Question

first national bank has assets consisting of $100 million in home equity loans with a modified duration of 2 plus $100 million in mortgages with a modified duration of 5, and liabilities of $200 million in deposits with an average modified duration of 2. The market value of FNB's assets and liabilities is very close to book value. FNB's treasurer wants to use a five-year swap (with a 4.2 modified duration) to neutralize the bank's duration position. Caculate and describe the 5-year swap position the treasurer should enter into to do so.

Answer 1

first national bank has assets consisting of $100 million in home equity loans with a modified duration of 2 plus $100 million in mortgages with a modified duration of 5

Weighted modified duration of assets = 100 / (100 + 100) x 2 + 100 / (100 + 100) x 5 = 3.5

Average modified duration of liabilities = 2

So, there is duration gap between assets and liabilities.

• First national bank needs to use swaps to cover the gap between the duration of its asset and liabilities and thus to mitigate its exposure to interest rate risk.
• The bank must borrow at a floating rate and use the proceeds to buy long-term fixed rate assets in order to mitigate their asset interest rate exposure.
• Thus the bank secures future income payments at a certain fixed rate, which it can use to pay the interest on its long-term fixed rate liabilities.
• Similarly, it can use the income from its floating-rate assets to repay the income on its borrowed floating-rate instruments. Thus, it neutralizes its risk-exposure.