A stock has a beta of 1 90 and an expected return of 15 percent A risk-free asse

Question

A stock has a beta of 1 90 and an expected return of 15 percent A risk-free asset currently earns 3 6 percent What b the expected return on a portfolio that is equally invested in the two assets? (Do not round intermediate calculations. Enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.) Expected return percentage If a portfolio of the two assets has a beta of 95. what are the portfolio weights? (Do not round intermediate calculations. Round your answers to 4 decimal places, e.g.. 37.1616.) Weight of stock Risk free weight If a portfolio of the two assets has an expected return of 7 percent, what is its beta? (Do not round intermediate calculations. Round your answer to 3 decimal places, e.g., 37.161.) Beta If a portfolio of the two assets has a beta of 3 80 what are the portfolio weights? (Do not round intermediate calculations. Negative amounts should be indicated by a minus sign. Enter your answers as a whole number.) Weight of stock Risk-free weight

Explanation / Answer

B=beta, Rf=Risk Free Rate, MRP=Market Risk Premium, Ws=weight of Stock

a)expected return on equally invested portfolio= (0.5*15)+(0.5*3.6)=9.3%

b) Portfolio beta= Ws*1.9+(1-Ws)*0

Given Portfolio beta=0.95 hence 0.95=Ws*1.9+0

Ws=0.95/1.9=0.5

Weight of Risk free asset=0.5

c) Given Portfolio return=7%

hence 7=15*Ws+3.6*(1-Ws)

7=11.4Ws+3.6 =>Ws=3.4/11.4=0.3

Ws=0.3

Weight of risk fre asset=0.7

hence portfolio beta=1.9*0.3+0.7*0=0.57

d) 3.8=1.9*Ws+(1-Ws)*0

hence Ws=2 i.e Weight of stock=200%

Weihgt of risk free asset=1-200%=(-100%) which means that investors has borrowed money at risk free rate to finance stock purchase.

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