Partial buy-outs

It is quite common for a pension scheme to want to reduce its risk, but to be unable to afford a full buy-out.  The question is how best to reduce risk with the funds available, i.e. which liabilities to buy out first.  One argument we have come across is to buy out the older pensioners first, since their life expectancy can be more volatile against your funding assumption.

The answer to this depends on what way you want to measure the risk.  If you are looking at the possible percentage change in life expectancy or reserve, then older pensioners do indeed have a higher volatility: an extra year of life is proportionately larger compared to the baseline life expectancy (similarly for reserves).  Reserve calculations are also more sensitive to changes in the base mortality tables at higher ages.

However, a more appropriate way to view this is in terms of the volatility of the scheme finances as a whole.  For smaller schemes we come back to concentration riskit is the people with the largest pensions who have the largest impact on the scheme.  Buying out all or part of their benefits will reduce the year-on-year volatility, and also the stochastic risk in run-off, i.e. the so-called tail risk where a small number of scenarios lead to material extra costs.

Another aspect of tail risk is the direction of future mortality trends.  For larger schemes, the stochastic risk in run-off is usually manageable, but the scheme still runs the risk that mortality trends go against it.  In this case it is not the oldest pensioners who comprise the greatest risk, but rather the younger ones: they have the longest life expectancy and therefore the greatest chance of benefiting from an "adverse" mortality trend.

It is not uncommon for these risks to be combined, i.e. for the largest concentration of liabilities to be amongst the younger recent retirals.  In such cases there is no doubt where the greatest source of tail risk lies for a pension scheme.  In section 8 of our recent paper we explored tail risk for three different-sized portfolios of pensions in payment.

Longevity tail risk in the Projections Toolkit

All models in the Projections Toolkit are open-tailed, i.e. they are suitable for applications involving tail-risk estimation (such as Solvency II).

Previous posts

The Lee-Carter Family

In a recent paper presented to the Faculty of Actuaries, Stephen Richards and I discussed model risk and showed how it can have a material impact on mortality forecasts.  Different models have different features, some more desirable than others.  This post illustrates a particular problem with the original Lee-Carter model, and shows how it can be combatted via smoothing.  The choice of which parameters to smooth in the Lee-Carter model leads to a general family

Tags: Filter information matrix by tag: model risk, Filter information matrix by tag: Lee-Carter, Filter information matrix by tag: mortality projections

Expectations v. extrapolations

The CMI has published two working papers along with its new mortality projection model.  The proposed new model blends current improvement rates into an expected long-term average rate of improvement.  The hope is that such models can incorporate expert opinions on mortality trends to improve the accuracy of projections.
Tags: Filter information matrix by tag: CMI, Filter information matrix by tag: mortality projections

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