Question

                                    Bank of Baruch           ($ million)                                                     

Assets:                                                            Liabilities:

91 day US Treasury bills        $ 150m            1 year Certificates of Deposit $ 825m

2 year commercial loans         $ 75m            5 year Bonds                                 70m

Fixed rate, 9% p.a. annually

10 year corporate loans-floating rate:            Overnight Fed Funds                  100m

LIBOR+50bp, semiannual roll date             91-day Commercial Paper           270m           

                                                $ 505m           Equity                                            65m           

10 year floating rate mortgages                     

quarterly roll dates                $ 600m

Notes: Commercial paper is a pure discount instrument. The 5 year bonds pay 8.5% p.a. semiannually with a yield of 7.5% p.a. and have a duration of 4.2 years. The 1 year Certificates of Deposit pay 2.75% p.a. annually. All values are market values.

What is the bank’s duration gap?

Answer 1

Bank's duration gap is the difference between the duration of assets and liabilities held by the Bank.

Calculation of Bank Duration Gap
Assets	Amount (in $ Mn)	Duration (in year)	Amount * Duration
91 day US Treasury bills	150.00	0.25	37.40
2 year commercial loans	75.00	2.00	150.00
10 year corporate loans-floating rate	505.00	10.00	5,050.00
10 year floating rate mortgages                     quarterly roll dates	600.00	10.00	6,000.00
	1,330.00	22.25	11,237.40
Weighted average duration of assets {(Amount*Duartion)/Amount}		A	8.45
Liabilities	Amount (in $ Mn)	Duration (in years)	Amount * Duration
1 year Certificates of Deposit	825.00	1.00	825.00
5 year Bonds	70.00	4.20	294.00
Overnight Fed Funds	100.00	0.06	5.66
91-day Commercial Paper	270.00	0.25	67.32
	1,265.00		1,191.98
Equity	65.00
	1,330.00
Weighted average duration of Liabilities {(Amount*Duartion)/Amount}		B	0.94
k (Liabilities/ Assets)		K	0.95
Bank's duration gap (in years) {(A-(B*K)}			7.55