Question

1. Suppose the yield on short-term government securities (perceived to be risk-free) is about 3%. Suppose also that the expected return required by the market for a portfolio with a beta of 1 is 13.5%. According to the capital asset pricing model: (15 points)

1. What is the expected return on the market portfolio?
2. What would be the expected return on a zero-beta stock?
3. Suppose you consider buying a share of stock at a price of $41. The stock is expected to pay a dividend of $2 next year and to sell then for $43. The stock risk has been evaluated at beta = -.5. Is the stock overpriced or underpriced?

Answer 1

1 Using CAPM model
a. Expected Return = Risk Free rate + beta * ( Market Portfolio - Risk Free rate) =3% +1*(13.5%-3%) = 13.50%

2. Zero- Beta Stock
Beta =0
Expected Return = Risk Free rate + beta * ( Market Portfolio - Risk Free rate) =3% +0*(13.5%-3%) = 0%

3. Required Rate =(Stock Price Next year - Stock Price Current year + dividend )/Stock Price Current Year =(43-41+2)/41 =9.76%

if Beta = -0.5
Then Expected Return = Risk Free rate + beta * ( Market Portfolio - Risk Free rate) =3% +-0.5*(13.5%-3%) = -2.25%
The stock is overprice because stock price is more than Required rate