(6—13) :ricol Returns: xpecred ond lire-d Rates of Return You have observed the following returns over time: Year Stock X Stock Y Market 2006 14% 13% 12% 200? 19 3' 10 2008 —10 —5 —12 2009 3 1 1 2010 20 11 15 Assume that the risk—free rate is 6% and the market risk premium is 5%. acts» ('1 What are the betas of Stocks X and Y? What are the required rates of return on Stocks X and Y? . What is the required rate of return on a portfolio consisting of 80% of Stock X and 20% of Stock Y? If Stock X's expected return is 22%, is Stock X under- or overvalued?

Part a

Beta of stock X = 1.35

Beta of stock Y = 0.65

Part b

Stock X

The required rate of return =12.75%

Stock Y

Required rate of return = 9.25%

Part c

The required rate of return of a portfolio = 12.05%

Part d

Stock X is undervalued

Step-by-step explanation

Part a

Beta = covariance between the stock and the market/ variance of the market

Covariance = ∑ (Return of stock - expected return of the stock) * (return of the market - expected return of the market)/ (n - 1)

Where n is the number of periods

Variance of the market = ∑ (M - Mean M) ^ 2/ (n - 1)

                       = 478.8/ 4

                      = 119.7

Covariance between stock X and the market = ∑ (X - Mean X) * (M - Mean M)/ (n - 1)

                           = 645/ 4

                           = 161.25

Beta of stock X = 161.25/ 119.7

                = 1.35

Covariance between stock Y and the market = ∑ (Y - Mean Y) * (M - Mean M)/ (n - 1)

                              = 311.6/ 4

                              = 77.9

Beta of stock Y = 77.9/ 119.7

                         = 0.65

Part b

Using the Capital Assets Pricing Model (CAPM);

Required rate of return = risk-free rate + beta * market risk premium

Stock X

Required rate of return = 6% + 1.35 * 5%

                  = 12.75%

Stock Y

Required rate of return = 6% + 0.65 * 5%

               = 9.25%

Part c

Required rate of return of a portfolio = proportion of stock X * required rate of return of stock X + proportion of stock Y * required rate of return of stock Y

                      = 0.8 * 12.75% + 0.2 * 9.25%

                      = 10.20% + 1.85%

                     = 12.05%

Part d

Stock X is undervalued because the required rate of return is less than the expected return.