Question

Fran is a money manager who has been managing a $6 million portfolio that has a beta of 1.25 and a required rate of return of 10.375%. The risk-free rate is 3.5%. Suppose Fran receives another $800,000 into the portfolio and invests the money in a stock with a beta of 0.90.

a) What is the market risk premium?

b) What is the beta of the $6.8 million dollar portfolio?

c) What is the required rate of return on the $6.8 million portfolio?

Answer 1

Given about Fran's portfolio,

Portfolio value = $6 million

Beta = 1.25

required return Ro = 10.375%

Risk free rate = 3.5%

a). So, Market risk premium using CAPM model is

Market risk premium MRP = (Ro - RF)/Beta = (10.375 - 3.5)/1.25 = 5.5%

b). Beta of the new $6.8 million portfolio is weighted average of its assets.

=> Beta of new portfolio = (old portfolio value/new portfolio value)*Beta of old portfolio + (new investment/new portfolio value)*Beta of new investment = (6/6.8)*1.25 + (0.8/6.8)*0.9 = 1.21

c). Required rate of return on new $6.8 million portfolio using CAPM is Rf + it's beta*MRP

=> Required rate of return on new $6.8 million portfolio = 3.5 + 1.21*5.5 = 10.15%