In this note we look at a simplified approach to constructing a “Loss Index”. This may be a useful measure in looking at the historical movement of losses (expressed in percentage terms) that have arisen from a defined benefit pension transfer to a personal pension plan. The loss of pension scheme benefits and the value of the personal pension plan are separately modelled and then the results combined to produce the loss index.
The annuity value
The value of pension scheme benefits can be simplified to the modelling of an annuity which is subject to market interest rates, inflation and is contingent on the survival of the member. Those factors determine the value of the annuity and, more importantly, changes in these factors give rise to changes in the value of the annuity.
The significant change to the value of the annuity over the period of analysis (in this case the six years from 31/03/2017 to 31/03/2023) is driven by long term interest rates and for the purposes of this analysis it is the (forward) real[1] gilt yields and the changes in those yields over the period of the analysis that is relevant. We use these gilt yields to construct annuity factors for 5, 10 and 15 year terms to retirement and we adopt a market standard methodology in arriving at these annuity rates taking into account inflation (RPI, capped at 3% each year) and mortality factors. The chart below shows the relative performance of the annuity values over the period (assuming 31/03/2017 as the base value):
A proxy benchmark
In this model we adopt the FTSE Private Investors Income Index (“PII”) as a proxy benchmark for the personal pension plan and compare that also to a “50:50” index (50% of PII and 50% of FTSE All Share Index). The chart below shows the historical performance of this index over the same six-year period (adjusted to reflect personal pension charges of 1.25% per annum):
A loss index
We can define our index as the ratio of the pension value divided by the derived proxy index. We calculate the pension value by adjusting the annuity value for revaluation (based on historical CPI), survival and discounting to retirement.
As of 31 March 2017, the index is assumed to have value 100. Values greater than 100 are losses and values less than 100 are gains. The maximum value of the index found is 115 (approx.) as of 31/03/2020 and the minimum value found is 85 (approx.) as of 31/03/2023.
[1] Real gilt yields are derived from index linked government bonds or “gilt linkers”
