# 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 risk*: it 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.

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