Question

7.3 - Appendix

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%

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.

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

The contract size for Treasury future is usually $100,000. Each contract trades in handles of $1,000, but these handles are split into thirty-seconds, or increments of $31.25 ($1,000/32) a)$ Price of Futures Contract = $102.5 b)$ Value of futures Contract = $100000+$2000+($1000*16/32) = $102500 c) 1000 Future Contracts e) Assets Amount($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 Duration Gap = Average duration of Assets-(Liabilities/Assets)*Average Duration of liabilities Interest Rate = 0.06 Change in Interest rate = 0.075-0.06=0.015 Chane in Asset as a % = - Average Duration *(Change in Interest rate/(1+Interest Rate)) = -8.77% F) Change in Value of Futures contact on account of Change in Interest rate from 6 to 7.5% Formula Duration/((1+YTM)/2)*Market value of bond*0.015 = $14042 g) To, CEO, ABC Bank On account of change in interest rate from 6 to 7.5% Value of bank assets decreased by $43.87 and Futures contract value decreased by $14042 since Treasury bond value is inversely related with Interest rate increase

In order to overcome this in Future we have to enter in to Interest rate Forward rate so that Our Portfolio values will not be effected by change in interest rates