19. Consider this arbitrage strategy to derive the parity relationship for spreads: (1) enter a long futures position with maturity date T 1 and futures price F ( T 1 ); (2) enter a short position with maturity T 2 and futures price F ( T 2 ); (3) at T 1 , when the first contract expires, buy the asset and borrow F ( T 1 ) dollars at rate r f ; (4) pay back the loan with interest at time T 2 .

a. What are the total cash flows to this strategy at times 0, T 1 , and T 2 ?

b. Why must profits at time T 2 be zero if no arbitrage opportunities are present?

c. What must the relationship between F ( T 1 ) and F ( T 2 ) be for the profits at T 2 to be equal to zero? This relationship is the parity relationship for spreads.