Your research has found that the returns of all securities in the economy share oil price as one common factor, Rie=i+iOt+ei where Rie is the

Your research has found that the returns of all securities in the economy share oil price as one common factor,

Rie=αi+βi×Ot+ei

where Rie is the excess return Ri − Rf . Consider two well diversified portfolios, A and B with following characteristics:

Answer the following questions (they can all be answered independently).

1. Suppose R_f = 5% and E(O_t) = 4%. Check if there are arbitrage opportunities in this market.
2. Suppose α_A = 0.5% and α_B = 1%. Calculate the weights of A and B in a zero-beta portfolio. Then describe how you would exploit the arbitrage opportunity and what is the return of doing so.
3. Given the information provided, What must be the risk-free rate R_f and E(O_t) in this economy if there are no arbitrage opportunities?