Question

A bank has made a 1-year loan at 4%. To fund the loan, it issued a 6-month deposit at 2.5%. It also purchased a 6x12 FRA at 3%. On the settlement date of the contract, 6-month LIBOR is 5%, and the bank issues a 6-month deposit at LIBOR. What is the bank’s interest margin (spread), in %, for the first six months and for the next?

1. 1.5% and 1.5%
2. 1.5% and 1%
3. 1.5% and −1%
4. 1% and −1%
5. 1% and 1%
6. 1.5% and 2%

Answer 1

Let's say the notional amount distributed as loan initially at 4%p.a. rate of interest = -$100

To fund the loan, the amount of deposit has been issued for 6-month at 2.5% p.a rate of interest = $100

Bank enters into 6*12 FRA at 3% fixed rate = $0

After 6 months:

Bank paid back to the depositor at 2.5%p.a. rate of interest = 100*(1+.025*180/360) = -101.25

The bank received 2% of the interest from loan = 102.00

Banks Interest margin = 102-101.25/100 = 0.75%

but this 0.75% is for 6 months, we need to annualized it = 075%*360/180 = 0.75*2 = 1.50%

After 1 year:

Bank will receive loan amount with interest = $104

*Bank will pay its depositor at 3% = -$103

Banks interest margin = 104-103/100 = 1%

But this 1% is for 6-months only, we need to annualize it = 1%*360/180 = 1%*2 = 2%

Option F is correct answer.

*Bank came in FRA agreement at the start and settle the payment at the end of the FRA period. Bank pays the counterparty at 3% and receives LIBOR at 5% and also the bank has issued a deposit after 6 months at the LIBOR rate. That means the bank needs to pay 5% at the completion of 360 days. LIBOR received from counterparty and LIBOR paid to depositor cancels out and ultimately the bank needs to pay only 3% after 360 days.  Hence, we calculated interest payments at 3% rate.