1. Use the following facts for (all parts of) this problem:

There is only one factor that affects stock returns, and it is the growth in industrial production

There are three possible states of the world: Ugly, Bad and Good. We know exactly how much return the following three securities (A, B and C) will yield in each of the possible states:

StateUglyBadGoodProbability1/31/31/3Growth in production0%5%10%Stock A16%6%-4%Stock B4%9%14%Stock C2%12%22%

Securities A, B and C sell for 50 rupees each

(a) Calculate the values of F (unanticipated growth in industrial production) for the only factor in all three states

(b) Calculate from the above table, the expected returns of each of the three securities, and their factor sensitivities to the industrial production factor

(c) Using only securities A and B, calculate the implied risk-free rate, and the factor premium for the industrial production factor

(d) Now, using only securities A and C, calculate the implied risk-free rate, and the factor premium for the industrial production factor

(e) Comparing your answers from (c) and (d) above, is there an arbitrage opportunity in this economy?