Modelling one side of a two-sided problem

Ah models, my old friends. You’re always wrong, but sometimes helpful. Often dangerous too.

A recent article in The Actuary magazine addressed whether “de-risking in members’ best interests?”  I say “recent” even though it’s from August because I am a little behind on my The Actuary reading.

In the article, the authors demonstrate that by modelling the impact of covenant risk, optimal investment portfolios for Defined Benefit (DB) pensions actually have more risky assets than if this covenant risk is ignored.

The covenant they refer to is the obligation of the sponsor to make good deficits within the pension fund. Covenant risk then is the risk that the sponsor is unable (typically through its own insolvency) to make good on this promise.

On the surface it should seem counterintuitive that by modelling an additional risk to pensioners, the answer is to invest in riskier assets, thus increasing risk.

The explanation proffered by the authors is that the higher expected returns from riskier assets allow the fund to potentially build up surplus, thus reducing the risks of covenant failure.

I can follow that logic, particularly in the case where the dependence between DB fund insolvency and sponsor default is week. It doesn’t mean it’s a useful result.

The optimisation considered only one side of the equation – what is in members’ best interests. It ignores the other side of the problem – the financial impact (expectation and variability around that) for the sponsor’s financial position.

To take it to the extreme, if every sponsor just liquidated all its assets and transferred them to the DB fund, that would be a pretty good outcome for fund members. Not so much for the sponsor.

Without having seen the detailed model results, what I expect is happening is that the increased allocation towards risky assets is increasing expected returns (as it should) but also increasing the risk to the sponsor of having to put in additional funds. Any time this is done and the sponsor doesn’t default, there is no downside for fund members. The only risk to fund members is the combination of being underfunded and sponsor default.

The risk to the sponsor of increased frequency of injections required has been well established for decades. Depending on what you are willing to assume about risk premiums for risky assets and the assumed risk appetite, the higher expected return might outweigh the increased risk. This is not a point to be glossed over let alone left entirely untouched.

It also raises an awkward question about what they’ve modelled in terms of the covenant in the “no covenant risk” scenario. Surely if one models the covenant and not risk to the covenant, all benefits should always be paid to the members, regardless of asset mix?

I’m not at all convinced that these results are reliable. But either way, the fact that they are optimising and showing results for only one side of a two sided problem makes the approach utterly flawed.

Published by David Kirk

The opinions expressed on this site are those of the author and other commenters and are not necessarily those of his employer or any other organisation. David Kirk runs Milliman’s actuarial consulting practice in Africa. He is an actuary and is the creator of New Business Margin on Revenue. He specialises in risk and capital management, regulatory change and insurance strategy . He also has extensive experience in embedded value reporting, insurance-related IFRS and share option valuation.