Consider this arbitrage strategy to derive the parity relationship for spreads:
(1) Enter a long futures position with maturity date T1 and futures price F (T1);
(2) Enter a short position with maturity T2 and futures price F (T2);
(3) At T1, when the first contract expires, buy the asset and borrow F (T1) dollars at rate rf.
(4) Pay back the loan with interest at time T2.
a. What are the total cash flows to this strategy at times 0, T1, and T2?
b. Why must profits at time T 2 be zero if no arbitrage opportunities are present?
c. What must the relationship between F(T1) and F (T2) be for the profits at T2 to be equal to zero? This relationship is the parity relationship for spreads.