Question

BankBoston Balance Sheet

Assets		Liabilities
Cash	30	Core Deposits	20
Federal Funds (8.5%, .36)	20	Federal Funds (8.5%, .401)	50
Loans (Fixed) (12%, x)	105	Euro CDs (9%, .401)	130
Loans Floating (Libor +4%, .36)	65	Equity	20
Total Assets	220	Total Liabilities and Equity	220

Notes: Libor is 11%. Fixed rate loans have five-year maturities, and are priced at par, principal is repaid at maturity.

1.What is the duration of the fixed rate loans?

2.What is the duration of BankBoston’s assets?

3.What is the duration of BankBoston’s liabilities?

4.What is the duration gap?

5.What is the impact on net worth if interest rates rise by 1%?

6.What is the impact on net worth if interest rates fall by .75%?

Answer 1

1. Fixed rate loans are priced at par having interest rate of 12%. Par value is $105 so coupon amount=105*12%=$12.60 for 5 year period.

1 2 3 4=2*3 5=1*4 year cash flow($) df @12% PV of cash flow($) PV of cash flow*time($) 1 12.6 0.893 11.250 11.250 2 12.6 0.797 10.045 20.089 3 12.6 0.712 8.968 26.905 4 12.6 0.636 8.008 32.030 5 117.6 0.567 66.729 333.647 105.000 423.922 Duration=5/4 4.0373 years

2. Duration of assets= (30*0+20*0.36+105*4.0373+65*0.36)/220=2.066 years

3. We have not been provided with the rate of interest on core deposits. Accordingly duration for core deposits could not be calculated. As a result duration of liabilities can't be calculated.

4. In the absence of duration of liabilities we cannot calculate duration gap.

5 and 6. Without 3 and 4, these cannot be calculated.