A 30-day Federal Fund (FF) futures contract is an instrument that enables banks to lock in a Federal funds interest rate for the 30-day period ending on the expiration of the contract. FF futures are quoted as prices rather than as rates. The price quoted is 100 minus the 30-day Fed funds rate, with the rate being expressed as a percentage (not in decimal form). For example, if you buy/sell 1 FF futures at a price of $96.82, you lock in a Fed funds rate of 100 − 96.82 = 3.18% on your future lending/borrowing. The security underlying the FF futures is a $5,000,000 30-day deposit or loan. Consider a bank that has surplus cash of $10 million. The bank plans to lend this $10 million in the Fed funds market over June but to hedge its risk, it decides to lock in a return by buying FF futures that expire on June 30.

a) Calculate the change in the value of one FF futures contract for a 1 basis point change in the Fed funds rate.

b) Suppose that the bank bought the futures today for $99.780, and their price at expiration (June 30) was $99.824. Explain how the bank will meet its objective of locking in a return on its Fed funds lending over June.