Question

The market price of a security is $50. Its expected rate of return is 14%. The risk- free rate is 6% and the market risk premium is 8.5%. What will be the market price of the security if its correlation coefficient with the market portfolio doubles and all other variables remain unchanged)? Assume that the stock is expected to pay a con- stant dividend in perpetuity.

Answer 1

SOLUTION Bi = OiM/om OiM = PiMOOM When Pim doubles, OiM & Bi also doubles. Thus (as per CAPM) the risk premium would be double too, which means: Eſri) = rf + Bi [E(rm) – rf] Eri) - If= Bi [E(IM)-rf] If ſi doubles, E(Ti) -rf doubles. Current Risk Premium: E(ri) - If=[14% -6%] = 8% New Risk Premium: E(Ti) – If = 16% New discount rate (expected return) for the security: E(ri) = [16% +6%] = 22% Assuming that the stock pays a constant perpetual dividend, dividend (D) need to satisfy the equation for the present value of perpetuity: Price =[D / E(ri)] Solve for D given the original price and r: D= [Price * E(r;)] = [$50 * 0.14] = $7.00 With dividend remains constant, we will compute the new price: Price = D/E(ri) = [$7.00/0.22] = $31.82 A rise in stock's risk has reduced its value by 36.36% (=$31.82/$50 - 1) Now we may model the change in risk as a change in B (not a change in o) as are aware that total risk (o) is not the "priced" relationship. The relationship among the stock and all other stocks measured by B is significant, "priced" relationship. Thus as per CAPM, it is compensated for the portion of market risk, measured as B that is selected to incur. It is not compensated for total risk, measured as o.