After conducting a rate-sensitive analysis,a bank finds itself with the following amounts of rate-sensitive assets and liabilities (RSAs and RSL)and fixed-rate assets and liabilities (FRAs and FRLs); the rate of return and cost rates on the accounts are also given: Suppose the institution wishes to fully hedge the interest rate risk with a swap. A swap is available with whatever notional principal is needed that pays fixed at 4.95 percent and pays variable at LIBOR. LIBOR is currently 5.11 percent. By how much would profits change right now if the bank engages in the swap?

Question

After conducting a rate-sensitive analysis,a bank finds itself with the following amounts of rate-sensitive assets and liabilities (RSAs and RSL)and fixed-rate assets and liabilities (FRAs and FRLs); the rate of return and cost rates on the accounts are also given:  Suppose the institution wishes to fully hedge the interest rate risk with a swap. A swap is available with whatever notional principal is needed that pays fixed at 4.95 percent and pays variable at LIBOR. LIBOR is currently 5.11 percent. By how much would profits change right now if the bank engages in the swap?

Quizplus · Accepted Answer

To fully hedge the interest rate risk, the bank needs to pay fixed and receive variable on the notional principal amount. The fixed rate on the swap is 4.95% and LIBOR is currently at 5.11%, so the bank will receive 5.11% variable rate on the notional principal amount.

Let's first find the notional principal amount needed to fully hedge the interest rate risk:

Net rate-sensitive gap = RSAs - RSLs = 50,000 - 100,000 = -50,000

Notional principal amount = Net rate-sensitive gap / (Fixed rate - Variable rate)
= -50,000 / (0.0495 - 0.0511) = 2,469,136.66

So, the bank needs a notional principal amount of $2,469,136.66 to fully hedge the interest rate risk.

Now, let's see how profits would change right now if the bank engages in the swap:

Current interest income on RSAs = RSAs * Variable rate = 50,000 * 0.0511 = $2,555

Current interest expense on RSLs = RSLs * Fixed rate = 100,000 * 0.055 = $5,500

Current interest expense on FRAs = FRLs * Fixed rate = 1,000,000 * 0.065 = $65,000

Net interest income before swap = Current interest income - Current interest expense = 2,555 - 5,500 - 65,000 = -$67,945

After engaging in the swap, the interest expense on RSLs and the interest income on the swap will change:

New interest expense on RSLs = RSLs * Variable rate = 100,000 * 0.0511 = $5,110

New interest income on swap = Notional principal amount * (Fixed rate - Variable rate)
= 2,469,136.66 * (0.0495 - 0.0511) = -$126,854.39 (negative because the bank is paying fixed and receiving variable)

Net interest income after swap = Current interest income - New interest expense on RSLs - Current interest expense on FRAs + New interest income on swap
= 2,555 - 5,110 - 65,000 - (-126,854.39) = $202,599.39

Therefore, profits would increase by $202,599.39 if the bank engages in the swap, which is closest to option D, -$195,200.

After Conducting a Rate-Sensitive Analysis,a Bank Finds Itself with the Following