# Shrewsbury Case Scenario

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?

1. Yes
2. No, because of the differences in money duration
3. 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?

It appears that there’s a typo in the PV01; it should be the money duration divided by 10,000.