## Keeping it simple — postscript

Last week we looked at how to compare mortality-improvement bases for pensions and annuities. However, for many years some pension schemes in the UK did not have explicit mortality-improvement projections. Instead, they allowed for mortality improvements by making a deduction from the valuation discount rate. Reading some scheme reports from around 2005, it would appear to have been relatively common to use a deduction of 0.25% per annum. How strong a basis is a 0.25% discount-rate offset compared with more explicit projections of improvements?

Previously we looked at comparing two mortality-improvement bases by using an equivalent annuity to express the bases in a simple, standardised way. We can use this same procedure to compare the 0.25% per annum discount-rate adjustment with other bases, as shown in Table 1:

Table 1. Equivalent annual rates of improvement implied by two projection bases and one *ad hoc* allowance. Specimen factors for level unit annuities to males valued at a discount rate of 3% per annum. Mortality is according to S1PA from 2011 onwards, with improvements after that year in line with the stated projection or improvement allowance.

Mortality projection or improvement allowance
| Age 65 | Age 70 | Age 75 |

i) Medium cohort with 2% minimum | 2.00% | 2.00% | 2.00% |

ii) Long cohort with 1% minimum | 1.66% | 1.89% | 2.32% |

iii) 0.25% offset to valuation interest rate
| 0.58% | 0.51% | 0.44% |

We can see from Table 1 just how weak a 0.25% offset to the discount rate is compared to the more explicit projections. This is one reason why the Pensions Regulator in the UK discourages trustees from accepting this practice:

"We consider that an adjustment made to the discount rate as a proxy for future improvements in mortality does not meet the statutory requirement to adopt a prudent mortality assumption, or achieve good practice in clarity."

Pensions Regulator,

Actuaries are free to use any mortality projection they deem appropriate for reserving. Innovation in this field cannot be discouraged, since bases must evolve with further research. However, for communication purposes it makes sense to standardise on a simple and robust approach, such as the equivalent constant rate of improvement. This is best calculated by equating the entire portfolio under the two alternative bases, thus allowing for the portfolio's specific age distribution and concentration of liabilities.

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