Question

CAPM AND PORTFOLIO RETURN

You have been managing a $5 million portfolio that has a beta of 1.75 and a required rate of return of 12%. The current risk-free rate is 4.50%. Assume that you receive another $500,000. If you invest the money in a stock with a beta of 1.90, what will be the required return on your $5.5 million portfolio? Do not round intermediate calculations. Round your answer to two decimal places.

%

Answer 1

As per portfolio

As per CAPM

expected return = risk-free rate + beta * (expected return on the market - risk-free rate)

12 = 4.5 + 1.75 * (Market return% - 4.5)

Market return% = 8.79

Expected return for new investment

As per CAPM

expected return = risk-free rate + beta * (expected return on the market - risk-free rate)

Expected return% = 4.5 + 1.9 * (8.79 - 4.5)

Expected return% = 12.65

Total New Portfolio value = Value of Old portfolio + Value of Additional investment

=5000000+500000

=5500000

Weight of Old portfolio = Value of Old portfolio/Total New Portfolio Value

= 5000000/5500000

=0.9091

Weight of Additional investment = Value of Additional investment/Total New Portfolio Value

= 500000/5500000

=0.0909

Expected return of New Portfolio = Weight of Old portfolio*Expected return of Old portfolio+Weight of Additional investment*Expected return of Additional investment

Expected return of New Portfolio = 12*0.9091+12.65*0.0909

Expected return of New Portfolio = 12.06