Con Keating: Discount rates and DB pension scheme valuation - A history lesson

The question most frequently asked - what discount rate should be used for valuing the liabilities of pension schemes? - is problematic. Surprisingly, academics and practitioners have spilled gallons of ink, and exchanged more than a few uncivil words debating this question.

The problem arises in large part because of the specific method being applied for these valuations; the liabilities (in the case of pension schemes, projected pension benefit payments) are taken and then discounted using some rate or other. There is no consideration given to how these liabilities came about in the first place. History and information have been discarded in this process.

There are circumstances in which the use of the mandated rates may be justified. For example, the use of buyout discount rates applied solely to the projected payments will produce an unbiased estimate of the cost of buying out those liabilities. Equally, using the expected rate of return on assets will produce an unbiased estimate of the value of those liabilities, if the investment return is realised, and this may be compared with the value of those assets to establish their sufficiency.

However, these approaches do not answer the central question: what is the cost (and value) of these liabilities to the company. The methods in use are answering different questions. The approaches in use are interesting but they are counterfactuals to this central question of cost to the company. Of course, as counterfactuals, they fail the test of being "true and fair" values for the purposes of corporate accounting. They also raise the question of how much of the defined benefit (DB) pension legislation in effect would be robust to challenge on this basis.

The cost of any pension liability at any point is usually in large part determined by the terms under which it was created. In this, it is analogous to the cost of issuing another form of liability, a corporate bond. If a company issues a 6% bond, its cost is 6%. If this is a zero-coupon bond, its accrued value will rise by 6% per annum until maturity. If I buy such a zero-coupon bond, as an investor, my return will be 6%. With coupon issues and intermediate cash flows, the achieved compound return may vary from this depending upon the reinvestment opportunities available at those times - in bond market parlance, these are convexity effects, but the cost to the company remains 6%.

Let us take the analogy a little further. Under fair value accounting, and the pension valuation methods in use, identical sets of future cash flows will have the same value today. So, a 6% zero-coupon bond issued some time ago will have the same present value as a newly issued 12% bond. Let us arbitrarily set the future maturity of these bonds at 5 years, in order to supply some concrete figures. This approach will use the 12% prevailing rate to discount both bonds, and as they have identical future cash flows, will value both at the same amount, 56.74%.

However, they would not trade in a bond market in this manner. The reason is that the value of the admitted claims in insolvency, being based upon the accrued contractual obligations of the company, would differ. The admitted claim of the12% bond would be 56.74%, but the 6% bond would have an admitted claim value of 74.73%. This difference would be recognised in markets, and priced to the extent that insolvency was likely.

Some take this as an argument, that government bond yields, by convention default risk-free, should be used in scheme valuation and funding. However, this argument is ill-founded. This can be seen immediately by considering these two bonds as secured instruments. For 100% collateral, the 12% bond would require funding of 56.74% and the 6% bond funding of 74.73%. Pension liabilities funding requirements should be no different, even if these liabilities were risk-free.

Of course, interest rates have fallen in recent times. A new (five-year, zero coupon) bond might today be issued at, say, 3%, in which case it would need funding at 86.26%. The old 6% bond would still be funded at 74.73% - and the company would be performing properly, discharging its obligations. The bondholder would not have any ability to call for further collateral funding. It is something of a mystery why pensions should have this option, to be able to call for further funding when it is still fully compliant with its obligations.

The read-across to pension liabilities is direct. A company has set an implicit rate of return on the pension accrual under the terms of the award; a contractual accrual rate (CAR). This is determined by the contribution made and the projection of benefits ultimately payable. This is the cost of the pension liability to the company. It is true that the projections of benefits are much more uncertain than the maturity proceeds of a conventional zero-coupon bond, but all of the methods operate on these same projections.

The contractual accrual rate for the scheme is the weighted average of the rates introduced by all awards, both across members and over time. It is this contractual accrual rate which should be used to calculate the accrued liability of the scheme.

It is within the assumptions driving these projections that prudence may be introduced. It is inappropriate to alter the discount rate in pursuit of prudence. Technically, the role of the discount rate here is as a measure. In long-term situations, the discount rate is a compound rate, an average, directly comparable to the yield on a zero-coupon bond. In a historical setting, it is obviously a risk-experienced rate, the average of previously prevailing rates; this extrapolates to the use of discount rates in a prospective setting, which renders much of the risk-management literature on DB pensions otiose.

There are many desiderata of measures, often context specific. In the context of pensions valuations, one central such property is that of time consistency, that the value arrived at by accrual should equal the value arrived at by discounting. The contractual accrual rate has that property. Measures such as market-consistent bond yields or expected returns do not possess that property.

No discussion of pension scheme valuation would be complete without mention of another source of bias and error. The mixed attribute nature of solvency determination, the use of market values for assets and a discounted present value for liabilities, is such a source. In this regard, earlier standards, which used a common discount rate for the valuation of both the liability projections and asset cash flow estimates was superior[i]. Even if we consider asset prices to be the result of some discounting of their future cashflows, the implicit discount rate is in most cases unknown and unknowable. Perhaps, this uncertainty motivates some of the recent purchases of bonds where this uncertainty is minimal, but that also implies a very high level of risk-aversion given the relative performance of the various asset classes.

It may not be practical to go back and reconstruct the contractual accrual rate for legacy schemes, but it certainly is practical to introduce this CAR method for collective defined contributions schemes when they come into existence.

Con Keating is head of research at Brighton Rock Group

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• Topics
• Defined Benefit
• Con Keating
• DB liability valuations
• actuarial valuation
• discount rates