Question

22-4 d is not .6495

Use the data provided for Gotbucks Bank, Inc., to answer this question.

Gotbucks Bank, Inc. (in $ millions)
Assets			Liabilities and Equity
Cash	$	35	Core deposits	$	36
Federal funds		25	Federal funds		55
Loans (floating)		110	Euro CDs		135
Loans (fixed)		70	Equity		14
Total assets	$	240	Total liabilities and equity	$	240

Notes to the balance sheet: Currently, the fed funds rate is 9 percent. Variable-rate loans are priced at 3 percent over LIBOR (currently at 10 percent). Fixed-rate loans are selling at par and have five-year maturities with 11 percent interest paid annually. Assume that fixed rate loans are non-amortizing. Core deposits are all fixed rate for two years at 7 percent paid annually. Euro CDs currently yield 8 percent.

a.	What is the duration of Gotbucks Bank’s (GBI) fixed-rate loan portfolio if the loans are priced at par? (Do not round intermediate calculations. Round your answer to 3 decimal places. (e.g., 32.161))

Duration

years

b.	If the average duration of GBI’s floating-rate loans (including fed fund assets) is .41 year, what is the duration of the bank’s assets? (Note that the duration of cash is zero.) (Do not round intermediate calculations. Round your answer to 3 decimal places. (e.g., 32.161))

Duration (assets)

years

c.	What is the duration of GBI’s core deposits if they are priced at par? (Do not round intermediate calculations. Round your answer to 3 decimal places. (e.g., 32.161))

Duration (deposits)

years

d.	If the duration of GBI’s Euro CDs and fed fund liabilities is .406 years, what is the duration of the bank’s liabilities? (Do not round intermediate calculations. Round your answer to 4 decimal places. (e.g., 32.1616))

Duration (liabilities)

years

e-1.	What is GBI’s duration gap? (Do not round intermediate calculations. Round your answer to 4 decimal places. (e.g., 32.1616))

Duration gap

years

e-2.	What is the expected change in equity value if all yields increase by 200 basis points? (Enter your answer in dollars not in millions. Negative amount should be indicated by a minus sign. Do not round intermediate calculations.)

Expected change in equity value

$

e-3.	Given the equity change in e-2. what is the expected new market value of equity after the interest rate change? (Enter your answer in dollars not in millions. Negative amount should be indicated by a minus sign. Do not round intermediate calculations.)

New market value

$

Answer 1

Soln : a) Duration is the sensitivity of pricing with the change in interest rate of the instrument bond, loan etc. Please refer the table, we have considered yield as =11%, Price at Par, P = 70

Years(t)	1	2	3	4	5
Coupon	7.7	7.7	7.7	7.7	77.7
Discount facor at 11%	0.9009009	0.8116224	0.7311914	0.658731	0.59345133
PV	6.94	6.25	5.63	5.07	46.11
Sum of pV = V	70.00
t*PV	6.9369	12.4990	16.8905	20.2889	230.5558
Duration = sum of t*PV/V	4.10

b) Now duration of federal fund and floating rate is given as 0.41 year , for fixed loan we have calculated as 4.10 years

So, duration of assets = weighted average duration of all assets/Total assets = (35*0 +(25+110)*0.41 +70*4.10)/240 = 1.43 years.

c) Duration of core deposits , when they are at par yield is taken as 7% and price = 36

Years(t)	1	2
Payment	2.52	38.52
Discount factor d @7%	0.935	0.873
PV = payment*d	2.355	33.645
t*PV	2.355	67.290
Duration = sum of t*PV/Price	1.935

We can see duration of core deposits = 1.935 years (Calcuated above)

d) duration of Euro CDs and fed funds liabilities = 0.406 years ,

So , duration of liabilities = weighted average of duration/total liabilities = (1.935*36 + 55 *0.406 +135*0.406) /226 = 146.785/226 = 0.6495 years