A number of extremely strange beliefs have emerged in the course of correspondence arising from earlier articles that introduced methods for the evaluation of pension liabilities which do not invoke any external factor.
Take the idea of using market prices universally. Suppose we buy a ten-year bond with a coupon of 5% at par, and that five years later we see the company issue a five-year par bond with a 10% coupon; we don’t get to call the company and have our coupon increased. We continue to receive just the 5% and that remains the cost of that borrowing to the company. The market price is irrelevant. What matters is the contract made at issuance.
Then, there is the idea that two cash flows occurring at some date in the future should have identical values today, that these are unconditional. In an earlier article , we showed that two identical future payments from a particular debtor could have different values and that the difference arose from differences in the terms of the contract which created them. Now I will go one step further and indicate why such cash flows should have different values.
Consider the situation where two companies issue ten-year zero-coupon bonds on the same day, one yields 5% and the other 10%; there is some difference in risk between them. Now suppose that we need to value both on a common liquidation date, say five years prior to maturity. At this date the (risk-free) discount rate is 7%. Applying this rate to each we return the common value of £71.30. Now if we are the holder of the 5% bond we have reason to feel aggrieved since we would need £78.35 to buy a replacement 5% yield. By contrast, the 10% bondholder only needs £62.09 to purchase a replacement 10% yield, and has profited from the liquidation. Risk, and loss, has been transferred to the most cautious. Again, what matters are the original contractual terms.
Finally, among these strange ideas is the belief that using a ‘risk-free’ discount rate, somehow, imparts the property of ‘risk-freeness’ to the cash-flow being discounted. Even if we overlook the fact that ‘risk-freeness’ is an abstract concept that is empirically unobservable, this amounts to transubstantiation, an alchemical transmutation. All that using low government yields as discount rates does is return higher present values than other rates. Using such ‘risk-free’ rates to discount a zero-coupon corporate bond merely makes that bond appear more onerous than under the contracted terms.
The accrual rate that was introduced in earlier articles is a contractual rate. It is the rate of return on contributions implicitly committed to scheme members by the sponsor employer that is sufficient to meet the projected benefits promised. It is the employer’s cost of production of the pension. This is a primary metric of the value for money of a pension arrangement.
There is a very widespread unease with the current state of affairs in the DB world. This is evident from the multitude of groups and bodies currently investigating the issues, their causes and possible remedies. Many ideas are being floated, such as modification of members’ rights and sponsor obligations. There is a basic problem in that while the phenomena giving rise for concern may have been correctly identified, there has been no true quantification of their magnitude. It is one thing to say that it cannot be right that so much additional money has been contributed to so little visible effect, but quite another to state how much, if anything, should have been contributed. The problem is separation of perception and substance, illusion from reality. This article is concerned with bridging that gap.
Figure 1, below, shows the evolution, since 1950, of gilt yields together with the accrual rate, the contracted rate of the illustrative scheme used in earlier articles. It is immediately obvious that the accrual rate is far smoother than the long-term gilt yield. There are periods when the contracted accrual rate is higher than the gilt yield, and times when it is lower. A comparison of the distributions of gilt yields and the accrual rate is provided later.
The smoothness of the contracted accrual rate arises from the marginal nature of changes to it; to contributions and to experience relative to projections for longevity and inflation as well as modifications to the assumptions driving those projections. The current contractual accrual rate used in the valuation of this scheme utilises contributions which date back as far as 1952, and has projected pension benefits payable as far as eighty years in the future – it is a complex and very long-term average. This was illustrated in an earlier article . This is not a weakness of DB pensions but rather an attractive aspect of the risk-pooling and risk-sharing of DB arrangements, which serves to lower the cost of pension provision.
The abrupt change in direction of the accrual rate in 1981 has a number of sources. The first was that the contribution rate was increased from 10% to 12% of pensionable salaries in that year, along with a revision of the post-retirement inflation indexation from average earnings to retail price indexation. This was accompanied by falls in experienced inflation and the rate of earnings growth. It should be noted that many factors operate through more than one channel. For example, high experienced wage growth increases both contributions and the amount of the initial pension payable on retirement, which is then increased further by post-retirement retail price inflation.
The figure also shows proportional errors in liability estimates; proportional errors are reported due to the non-stationary nature of the liabilities. A positive number indicates that liabilities are overstated relative to their contracted values, while a negative value indicates understatement. It is notable that the largest understatement (-55.4%) occurred in 1974, at which time, though all UK financial markets were plumbing new depths, no crisis in pensions was generally reported. The distributions of accrual rates and gilt yields are compared in figure 2. The errors are very large indeed.
A further revision to scheme rules was enacted in 2001, when the contribution rate was raised to 16% and members were allowed to contribute up to a further 5% of their pensionable salary, on marginally more favourable terms than those applying to sponsor contributions. While this might have been expected to have as dramatic an effect as the 1981 revision, it did not as inflation in wages and prices was moderating and longevity beginning to increase at unprecedentedly high rates.
The summary statistics for the distributions of Gilt Yields and Accrual Rates are:
Perhaps the most alarming characteristic of the gilt yield, beyond its extreme range, is its extremely high volatility. It is more than twice that of the contracted accrual rate and over fifty percent of its own average.
Figure 2: Gilt Yield and Accrual Rate Distributions
A battery of formal statistical tests, both parametric and non-parametric, reject the hypothesis that these distributions are similar. In other words, the use of gilt yields is a very poor proxy for the contracted accrual rate of pension promises; nor does that gilt proxy bring any ancillary advantages to the valuation process. As the table 2 below shows, the resultant error terms, the difference between the gilt-based present value estimates of liabilities and accrual rate liabilities, are both positively biased, overstating their quantum, and incredibly volatile. It is difficult to believe that this gilt-based approach provides any practical, let alone rational, foundation for scheme management decisions.
Of course, valuations for pension scheme regulatory purposes differ from the market-consistent yield-based accounting described here. These regulatory valuations are usually based upon the expected returns of investment portfolios, but there is a substantial argument brewing in actuarial circles as to how these expected-return discount rates might best be constructed. If the construction process starts from gilt yields and builds upon those, adding various risk premia, it will retain many of the characteristics of the gilt analysis shown in this article.
By way of ending, a thought experiment seems appropriate. Let us suppose that the PPF 7800 index has the same contracted accrual rate structure as our illustrative scheme and that is a very big supposition, then what might the reported deficits of the PPF 7800 index look like. The results, What-If, are shown in Table 3. The difference is stark. Far from being in trouble, from the contracted accrual viewpoint this collection of schemes is in rude health. Indeed, this analysis suggests that when examining the disadvantages of the existing methods, we should consider rather more than the costs of arbitrary interest rate hedging, as it indicates that much, and possibly all of £120 billion of deficit repair contributions may have been unnecessary.
First Actuarial’s best estimate index (the FAB index) uses the long-term best estimates of the returns of asset portfolios actually held rather than the gilts-plus return estimate widely used in practice. It also values full scheme benefits rather than the reduced benefits valued under the PPF 7800 index. Further detail may be found here.
As the actuary from Mercer, David Fogarty recently observed in a letter to the FT: “One thing that would be avoided is the sweeping assertion that current longer-dated bond yields are somehow a predictor of interest rate conditions in 10 and 30 years’ time.” The source of the FAB index outperformance of the PPF 7800 lies in the asset side of the scheme balance sheet, and it, also, is highly significant.
While it may be too late to resurrect widespread DB pension provision for the current generation, it is becoming clear that we owe it to the next generation to get DB accounting, regulation and management right. In later articles, we will explore asset valuation, alternates to Solvency regulation, such as cash-flow modelling, and member security.