Financial institutions management

FINANCIAL INSTITUTIONS MANAGEMENT

REVIEW FOR EXAM 1.

. Problem 1

Suppose you have the bank with the following balance sheet information. Market yields are in parenthesis, and amounts are in millions.

Assets	Duration	Amount ($ mill)		Liabilities + Equity	Duration	Amount ($ mill)
Cash				Demand deposits
1 month discount T bills (4%)				Overnight loans
1 year discount T bills (4.5%)				1 year CDs
3 year commercial loans, 10% fixed every year	2.7			2 year saving deposits with interest at maturity
5 year munis bonds, 8% floating, reset every 6 months	4.2			7 year subordinated debt, 6 % fixed rate annually	5.8
15 year mortgages, 11% floating reset every year	9.5			Equity
Total Assets				Total Liabilities + Equity

1. What is the funding or repricing gap if the planning period is 270 days, 1 year? Recall that cash and demand deposits do not have interest. Moreover, $20 million one-year runoffs are expected on 3-year commercial loans and 5 million, 6 months runoffs are expected on 2 year CDs.

RGAP (270 days) = 75 + 70 – 30 – 5 = $110 mill

Funding gap using a one-year planning period = (75 + 80 + 70 + 115 + 20) – (30+175+5) = $150 million.

2. What is the impact on net interest income over the next year if all interest rates fall by 75 basis points?

Net interest income will decline by: DNII = FG(DR) = +150(-.0075) = -$1.125 m.

3. Calculate the Maturity Gap for the bank. Based on this, what is your interest rate risk?

M_A = [0*$20 + 0.0833*$75 + 1*80 + 3*140 +5*70 + 15*115 ]/$500 =2581,248/500 = 5.162 years

M_L = [0*$60 + 1*$175 + 2*120 + 7*85]/$470 = 1010/470 = 2.149 years

MGAP = 5,162 – 2.149= 3,013 years.

Risk: interest rate increase because the market value of assets will fall by more than the market value of liabilities and market value of equity will decrease.

4. Appling the duration gap analysis calculate the change in the market value of equity if interest rates increase by 75 basis points. The current interest rate is 8%.

Da = [0*$20 + 1/12*$75 + 1*80 + 2.7*140 +4.2*70 + 9.5*115]/$500 = 1844.5/500=3.689

Dl = [0*$60 + 1*$175 + 2*120 + 5.8*85]/$470 = 908/470 = 1.931

DGAP = 3.689 – 1.931*470/500=1.8748

MVE= -DG * (A) * DR/(1 + R) = -1.8748 * 500 000 000 * 0.0075/1.08 = - 6 509 722.222

5. What variables are available to the financial institution to immunize the balance sheet? In order

to answer this questions discuss:

a) How much would each variable need to change to get DGAP equal to 0?

The desirable duration gap is zero. So you can reduce duration of assets, increase duration of

Liabilities, or to apply both ways at the same time. Duration of assets should be 1.81514 years if we

keep duration of liabilities and leverage ratio constant. Duration of liabilities should be increased to

3.689 years if we keep duration of assets and the leverage ratio constant.

b) Explain why FIs (manly banks) are not able (or not willing) to restructure the balance sheet.

Restructuring of the balance sheet is costly and time consuming. Restructuring of the balance sheet also lead to the conflicts in the bank functions. First of all, banks rely on bank-customer relationships, that’s why it is not easy to sell or buy assets (mainly loans) or borrow long term (only volatile liabilities can be managed in this case). Secondly, reduction of the duration gap to zero will undermine the asset transformation function of FIs, that is crucial in the effective financial system operation.

6. Suppose you decided not to restructure the balance sheet but to apply hedging to protect the total balance sheet against the interest rate risk. How many contracts are necessary to fully hedge the bank, if you want to hedge with Treasury Bills future contracts that currently quoted at 98$? The duration of the underlying T bills = 0.9 years. Assume, that you have the br = 1.2

Number of futures contracts to sell = (1.8748 * 500 000 000) / (1.2 * 0.9 * 980 000) = 1 118.75 or 1119 contracts

7. Verify that the change in the futures position will offset the change in the cash balance sheet position calculating the residual gain or loss. Assume that the market interest rate is expected to raise by 75 basis points.

For an increase in rates of 75 basis points, the change in the cash balance sheet position is:

1) Expected DE = -DGAP[DR/(1 + R)]A = - 6 509 722.22

2) The change in value of 1119 contracts = 0.9 x 1119 x 980 000 x 0.0075/1.08 = - 6 853 875

3) Gain = $344 152.78

Problem 2 (from Homework 2)

The current YTM is 7%. You hold 6% annual coupon bond with 4 years remaining maturity, 10000$ par value.

A) What is the modified duration of this bond?

B) Compute the convexity of the bond. Apply 50 basis points change in yields.

C) What is the estimated price change of the bond with convexity adjustment if interest rates increase by 50 bps (use Modified durations from a)? How well the model predicts the change in the bond price? (calculate the degree of error to conclude)

A)

t	CF	PV	PV x t
		560.75	560.75
		524.06	1048.126
		489.78	1469.34
		8086.69	32346.76
Total		9661.28	35424.976

D = 35424.976/9661.28= 3.667 y

MD = 3.667/1.07 = 3.427

B) What is the estimated price change of the bond with convexity adjustment if interest rates increase by 50 bps (use Modified durations from a)? How well the model predicts the change in the bond price? (calculate the degree of error to conclude)

	PV
R 0.5%	9 497.60	(FV = 10000, n = 4, PMT = 600, I = 7.5%)
R 0.5%	9 828.71	(FV = 10000, n = 4, PMT = 600, I = 6.5%)

P₀= $9661.28 (i=7%, n=4, PMT=$600, FV=$10000)

CX= [$9497.60 + $9828.71 – 2*$9 661.28] / [$9661.28*(0.005)⁵] = 15.53

C)

If R 0.5%

d P= -3.427*0.005* 9 661.28 + ½ * 15.53 * (0.005²) * 9 661.28= -165.55 + 1.875 = -$ 163.67

New Price = 9661.28 – 163.67 = 9497.605

Error = 9497.605 - 9 497.60 = 0.01

If R 0.5%

d P= -3.427* - 0.005 * 9 661.28 + ½ * 15.53 * (- 0.005²) * 9 661.28= + 165.55 + $ 1.875 = 167.425

New Price = 9661.28 + 167.425 = 9 828.705

Error = 9828.71 - 9 828.705 = 0.01

Problem 3

A Bank 1 has $70 million of commercial loans with a fixed rate of 12 percent. The loans are financed by $70 million of CDs at a variable rate of LIBOR + 2 percent. Bank 2 owns $70 million of floating-rate loans yielding LIBOR + 1 percent. These loans are financed by $70 million of fixed-rate deposits costing 9%.

a. Diagram the swap relationships between two banks. Which bank is the buyer and which one is the seller? What are the risk exposures of each bank?

Bank 1 is the buyer

b. Suppose one feasible swap for the bank 2 is to pay the Bank 1 LIBOR + 3.5 percent, and for the Bank 1 to pay 11 % to bank 2. Calculate the net financing cost for each bank.

Bank 1Bank 2

Net financing cost rate 9.5% L + 1.5%

The swap is not acceptable because bank 2 can not pay L+1.5%

Problem 4.

You are a pension fund manager who managers portfolio of bonds. Investment horizon is 4 years. All bonds have 5 year maturity, 10 000$ face value and 10% annual coupon. Duration of these bonds is 3.99 years. The current yield to maturity is 20%.

a) Calculate the Cash Flow the investment manager receives in 4 years if there is no changes in

interest rates over 4 years.

Solution:

Coupon interest payments over four years = 1000 x 4 = $4000

Net reinvestment income = 1000(1.2)³ + 1000(1.2)² + 1000(1.2) + 1000 - 4000 = 1368

Value of bond at end of year four = 11000/1.2 = $9 166.67

Total future value of investment $14 534.67

b) Calculate the Cash Flow the investment manager receives in 4 years if interest rates decrease by

200 bps at the end of the second year.

Solution:

Coupon interest payments over four years = 1000 x 4 = $4000

Net reinvestment income = 1000(1.2)³ + 1000(1.18)² + 1000(1.18) + 1000 - 4000 = 1300.4

Value of bond at end of year four = 11000/1.18 = $9 322.03

Total future value of investment $14 622.43

c) Change in the reinvestment income is 68$, however, the change in the value of the bond at the year 4 is (-155.38). The change in the interest rates affects the value of the bond to larger extend compare to the reinvestment income. That’s why we have slightly different amounts and we benefit from interest rates decrease $87.76.

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