Question

Bank Balance Sheet (Note: Use this information for all three problems)

Item                             Amount            Duration       Interest Rate       

Cash-type Securities       $50m                1.2 year             2.25%

Commercial Loans          $100m             2.4 years           4.50%

Mortgages                     $350m             8.0 years           6.50%

Core Deposits                $270m             1.0 year             2.00%

Notes Payable                $180m             2.0 years           4.50%

2. On-Balance Sheet Immunization Analysis (Use balance sheet information above, 6 points)

Immunization formulas: 1) Setting D_A x A = D_L x L will immunize the bank against interest rate risk.

2) Setting the Leverage-Adjusted Duration Gap equal to 0 will also immunize the bank against interest rate risk

(0 = D_A – k D_L ).

a. Calculate the duration of assets as a group and the duration of liabilities as a group, using a weighted-average approach (weight each item by the percentage it represents of the total amount). Also, calculate and report the adjusted duration gap.

Assume the bank wants to leave its assets unchanged, and change the composition of its liabilities, but keep the current dollar amount of liabilities the same.

b. What D_L would immunize the bank against interest rate risk? Use either immunization formula.

c. Assume the bank wants to keep its core deposits unchanged, but can issue new zero coupon bonds of any maturity to replace all of the current notes payable, and thereby achieve the desired D_L. Calculate the required maturity of the zero-coupon bonds to immunize the bank against interest rate risk.

d. If the strategy in part b immunizes the bank from interest rate risk, and interest rates do rise from an average rate of 6.0% to 7.0%, calculate the new value of the bank’s assets (A), the bank’s liabilities (L) and the net worth (E). Use the formula: %A or %L = -D x [ ΔR / (1 + R) ]

e. Explain the main implications of this exercise in a full essay of a full paragraph or more, and refer specifically to your numerical results above.

Answer 1

Assets	Amount($M)	Weight(%)	Duration	Weighted Duration
Cash-type Securities	50	0.1	1.2	0.12
Commercial Loans	100	0.2	2.4	0.48
Mortgages	350	0.7	8	5.6
Total	500			6.2
Liabilities	Amount($M)	Weight(%)	Duration	Weighted Duration
Core Deposits	270	0.6	1	0.6
Notes Payable	180	0.4	2	0.8
Total	450			1.4

By Changing the composition of Liabilities Core Deposits = 180$m & Notes Payable = $270M

Interest Rate = 0.06
Change in Interest rate = 0.07-0.06=0.01
Chane in Asset as a % = - Average Duration *(Change in Interest rate/(1+Interest Rate))
	-5.85%
Change in Value of Assets		-29.25
New Value of Assets		470.75
Chane in Liabilities as a % = - Average Duration *(Change in Interest rate/(1+Interest Rate))
	-1.32%
Change in Value of Liabilities		-5.94
New Value of Liabilities		444.06