Question 4 Use the following to answer questions a) f). Bank of Big Bucks Assets: 270 day Treasury bills $500m 2 year consumer loans Fixed rate, 12% p.a. annually $275m 7 year commercial loans $350m Fixed rate, 9% p.a. annually 10 year fixed rate mortgages $675m Fixed rate, 6.5% p.a. annually 10 year floating rate mortgages $125m LIBOR+50bp, monthly roll date ($ million) Liabilities and Net Worth: 1 year Certificates of Deposit Demand Deposits 2 year Int'l Bonds Fixed rate, 7.5% p.a. annually Overnight borrowing $550m $750m $175m $350m Equity $100m Notes: The 1 year Certificates of Deposit pay 1.95% p.a. annually and will be rolled over at maturity. The 7 year commercial loans have a duration of 5.486 years. The fixed rate mortgages have a duration of 7.656 years. All values are market values and are trading at par. Assumption: 30 days per month; 90 days per quarter; 360 days per year. What is the bank's duration gap? a. -0.49 years b. +4.24 years c. -0.94 years d. -2.81 years e. +3.69 years b) What is the bank's interest rate risk exposure (i.e. exposed to rising or falling rates)? c) What is the on-balance-sheet impact on the bank if all interest rates increase 25 basis points? (i.e. suppose AR/(1+R) is equal to an increase of 25 basis points.) d) Suppose you are a risk manager of the bank. Construct an appropriate swap hedge for your bank. i). Specify whether your bank should be a fixed- or variable-rate payer in the swap, and ii). Calculate the notional of swap, Ns, for a perfect hedge. Suppose the fixed side of the swap has a duration of 12 years, while the variable side of the swap is floating on a biennial base. Question 4 Use the following to answer questions a) f). Bank of Big Bucks Assets: 270 day Treasury bills $500m 2 year consumer loans Fixed rate, 12% p.a. annually $275m 7 year commercial loans $350m Fixed rate, 9% p.a. annually 10 year fixed rate mortgages $675m Fixed rate, 6.5% p.a. annually 10 year floating rate mortgages $125m LIBOR+50bp, monthly roll date ($ million) Liabilities and Net Worth: 1 year Certificates of Deposit Demand Deposits 2 year Int'l Bonds Fixed rate, 7.5% p.a. annually Overnight borrowing $550m $750m $175m $350m Equity $100m Notes: The 1 year Certificates of Deposit pay 1.95% p.a. annually and will be rolled over at maturity. The 7 year commercial loans have a duration of 5.486 years. The fixed rate mortgages have a duration of 7.656 years. All values are market values and are trading at par. Assumption: 30 days per month; 90 days per quarter; 360 days per year. What is the bank's duration gap? a. -0.49 years b. +4.24 years c. -0.94 years d. -2.81 years e. +3.69 years b) What is the bank's interest rate risk exposure (i.e. exposed to rising or falling rates)? c) What is the on-balance-sheet impact on the bank if all interest rates increase 25 basis points? (i.e. suppose AR/(1+R) is equal to an increase of 25 basis points.) d) Suppose you are a risk manager of the bank. Construct an appropriate swap hedge for your bank. i). Specify whether your bank should be a fixed- or variable-rate payer in the swap, and ii). Calculate the notional of swap, Ns, for a perfect hedge. Suppose the fixed side of the swap has a duration of 12 years, while the variable side of the swap is floating on a biennial base