A Bank Has Assets of $500,000,000 and Equity of $40,000,000

Multiple Choice

A bank has assets of $500,000,000 and equity of $40,000,000. The assets have an average duration of 5.5 years, and the liabilities have an average duration of 2.5 years. An 8-year fixed-rate T-bond with the same coupon as the fixed-rate on the swap has a duration of 6 years, and the duration of a floating-rate bond that reprices annually is one year. The bank wishes to hedge its balance sheet with swap contracts that have notional contracts of $100,000. What is the optimal number of swap contracts into which the bank should enter?

A) 2,500 contracts.
B) 2,760 contracts.
C) 13,800 contracts.
D) 3,200 contracts.
E) None of the abovE.