Question

Suppose the rate of return on short-term govemment securities (perceived to be risk free) is about 5%. Suppose also that the expected rate of return required by the market for a portfolio with a beta of 1 is 12%. According to the capital asset pricing model (security market line): a. What is the expected rate of return on the market portfolio? b. What would be the expected rate of return on a stock with B 0? c. Suppose you consider buying a share of stock at $40. The stock is expected to pay $3 dividends next year and you expect it to sell then for $41. The stock risk has been evaluated at B -.5. Is the stock overpriced or underpriced?

Answer 1

Part-1) E(ri)=rf+B[E(IM) - If] E(TM)= [E(r) – rf]/B - 1 = [0.12 -0.05]/1 +0.05 = 12% Part-2) E(ri) = rf + B1[E(IM) - [f] =0.05 + 0[0.12 -0.05] = 5% Part-3) As per CAPM: E(r) = 18+ B[E(TM) - If]=0.05 +-0.5[0.12 -0.05] = 1.5% As CAPM, the price has to be: Po = [E(P1) + E(D1)]/[1 + E(R)] = [$41 + $3]/(1.015) = $43.35 As market price is $40, thus stock is underpriced. It is vital that market participants should buy the stock and raise its price until it reaches $43.35 to ensure that the holders of the stock are compensated only for the market risk they suffered.