4. This Information will be used for all the following questions. Bank Dynasty has the following balance sheet in market value: Assets (mil$) Liabilities & Eqt (mil$) Cash 8-yr Loan 5-yr Floating-Rate Loan (reset every 0.5 year) 40 Demand Deposits 150 1-yr Debt 110 10-yr Debt Equities 60 70 140 30 Total Assets 300 Total Liab. & Eqt. 300 Further information: (1) Assume there is no default risk in all the loans and debt. All loans and debt are non-amortizing. (2) The 8-year loan and the 1-year debt are zero-coupon loan/debt and compounding annually. The 5-year floating-rate loan and the 10-year debt pay coupons semi-annually. (3) The 8-year loan has yield of 10%. The yield of the 1-year debt is 5%. The 5-year floating-rate loan has the coupon rate and yield equals to SIBOR (currently 5%) plus 4%. And the yield of the 10-year debt is 12%. All rates are annual rates. (4) The 10-yr debt has a face value of 150 mil$. [Round your answers to 4 decimal places for this question. 20 marks in total.] A) What is the modified duration for the 10-yr debt? (5 marks) B) What is the modified duration gap of this bank? (5 marks) C) If the market interest rate is expected to increase by 0.5% for all maturity, what is the expected impact on the bank's market value of equities? (3 marks) D) The bank decides to restructure its liabilities to hedge the interest rate risk. The CFO is told that only the accounts in the 1-yr and 10-yr debts can be changed to do Asset-Liability Management (ALM) for modified duration immunization. Other accounts including the demand deposits and the equities, as well as the size of the balance sheet, cannot be changed. How may the bank achieve that? (7 marks) 4. This Information will be used for all the following questions. Bank Dynasty has the following balance sheet in market value: Assets (mil$) Liabilities & Eqt (mil$) Cash 8-yr Loan 5-yr Floating-Rate Loan (reset every 0.5 year) 40 Demand Deposits 150 1-yr Debt 110 10-yr Debt Equities 60 70 140 30 Total Assets 300 Total Liab. & Eqt. 300 Further information: (1) Assume there is no default risk in all the loans and debt. All loans and debt are non-amortizing. (2) The 8-year loan and the 1-year debt are zero-coupon loan/debt and compounding annually. The 5-year floating-rate loan and the 10-year debt pay coupons semi-annually. (3) The 8-year loan has yield of 10%. The yield of the 1-year debt is 5%. The 5-year floating-rate loan has the coupon rate and yield equals to SIBOR (currently 5%) plus 4%. And the yield of the 10-year debt is 12%. All rates are annual rates. (4) The 10-yr debt has a face value of 150 mil$. [Round your answers to 4 decimal places for this question. 20 marks in total.] A) What is the modified duration for the 10-yr debt? (5 marks) B) What is the modified duration gap of this bank? (5 marks) C) If the market interest rate is expected to increase by 0.5% for all maturity, what is the expected impact on the bank's market value of equities? (3 marks) D) The bank decides to restructure its liabilities to hedge the interest rate risk. The CFO is told that only the accounts in the 1-yr and 10-yr debts can be changed to do Asset-Liability Management (ALM) for modified duration immunization. Other accounts including the demand deposits and the equities, as well as the size of the balance sheet, cannot be changed. How may the bank achieve that? (7 marks)
