfolio that consists of 35% of Bank Y and 65% X stock? (Make sure to solve it in two ways).

Explanation / Answer

The equation for CAPM is given by:

Re/ E(R)=Rf+(Rm-Rf)*B

Where

Re/E(R)=Required Rate of return/Expected Return

Rf= Risk free rate

Rm= Return of market portfolio

B=Beta of stock

a) E(R) on Bank Y stock = 2.25%+(15-2.25)*1.42=20.35%

b) E(R) on XX stock= 2.25%+(15-2.25)*(-0.80)=-7.95%

c) Beta of portfolio consisting of 35% of Bank Y stock and 65% of XX stock is calculated as follows:

= 35%*1.42+65%*(-0.80)=(-0.023)

d) Expected Return on portfolio can be calculated in the following two ways:

Method 1: Using Beta of the portfolio

E(Rp)= 2.25+(15-2.25)*(-0.023)= 1.956%

Method 2: Using return of the two stocks

E(Rp)= 35%*20.35%+65%*(-7.95%)=1.955%

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