I’ve been thinking about pension scheme valuations. Much of the discussion in this area is around what discount rate should be used to put a value on the liabilities. This means there is an implicit assumption that discounting the liabilities and comparing them with a value of assets is the best approach to assessing pension scheme solvency. But is it?

If you have obligations that are known with certainty, then it is easy to put a value on the obligations – just discount at the rate of the equivalent risk-free bonds, since holding these bonds would allow you to match your cash flow. That of course means you need to answer the question “what does risk free mean?” and consider the presence or absence of liquidity premia, but these are of secondary importance.

However, what do you do if there is uncertainty? Look at the cost of hedging the risk? Possibly, but this might not be prudent enough. For example, if you hedge longevity risk by buying an annuity, you pay for the removal of level risk (uncertainty over the base mortality of the annuitants) and trend risk (uncertainty over how mortality rates will change over time), but not volatility risk (the risk arising from randomness in small populations) – insurance companies can diversify volatility risk by insuring lots of pension schemes; an individual pension scheme clearly doesn’t have this advantage, so the market value of a hedge might underestimate the risk actually being taken by a pension scheme if it keeps this risk.

On the other hand, the hedges will include a profit margin, which might mean the cost of the hedge is greater than the value of the risk retained. In any case, this is all academic for non-hedgable risks. So what is the alternative? Well, you could use a cash flow approach. This would involve projecting both the assets and the liabilities on a stochastic basis until the last pensioner had died, allowing for all the uncertainties that exist. For the pension payments, this would include salary inflation (for current employees), price inflation (for deferred and current pensioners) and longevity (including level, trend and volatility risk); for the assets it would include the various investment risks. Then you’d need to set a criterion for solvency, say a 99.5% chance that there was money left over after the last pensioner had died, so your scheme was only solvent if you had enough assets for this to be true. However, the amount you needed would also depend on the assets you held – equities might have a higher rate of return than bonds, but their cash flows are also likely to have more volatility relative to the liabilities.

Sound sensible? It is – but there are a number of issues. First, a number of decisions need to be made in relation to the modelling. What rules will be used for the payment of contributions? You need to decide how quickly any shortfalls will be cleared, taking into account how much faith you have in solvency of the sponsor. What level of security to you want to use? Planning for a 1-in-200 year event may sound secure, but such a level is pretty meaningless. And, importantly, how will the assets be modelled? For a start, the parameters used will have a significant impact on the results – the choice between an equity risk premium of 3% and 4% could mean the difference between a contribution holiday and a disaster. More importantly, the choice of model and statistical distribution, in particular the fatness of the tails, will have a huge effect on the probability of insolvency.

A separate issue is a practical one. Such modelling is hard and, therefore, expensive. This means that whilst it is fine or use by large multinationals, it is not suitable for small, cash-strapped schemes. Having said this, the susceptibility of small schemes to mortality volatility risk maybe means that these are the schemes that would most benefit from such an approach.

So where does this leave us? Well, risk-free rates are still a good first-cut approach for pension liability valuation, but it might be useful to dig a little deeper and look at cash flows rather than discounted present values.