Q. 4 (10 points, 5 points for each part) Consider a forward contract of which the underlying commodity incurs a storage cost which is a constant fraction of its spot price, , and the storage cost occurs continuously. The time to expiration of the contract is T years from now. The annual riskfree interest rate is r (cc). Let St denote the spot price of the underlying commodity at time t, and Fo,T denote the forward price in a forward contract signed at t=0 expiring at t=T. (a) Construct a synthetic portfolio that will generate the same state-contingent payoff of a short position in the forward contract at t=T. (b) Suppose that S0erT>Fo,TeT. Does an arbitrage opportunity exist? If yes, specify an arbitrage strategy and verify that it is an arbitrage strategy in a payoff table. If no, explain why not