Question

Assume the risk-free rate is constant at 2.5%, please find out the possible arbitrage opportunity given the following information.

                        3-month futures price: $100

                        6-month futures price: $105

Answer 1

Risk free rate is constant @ 2.5%

therefore risk free rate from the end to 3 months to the end of 6 months = 2.5%

Therefore implied forward rate for 6 months = 100 x (1+2.50% x 3 /12) = $100.625

Therefore arbitrage is possible
Buy 3 month futures @ $100

Sell 6 month futures @ $105

Pay the above amount ($100) at the end of 3rd month by borrowing for 3 months

Therefore amount to be repaid after 6 months =  $100 x (1+2.50% x 3 /12) = $100.625

Amount receivable from sell of 6 month future = $105

Therefore arbitrage gains (received at the end of 6 months)= $105 - $100.625 = $ 4.375

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