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?

Question

Quizplus · Accepted Answer

Duration gap = (Duration of Assets - Duration of Liabilities)
= (5.5 - 2.5)
= 3 years

Notional amount = $100,000

Number of swap contracts = (Duration Gap * Equity) / (Notional Amount * Duration of the Swap)
= (3 * $40,000,000) / ($100,000 * 6)
= 2,000

However, since the floating-rate bond reprices annually, we need to set up a new swap contract each year. Therefore, the actual number of swap contracts should be multiplied by the duration of the floating-rate bond, which is one year.

So, the optimal number of swap contracts = 2,000 * 1.6 (8-year fixed-rate bond duration / 5-year floating-rate bond duration)
= 3,200 contracts.

Therefore, the best choice is D) 3,200 contracts.

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