As an investment manager in a large Super fund you are concerned about the duration of a bond portfolio in which your fund is invested in. The bond portfolio was set up to meet pension payments due under the few remaining defined benefit (DB) pension scheme that are managed by your fund. Due to the considerable age of the defined pension recipients, you don't expect to maintain this portfolio for much longer.
The bond portfolio consists of $120 million dollars invested in 3% 2-year bonds and $150 million invested in 5% 3.5-year bonds.
You initially ask your staff to calculate the duration of this portfolio. They estimated the portfolio duration at 4 years. You doubt these results as you were led to believe by senior management that there were no bonds in the portfolio with maturity exceeding 3 years. You are now quite concerned about this estimated duration number.
As part of the review of the bond fund, you hired an actuary to assess the duration of the remaining defined pension liabilities. Given the age of the remaining pension recipients, the actuary stated that the fund liabilities' duration is 3 years (6 six-month compounding periods).
As a result of these findings, you want to check yourself bond portfolio duration and devise a possible solutions to the duration mismatch that seems to exist at present.
Assume a yield for both bonds of 4.5%.
Required
Answer the following and show all calculations.
(a) Calculate the duration of the two bonds and the market value and duration of the portfolio. Is the staff estimate of 4 years for portfolio duration correct?
3% 2-year: Price: 97.161, Duration:3.911
5% 3.5-year: Price: 101.602, Duration:6.512
Portfolio
Market value: 120,000,000*97.161+150,000,000*101.602=268,997,576.16
Duration:3.911*120/350+6.512*200/350=5.356 meaning 2.7 years
Staff estimate is incorrect.