Question

7-20. Historical Returns: Expected and Required Rates of Return You have observed the following returns over time: Year 2011 2012 2013 2014 2015 Stock X Stock Y Market 14% 13% 12% 19 7 10 - 16 -5 -12 3 s11 20 11 15 - Assume that the risk-free rate is 4%, the market risk premium is 5%, the beta for Stock X is 1.50, and the beta for Stock Y is 0.46: a. What are the required rates of return for Stocks X and Y? b. What is the required rate of return for a portfolio consisting of 40% of Stock X and 60% of Stock Y? c. If Stock X's expected return is 13%, is Stock X under-or over-valued?

Answer 1

A) Required rate of return for stocks X and Y

Given : risk free rate = 4%

Market risk premium = 5%

Beta of x = 1.5

Beta of Y = 0.46

Required return of X = risk free rate + beta × market risk premium

= 4% + 1.5 × 5%

= 4% + 7.5%

= 11.5%

Required return of stock Y = Risk free rate + beta × market risk premium

= 4% + 0.46 × 5%

= 4% + 2.3%

= 6.3%

B) Required rate of return of the portfolio

Given : weight of X = 40% , weight of Y = 60%

Return of X = 11.5% , Return of Y = 6.3%

E(r) = weight of X × Return of X + weight of Y × Return of Y

= 0.4 × 11.5% + 0.6 × 6.3%

= 4.6% + 3.78%

= 8.38%

C) As the expectes return of stock (13%) is more than the return calculated using CAPM model in part (a), it is undervalued.