Part 1: Compute the duration on a 7-year, 5% annual bond that currently sells for $1,060.02. You should use a spreadsheet for this calculation. Show your equations in the spreadsheet for full points.
Part 2: Blue Sunday Bank has a portfolio of loans and securities, as well as deposits and money market borrowings, which are expected to produce the following cash inflows and outflows for the bank in the coming 5 years. Cash inflows are denoted with a “+”; cash outflows are denoted with a “-.“
|Expected Cash Flow (in millions)||Timing of Cash Flow|
|+ 1.9 million||1 year from today|
|– 1.4 million||1 year from today|
|+ 750,000||2 years from today|
|– 830,000||2 years from today|
|+ 350,000||3 years from today|
|– 400,000||3 years from today|
|+ 65,000||4 years from today|
|– 45,000||4 years from today|
|+ 10,000||5 years from today|
|– 40,000||5 years from today|
Complete the following, and label your work carefully so that it is clear for your instructor:
1.Assume the current discount rate that applies to these cash flows is 4.5%. In a spreadsheet, compute the duration of the total cash inflows and the duration of the total cash outflows; then compute the duration gap of this bank.
2.In your own words, explain the danger of the bank’s position. You may enter this answer in a cell within your spreadsheet.
3.What kind of hedging should the bank use to reduce its risk? Be specific about the hedging transaction and discuss its expected effect. Again, enter this answer in a cell within your spreadsheet.
4.Now assume that the bank has total assets of $30 billion and total liabilities of $25 billion, and all asset and liability cash flows are proportional to the cash flows given in this problem. How much would the value of the bank change if interest rates rise from 4.5% to 5.0%? What about if interest rates change from 4.5% to 4.2%? Assume that the total assets and total liabilities have the same duration profile as the cash flows given in this problem. Show your calculations in the spreadsheet.