Exhibit 2
Defined Benefit Plan Characteristics
| Description | Assets | Liabilities |
|---|---|---|
| Market Value in USD | 517,342,000 | |
| Liability, PBO* in USD | 500,000,000 | |
| Macaulay Modified Duration | 12.66 | 13.10 |
| Convexity | 21.40 | 22.51 |
| Dispersion | 6.48 | 6.70 |
| Cash Flow Yield (%) | 4.90 | 4.50 |
| PV01 | 654,281 | 684,276 |
Based on the data in Exhibit 2, will the client discussed most likely be able to immunize its DB plan given the interest rate scenario described by Silver?
- Yes
- No, because of the differences in money duration
- No, because of the differences in convexity and dispersion
Solution
C is correct. The money duration of the assets and liabilities are equal: 517,342,000 × 12.66 = 6,548,381,000, and 500,000,000 × 13.10 = 6,548,381,000. For parallel changes, the equal money durations and PV01 imply that assets and liabilities would move in tandem. Silver expects a bear steepener; that is, long rates will rise faster than short rates. In a bear steepener, long rates rise faster than short rates in a non-parallel fashion. Given that the assets have lower convexity and dispersion than the liabilities, they will underperform; that is, the liabilities would change by a greater amount than the assets.
Is this a trick question with regards to the PV01 given in the table? Assuming PV01 figures given are correct, then wouldn’t option B be correct as well?