Question

ii. Currently, the risk-free rate, krp, is 5 percent and the required return on the market, km, is 11 percent. Your portfolio has a required rate of return of 9 percent. Your sister has a portfolio with a beta that is twice the beta of your portfolio. What is the required rate of return on your sister's portfolio? a. 12.0% b. 12.5% c. 13.0% d. 17.0% e. 18.0%

Answer 1

The Correct Answer is c. 13.0%

As per Capital Asset Pricing Model (CAPM)

Re = Rf + (Rm-Rf) β

Where Re = Required rate of return

Rf = Risk free rate of return

Rm – Market Return

β – Beta of the stock

Rf = 5%

Rm = 11%

Re = 9%

Calculation of beta

Re = Rf + (Rm-Rf) β

9 = 5 + (11 - 5) β

9 = 5 + 6β

4 = 6β

β = 4/6

β = 0.6667

The beta of sister's portfolio is twice of 0.6667 i.e. 2 * 0.06667

= 1.3334

Calculation of Required rate of return of sister's portfolio

Re = Rf + (Rm-Rf) β

Re = 5 + (11 - 5) 1.3334

Re = 5 + 6 * 1.3334

Re = 5 + 8

Re = 13 %

or 13.0 %