Question

24. The balance sheet for Gotbucks Bank Inc. (GBI) is presented below ($ millions). $ 30 $ 20 50 Assets Cash Federal funds Loans (floating) Loans (fixed) Total assets Liabilities and Equity Core deposits Federal funds Euro CDs Equity Total liabilities and equity 105 130 20 65 $220 $220 Notes to the balance sheet: The fed funds rate is 8.5 percent, the floating loan rate is LIBOR (London Interbank Offered Rate) + 4 percent, and currently LIBOR is 11 percent. Fixed-rate loans have five year maturities are priced at par, and pay 12 percent annual interest. The principal is repaid at matu: rity. Core deposits are fixed rate for two years at 8 percent paid annually. The principal is repaid at maturity. Euro CDs currently yield 9 percent. a. What is the duration of the fixed-rate loan portfolio of Gotbucks Bank? b. If the duration of the floating-rate loans and fed funds is 0.36 year, what is the duration of GBI's assets? c. What is the duration of the core deposits if they are priced at par? d. If the duration of the Euro CDs and fed funds liabilities is 0.401 year, what is the duration of GBI's liabilities? e. What is GBI's duration gap? What is its interest rate risk exposure? f. What is the impact on the market value of equity if the relative change in all interest rates is an increase of 1 percent (100 basis points)? Note that the relative change in interest rates is AR/(1 + R = 0.01. g. What is the impact on the market value of equity if the relative change in all interest rates is a decrease of 0.5 percent (-50 basis points) h. What variables are available to GBI to immunize the bank? How much would each variable need to change to get DGAP to equal zero?

Answer 1

Ans a)

Five year loan(values in $ million)

Par Value = $ 65 Coupon rate = 12% Annual Payments =$ 65 * 12% = $ 7.8 YTM = 12% Maturity = 5 Years

Time	Cash Flow	PVIF	PV of cash flow	PV of cash flow * Time
1	$7.80	0.892857	$6.964	$6.964
2	$7.80	0.797194	$6.218	$12.436
3	$7.80	0.71178	$5.552	$16.656
4	$7.80	0.635518	$4.957	$19.828
5	$72.80	0.567427	$41.309	$206.543
			$65.000	$262.427

Duration of fixed rate loan = $ 262.427 / $ 65 = 4.0373

The duration is 4.037 years.

b)

Duration of GBI Asset = [30(0) + 20 (.36) + 105 (.36) + 65(4.037) ]/220 = 1.397 years

c)

Two-year core deposits (values in $ million)

Par value = $20 Coupon rate = 8% Annual payments R = 8% Maturity = 2 years

Time	Cash Flow	PVIF	PV of cash flow	PV of cash flow * Time
1	$1.60	0.92593	$1.481	$1.481
2	$21.60	0.85734	$18.519	$37.038
			$20.000	$38.519

Duration = $38.519/$20.000 = 1.9259

The duration of the core deposits is 1.9259 years.

d)

Duration of GBI Liabilities  = [20 × (1.9259) + 50 × (0.401) + 130 × (0.401)]/200 = 0.5535 years

e)

GBI’s leveraged adjusted duration gap is: 1.397 - 200/220 * (0.5535) =0.8938 years

f)

The duration gap of GBI is positive, so if the interest rate increase the net worth will decrease . For 1 percent increase in interest rate, the change in net worth is:

E = -0.8938 * (0.01) * $220 = -$1,966,360 (new net worth will be $ 20,000,000 - $ 1,966,360 = $18,033,640).

g)

The duration gap of GBI is positive,so if the interest rate decrease the net worth will increase. For a 0.5 percent decrease in interest rate, the change in net worth is:

E = -0.8938 * (-0.005) * $220 = $983,180 (new net worth will be $ 20,000,000 + $ 983,180 = $20,983,180)

h)

For Immunization the bank requires to have a leverage-adjusted duration gap of 0.0.

1. GBI use the combination of reduced asset duration and increased liability duration so that leverage-adjusted duration gap is attain 0.0 or,

2. GBI may reduce the duration of its assets to 0.5535 years by using more floating rate loans and fed funds .