Question

Suppose the yield on short-term government securities (perceived to be risk-free) is about 4%. Suppose also that the expected return required by the market for a portfolio with a beta of 1 is 10.0%. According to the capital asset pricing model:

a. What is the expected return on the market portfolio? (Round your answer to 1 decimal place.)
b. What would be the expected return on a zero-beta stock?
c-1. Using the SML, calculate the fair rate of return for a stock with a ? = –0.5.
c-2. Calculate the expected rate of return, using the expected price and dividend for next year. (Round your answer to 2 decimal places.)
c-3. Is the stock overpriced or underpriced?

Answer 1

a) The Beta of market portfolio of is always 1, hence the expected return of market portfolio will be 10%

Expected return = Rf+Beta(Rm-Rf)

=4%+1*(10%-4%)= 10%

b) Expected return of zero beta stock will be risk free return = 4%

Expected return = Rf+Beta(Rm-Rf)

=4%+0*(10%-4%)= 4%

C-1) Fair rate of return = 1%

Working:-

The expected return by SML of stock with Beta= -0.5

= 4%+(-0.5)*(10%-4%) =1%

C-2) Expected rate of return, using the expected price and dividend for next year

Ans:- Expected rate of return = 16%

Working:-

Expected rate of return

=(Price of share next year +dividend)/current price-1

=(78+9-75)/75 -1

=16%

C-3) Stock is Under priced

Reason:- The expected return(16%) on stock is higher than the fair rate of return (1%) hence the stock must be under-priced.