Consider the following securities and their sensitivities to two factors (the factors have zero means):

Stock A: rA,t = 8 + 5F1,t + 6F2,t + eA,t Stock B: rB,t = 6 + 4F1,t + 1F2,t + eB,t Riskfree: rf = 1

a. Construct a portfolio out of stocks A and B which is riskless in terms of factor 2. You may sell short either A or B if necessary. (i) What are wA and wB for this portfolio? (ii) How sensitive is this portfolio to factor 1 (that is, how many units of factor 1 risk)? (iii) Given your answers to a) and b), what is the risk premium per unit of factor 1 risk, l1?

b. Construct a portfolio out of stocks A and B which is riskless in terms of factor 1. You may sell short either A or B if necessary. (i) What are wA and wB for this portfolio? (ii) How sensitive is this portfolio to factor 2 (that is, how many units of factor 2 risk)? (iii) Given your answers to a) and b), what is the risk premium per unit of factor 2 risk, l2 ?

c. Given your answers to a.(iii) and b.(iii), what does the APT predict the returns would be on the above securities? (Hint: I'm not looking for the intercept a).

d. What does APT predict the return should be for stock C? Stock C: rC,t = 5 + 3F1,t + 4F2,t + eC,t

e. Is stock C underpriced or overpriced? How would you exploit this arbitrage opportunity? Explain your strategy.