20 points Consider the following information Rate of Return

(20 points) Consider the following information Rate of Return if State Occurs State of EconomyProbability of Stock A Stock B Recession Normal Boom State of Econom 0.20 0.60 0.20 0.06 0.07 0.11 -0.20 0.13 0.33 (a) Calculate the Expected Returns for the two stocks (b) Your portfolio is invested 30% in Stock A and 70% in Stock B. what is the expected return of the portfolio? (c) Suppose the risk-free rate is 2% and a diversified market portfolio offers 6% return. Calculate the betas for the stocks (d) What is the portfolio beta? 4

Solution

Expected return of A = 0.2*6% + 0.6*7% + 0.2*11% = 7.60%

Expected return of B = 0.2*-20% + 0.6*13% + 0.2*33% = 10.40%

b, expected return = 0.3*7.6% + 0.7*10.4% = 9.56%

c. beta for A = (7.6-2)/(6-2) = 1.40

beta for B = (10.4-2)/(6-2) = 2.10

d. portfolio beta = (9.56-2)/(6-2) = 1.89