Question

Consider the following table, which gives a security analyst's expected return on two stocks for two particular market returns: Aggressive Stock Market Return Defensive Stock 5% -2% 6% 25 38 12 a. What are the betas of the two stocks? b. What is the expected rate of return on each stock if the market return is equally likely to be 5% or 25% c. If the T-bill rate is 6% and the market return is equally likely to be 5% or 25%, draw the SML for this economy d. Plot the two securities on the SML graph. What are the alphas of each? e. What hurdle rate should be used by the management of the aggressive firm for a project with the risk characteristics of the defensive firm's stock?

Answer 1

Part-1) a= 0.06-0.12 0.02- 0.38 -2.00 and ß, = -0.30 0.05- 0.25 0.05- 0.25 Part-2) E(ra) = 0.5* (-0.02 0.38)= 18% E (ro) 0.5 (0.06 0.12) = 9% GRAPH 45 40 Part-3) The SML is comuted by the market expected return of [0.5 * (0.25 + 0.05)] 6% (which has B 0.15 or 15% 35 with BM 1, and r 0). 30- The equation for the security market would be: E(r) = 0.06 + B *(0.15 - 0.06) 25- LA 20- Part-4) The required return for the aggressive stock is: E(r)0.06 + 2.0 x (0.15 - 0.06) = 0.24 24% 15 a actual expected return - required return E(ro) 0.06 0.3 x (0.15 - 0.06) = 8.7% 104 18% - 24% = -6% 5 aDactual expected return - required return = 0.09 - 0.087 = +0.003 = + 0.3% 2. 1.5 0.5 1 2.5 Beta Part-5) The hurdle rate would be computed with the project beta (0.3), and not beta. The correct value for the discount rate would be 8.7% i.e. the required return for stock D Expected retum