From a past paper, case says: Client- the defined benefit pension plan for this client has an economic surplus of zero. In order to meet the liabilities for this plan, I will construct the portfolio duration to be equal that of the liabilities. In addition, I will have the portfolio payments be less dispersed in time than the liabilities. 2 questions 1. What does it mean by “I will have the portfolio payments be less dispersed in time than the liabilities”? Does this mean that payments are closer to the horizon date, as opposed to liabilities which are more spread out? 2. The case later says that the client will meet the necessary conditions for a multiple-liability immunization in the case of a non-parallel rate shift.
How can multiple liability immunisation meet conditions in the case of a non-parallel rate shift, don’t we assume parallel rate shifts?
Summary: 1. What does portfolio payments less dispersed in time than the liabilities mean? 2. How can multiple liability immunization meet conditions in the case of a non-parallel rate shift, don’t we assume parallel rate shifts for immunization?
b) Composite Duration of the Portfolio (Assets) should be equal to Composite Duration of the liabilities
c) The distribution of durations of individual portfolio assets must have a wider range than the distribution of the liabilities. The third condition requires portfolio payments to bracket (be more dispersed in time than) the liabilities. That is, the portfolio must have an asset with a duration equal to or less than the duration of the shortest-duration liability in order to have funds to pay the liability when it is due. And the portfolio must have an asset with a duration equal to or greater than the longest-duration liability in order to avoid the reinvestment rate risk that might jeopardize payment of the longest duration. This bracketing of shortest- and longest-duration liabilities with even shorter- and longer- duration assets balances changes in portfolio value with changes in reinvestment return.
The assets should have wider dispersion, not less, around the liabilities. Longest asset durations should be longer than the longest liability duration, and the shortest asset durations should be shorter than the shortest liability duration. Picture a scatter plot.