Problem 6. [10 pts]. Suppose Bank Y stock has a beta of 1.42, whereas XX stock h
ID: 2811420 • Letter: P
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%