Question

Suppose the yield on short-term government securities (perceived to be risk-free) is about 6%. Suppose also that the expected return required by the market for a portfolio with a beta of 1 is 14.0%. According to the capital asset pricing model:

 a. What is the expected return on the market portfolio? (Round your answer to 1 decimal place.) Expected rate of return %

 b. What would be the expected return on a zero-beta stock? Expected rate of return % 

Suppose you consider buying a share of stock at a price of $45. The stock is expected to pay a dividend of $4 next year and to sell then for $47. The stock risk has been evaluated at β = –0.5.

 c-1. Using the SML, calculate the fair rate of return for a stock with a β = –0.5. (Round your answer to 1 decimal place.) Fair rate of return %

 c-2. Calculate the expected rate of return, using the expected price and dividend for next year. (Round your answer to 2 decimal places.) Expected rate of return %

 c-3. Is the stock overpriced or underpriced? Underpriced Overpriced

Answer 1

a). r = rM = 14% (As the portfolio has the beta of 1)

b). r = rF = 6% (As the stock has zero-beta, which is same as the risk-free rate)

c1). r = rF + beta[E(rM) - rF]

= 6% + (-0.5)[14% - 6%] = 6% - 4% = 2%

c2). r = [P1 - P0 + D] / P0 = [$47 - $45 + $4] / $45 = 13.33%

c3). Because the expected return exceeds the fair return, the stock must be under-priced.