Pensions Conference 2012: Review of Workshop D1 - Quantifying and allocating mortality risk in small defined benefit pension schemes

Where there’s life there’s risk

Introduction

Catherine Donnelly presented this workshop and showed that small pension schemes can carry significant levels of mortality risk and that the risk can be quite lumpy and concentrated in a relatively small number of members.

Background

The context of the presentation was a small pension scheme that contained a homogeneous group of members.  Variation was then considered whereby an “Executive Section” was added to the membership to contrast the level of mortality risk in the scheme.  In both cases, techniques for allocating the existing risk were considered. 

Homogeneous membership

To measure variance (i.e risk), a co efficient of variation was defined as:

 co-efficient of variation = standard deviation of total liability / Expectation of total liability

The main conclusions of this part of the workshop were:

• In a homogeneous scheme, the co-efficient reduces towards zero as the number of members increases.
• Systematic risk cannot be eliminated by increasing the number of members.
• Idiosyncratic risk reduces as the number of members increases.

Executive Section (non-homogenous membership)

The co-efficient of variation was used to illustrate:

• Idiosyncratic risk can be reduced by increasing the number of members.
• Idiosyncratic risk increases as the executive section benefits increase relative to the main section benefits.

Risk Capital

This part of the workshop looked at how capital can be allocated across the membership to act as a cushion against unexpected losses.  Standard deviation was the measure used to allocate the risk capital.

The risk capital can be allocated in different ways:

• Benefit-weighted allocation
• Using covariances

Under the first approach, risk is allocated in proportion to the value of each member’s benefit (so executives are shown to be more risky).

Under the covariance principle a greater proportion of the risk capital is allocated to the executive members then under the benefit weighted allocation approach.

Conclusion

This workshop made us think about how much mortality risk exists in a scheme and how the mortality risk is allocated amongst the membership.  There could be wider applications too – for example the next steps could be to consider how this can help our thinking on mortality swaps.