Suppose the following two-factor model holds:

r_it r_f = a_i + b_i1(r_1t r_f) + b_i2(r_2t r_f) + e_it,

where r_it is the return on security i at time t, r_f is the riskfree rate, (r_1t r_f) and (r_2t r_f) are the excess returns of the two factors at time t, b_i1 and b_i2 are the sensitivities of i to the two factors, and e_it is the impact of unanticipated firm-specific events on i.

The expected returns of the factors, E(r_1t) and E(r_2t) are 5% and 8%, respectively. The riskfree rate r_f is 3%.

(a) Well-diversified Portfolio C has b_C1 = 1.5 and b_C2 = 0.3. Calculate Portfolio Cs expected return if no arbitrage opportunities exist.

(b) Suppose the expected return on Portfolio C is 2% higher than your answer in (a). Describe an arbitrage strategy, show why it is an arbitrage, and calculate the % profits. (You can use two correctly-priced factor portfolios, F1and F2.)

(c) There is another strategy that gives the same % return as the arbitrage in (b) but has a positive standard deviation. Briefly explain to your risk-loving friend why he should still execute the arbitrage strategy in part (b).