## Countdown to unisex pricing

In just over one year's time, insurers throughout the European Union will be prohibited from using a person's gender to price insurance risks.  This court ruling applies to individual contracts, but not (apparently) to group arrangements.

For insurers it is time to review their pricing bases and systems in good time for December 2012.  Gender has been used as a risk factor in insurance for a very long time: the oldest copy of the Journal of the Institute of Actuaries on my bookshelf shows that actuaries were separately calculating mortality tables by gender at least as far back as 1871.  As a result, it is quite possible that pricing and quotation systems have some subtle oddities, and these will need to be identified and addressed soon.

In our 2004 paper Financial aspects of longevity risk, Gavin Jones and I identified gender as the second strongest risk factor for annuitant longevity after age. Losing such an important variable is obviously a serious challenge for pricing annuity business, although we note that insurers will still be expected to use gender as a factor for reserving and risk management.  If the second most important risk factor is being forbidden by law, it is natural to ask: what risk factors might take its place?  Again, insurers will have to look now at their pricing and quotation systems and see what changes have to be made to accommodate these new risk factors.

In the case of individual annuities we have not only purchase price (or annuity level) and postcode, but also client-selected options such as escalation rate and the level of spouse's benefits.  These latter two variables are examples of self-signalling as to an annuitant's longevity — only someone who expects to live a long time will be worried about preserving the long-term purchasing power of their annuity.  Equally, married males tend to live longer than unmarried ones (marital status doesn't appear to affect female longevity as much).  Interestingly, annuitants who pick escalating benefits are more likely to pick spouse's benefits as well, and both of these variables are strongly correlated with pension size and geodemographic group.

It is at this point that a statistical model for annuitant mortality becomes an absolute business must.  If you were to rely on a series of two-way comparisons, for example, you would risk double-counting some of the effects on longevity.  A statistical model avoids this by simultaneously fitting all the desired risk factors and measuring the effect of each in the presence of the others.  Where there are important interactions, such as with age, these can be included as well and formally tested.  Conveniently, a set of risk factors can be fitted with and without gender present, thus giving you consistent models for both pricing and internal capital management.

NIgel Wright
(Nov 28, 2011)
Thanks for another interesting post, Stephen.

My understanding is that, not only will the insurance industry no longer be able to use gender as a pricing factor, they will have to avoid indirect gender discrimination in their pricing.

This means that insurers need to be careful in their statistical modelling if a particular factor starts acting as a proxy for gender.

An example would be purchase price; high purchase prices will tend to have a higher proportion of male lives than females. A model without gender might (counter intuitively) show heavier mortality for higher purchase prices. But giving a better rate for higher purchase prices would be indirect gender discrimination.

I'd be interested to hear your views on this and how the statistical modelling could deal with this.

A separate point is that joint life annuities might become relatively more attractive as insurers will assume that most will have a male and a female annuitant, so that one life will be assumed to have the heavier (male) mortality.
Stephen Richards
(Dec 2, 2011)
Indirect gender discrimination is indeed illegal, as a recent judgement on access to pension schemes for part-time staff reminds us. In this case scheme membership was denied to part-time workers, and it is relatively straightforward to show that women are disproportionately likely to work part-time: simply calculate the proportion of women amongst full-time and part-time employees and compare the two numbers.

For insurance pricing the situation is more complicated. There are typically more risk-factor combinations than the simple binary "full-time v. part-time" comparison. For example, if an insurer had four pension size-bands and four postcode-driven lifestyle groups, there would be sixteen proportions to consider. It is therefore in an insurer's interest to use as many different valid risk factors as possible: both to accurately price the risk, but also to minimise the chance a straightforward gender proxy might find its way into the resulting risk/pricing groups. Of course, statistical modelling is essential here to avoid double-counting the impact of a risk factor.

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