Mortality: Standard deviation
Enhanced annuities are fantastic. They pay larger pensions to those in poor health reflecting the associated shorter life expectancy. In many ways, they are the flip-side of charging more for life insurance to those in ill-health, and both are examples of insurers pricing appropriately for the risks assumed. While the insurance industry has been rating up ill-health life insurance premiums for centuries, enhanced annuities are a new phenomenon. The market started in the mid-1990s, but it was not until early this century that it really took off. It is now strongly established, with some 12 competing providers, covering the whole spectrum of medical conditions.
Here’s the rub
All very interesting, but ‘so what’ for standard (non-enhanced) annuities? Well, the existence of the enhanced market leads the least healthy people to buy enhanced annuities, leaving the healthiest to buy standard annuities. The effect of this selective dynamic is to significantly lighten the expected mortality of standard annuitants. The more lives buying enhanced annuities, the larger the selection effect, and the lighter the expected mortality of standard annuitants. Entry requirements are modest — minimum premiums are typically £5000 or £10 000 — so the selection effects are potentially far-reaching.
With enhanced annuities now representing a record proportion of the external market (almost 29% in the third quarter of 2008 according to Watson Wyatt), the selection effects and their consequences are more acute than ever. Companies selling standard annuities must price for this; this is an absolute. The cost of not doing so will far exceed the profit margin that insurers might otherwise believe, or in fact be kidding themselves, that they are making.
Modelling selection effects
With no enhanced market, it is easy to formulate a mortality assumption for standard and enhanced lives combined, for example by looking at the experience of a portfolio of annuities written prior to 2001 or thereabouts. This could be either by direct reference to own-experience data or by selecting a recent pensioner mortality table. However, there is an enhanced market, so allowance must be made. Given a model for the total population of lives (say 100% PCxA00), if we can additionally model the experience of the enhanced lives, the experience of the standard annuitants must be the balancing item. This therefore becomes an exercise in modelling enhanced lives, and we need to know only two things: the enhanced proportion, and how their excess mortality behaves.
Current market information suggests that around 25% to 30% of external business is enhanced. By overlaying this with a view on market trends, which have been increasing strongly of late, one can set an assumption on the enhanced proportion for pricing new business. Understanding internal policyholder behaviour, particularly given the modest barriers to entry, is a further complication, though not covered in this article. Also tricky is formulating a market-level assumption about the excess mortality of enhanced lives. For this we need to know two things: first, how much heavier than average the elevated mortality is at outset, and second, how the excess mortality behaves over time.
By referring to own-experience data, having written standard annuities both before and after the enhanced market, insurers have more insight as to the first requirement. They can turn the problem on its head and determine just how impaired the enhanced lives would have to be to explain the gap between the experience of average lives (for business written before the enhanced market) and the experience of healthy lives (for recently written standard business). However, even a new insurer can get a handle on this. As to the second requirement, the playing field is much more level as the history of the enhanced annuity market is not very long.
As it happens, both requirements can be addressed by referring to the recent Self-Administered Pension Scheme (SAPS) investigations of the CMI. It is instructive to compare the mortality of ‘ill-health’ pensioners to ‘average’ pensioners, where average is taken to mean ‘ill-health’ plus ’normal’. In Figure 1, this is shown as blue for men, and as pink for women. Very similar patterns are seen for the periods reported in the SAPS working papers.
Of course, care should be taken in using these results when setting assumptions. Socio-economic differences may exist between individual annuitants and the SAPS members. There may also be structural differences: some ill-health retirements may not be directly related to increased mortality, whereas enhanced annuities will always correlate with that.
A model of selection effects
That said, there seem to be natural conclusions to be drawn in terms of both the initial ratio of enhanced to average mortality and, subsequently, the pattern of decay of the excess mortality (known as mortality convergence). Armed with such assumptions, which should also allow for the attaching uncertainty, it is then a straightforward exercise to model three populations: (i) the average population (100% PCxA00); (ii) the enhanced proportion, with mortality in line with our newly formulated assumptions; and (iii) the standard (healthy) population, as the balancing item. The model can be further refined by overlaying views of mortality improvements in each population. The resulting difference in mortality rates between the average and healthy populations is really rather marked, and it adds significantly to price. Try this for yourself.
Control cycle
Given the selection effects, the current mortality experience of recently written standard business is very light across the life industry. However, it is not all bad news: the flip-side of having made selection allowances in pricing is that it is natural to allow for the resulting unwind when formulating assumptions for the business when in force. A similar model can be used to add back the effect of the unwind, either directly, using the implied term structure if the modelling systems can handle this, or indirectly, using annuity-equivalence techniques. Allowance needs to be made for selection levels having increased over time as the enhanced market grew (recent cohorts are more affected) and for the duration-dependent unwind (earlier cohorts will have unwound more).
Model risk
However, the use of a model to inform assumptions for in-force business increases the risk that the resulting assumptions are ultimately inadequate. This, in turn, leads to a requirement to hold capital against this risk. Stressing the parameter assumptions offers a way of determining capital requirements. How wrong would these be in the 1-in-200 event? What would the initial level of elevated mortality be, and by what age would mortality converge?
I noted earlier that insurers who have written standard business both before and after the enhanced market are best placed to determine initial levels of enhanced mortality. However, their data provides them with another advantage. Placing confidence intervals around both the average and healthy mortality experience gives a natural statistical framework in which to quantify uncertainty.
Suppose that the average mortality experience lies in the range 100% +/-10% of PCxA00 with 86% confidence and that healthy experience lies in the range 33% +/- 20% of PCxA00, again with 86% confidence. Assuming independence between the two populations, there is a 1-in-200 chance that the ‘gap’ is at least 97% of PCxA00. (Each tail of an 86% confidence interval contains a probability mass of 7%, and 0.072 = 0.5%.) Given the three-population model above and a judgmental view on the increased convergence period in the 1-in-200 scenario, one can then calculate the risk capital. Indeed, one might also manipulate the shape of mortality convergence to allow for model risk, separately from parameter risk.
A word about Solvency II
Finally, no commentary on capital would be complete without mentioning Solvency II. Internal longevity models are undoubtedly vital for all insurers carrying material longevity exposures. With such models in place, the question is just how much of the 25% QIS4 longevity shock would be left to cover selection risks after allowances are made for the risks relating to incorrect estimates of current mortality and future trends (which, incidentally, cannot safely be assumed to be weakly correlated, let alone independent)? One size does not fit all, and it is dangerous to pretend that it does.
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Exploding the myths
Myth 1: “We don’t sell enhanced annuities, so this doesn’t affect us”
Wrong. It is the existence of the market that gives rise to the selective effects.
Myth 2: “We do sell enhanced annuities, so this doesn’t affect us”
Wrong again. All this means is that you have two very different pricing exercises on your hands.
Myth 3: “It doesn’t affect our internal book”
Not true. Do you retain all of your retiring policyholders? Where do the leavers go? What product do they buy? How do you measure selection levels here?
Myth 4: “All myths come in threes”
QED
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Stephen Makin is head of longevity research at Prudential
Stephen Makin
