Question

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

Appendix 23A

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%

APPENDIX 23A.1-

Change E= -(Da-kDl) * A * Change R/ 1 +R

Change E= Change in FI Net Worth

Da- Duration of asset portfolio

Dl- Duration of liability portfolio

K- Ratio of an FI's liabilties to assets

A- Size of FI's Asset portfolio

Change R/1+R- Shock to interest rates

3. Off-Balance sheet futures hedge (Use balance sheet information above, 8 points)

T-Bond futures contracts for the delivery of $100,000 face value are trading at 102-16, and have a duration of 9.50 years. This problem is based on the material in Appendix 23A: Hedging with Futures Contracts.

a. What is the total dollar price of each futures contract (P_F)?

b. For this bank to achieve complete immunization, solve for F (total dollar value of futures contracts to immunize). Note: We don’t know the number of contracts yet or a specific interest rate change, so that information should not be used to solve for the dollar value F. Use only the information provided above to solve for F.

c. Using F from part b above, solve for the number of T-Bond futures contracts needed by this bank to hedge the interest rate risk (round to the nearest whole number of contracts).

d. Explain in a full essay what risk this bank faces, what position this bank would take on the T-Bond futures contracts to hedge against the interest rate risk it faces, why it would take that position, and graph that position in a fully-labeled futures payoff diagram.

Assume average interest rates rise from the original level of 6.0% to 7.50%.

e. Calculate the on-balance sheet change in the bank’s value (ΔE), and specify the sign (positive or negative)

f. Calculate the off-balance sheet change in the value of the futures contracts (ΔF), and specify if it’s a gain or loss.

g. Assume you are a financial analyst and risk management specialist for the bank above. Write a full, complete, and convincing essay (executive summary) of at least several complete paragraphs to your company’s CEO that summarizes the main conclusions from this third problem, and specifically refer to your numerical results from parts e and f.

Answer 1

a) $ price of each futures contract =(102+16/32)*1000 = $ 102500

b)

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

F= [Average duration of Assets-(Liabilities/Assets)*Average Duration of liabilities]*Assets value

F = $2470 Million

c) Number of future Contracts to be hedged = F/(Df*PF) = $2470,000,000/(9.5*102500)= 2536.58 =2537 Contracts(rounded off to nearest whole number)

d)Price of futures contract and interest rates are inversely related

The bank should sell futures contracts since an increase in interest rates would cause the value of the equity and the futures contracts to decrease. But the bank could buy back the futures contracts to realize a gain to offset the decreased value of the equity

e)

Expected Change in E = -DGAP[DR/(1 + R)]A = -$2470(0.015/1.065) Million

=-$34788732 f)The change in Futures contract value = -9.5(0.015/1.08525)$102,500 *2537 = $34145180

Results in loss of $ 643552