Division of labour

At this time of year insurers have commenced their annual valuation of liabilities, part of which involves setting a mortality basis.  When doing so it is common for actuaries to separate the basis into two components: (i) the current, or period, mortality rates and (ii) the projection of the future path of mortality rates (usually mortality improvements).  This sub-division is carried over into the regular Solvency II assessment of capital requirements, where there is always a minimum of two sub-risks for longevity:

1. Mis-estimation risk, i.e. the uncertainty over the current level of mortality.
2. Trend risk, i.e. the uncertainty over the future direction of improvements.

In practice a Solvency II assessment of longevity risk will contain more than this.  However, the above two components will be common to every Solvency II capital calculation for longevity risk — Richards, Currie & Ritchie (2012) list some further sub-risks that might be considered.

The separation of mis-estimation risk from trend risk is much more than an actuarial habit.  In fact, the nature of the investigations and calculations are different in almost every respect.  For example, a mis-estimation assessment is done using a portfolio's own experience data, where various portfolio-specific risk factors might be included.  Mis-estimation capital is therefore highly specific to a given portfolio — Richards (2014) gives two examples.

In contrast, few portfolios have a long enough time series of data to use in assessing trend risk, so population data are commonly used.  In theory this could make all industry participants in a country produce identical trend-risk assessments.  Table 1 gives a comparison of the features of mis-estimation risk and trend risk.

 Table 1. Contrasting features of mis-estimation risk and trend risk.

Although there are many differences between mis-estimation risk and trend risk, two particular aspects of trend risk stand out:

1. Basis risk, i.e. risk arising from using data other than that of the portfolio.  A mis-estimation assessment cannot be fully credible if it doesn't use the portfolio's own experience data.  In contrast, almost any assessment of trend risk includes basis risk because few portfolios have a long enough history of data of their own.
2. Model risk, i.e. risk arising from not knowing which (if any) model is the correct one to use.  With mis-estimation risk it is usually fairly straightforward to find a suitable mortality law to use, albeit work is required to find out which risk factors should be included.  In contrast, goodness-of-fit is not usually a useful decision-making criterion for selecting a projection model and the risk factors available are usually very few.  Cairns et al (2009) list some qualitative selection criteria for selecting a forecasting model for trend risk.

One consequence of the forced inclusion of basis risk and model risk is that a lot more actuarial judgement is required for setting capital for trend risk. As a result, trend risk and mis-estimation risk will probably always have to be handled separately.