Liability concept

DB pensions are a form of delayed compensation. For the work performed today, employees receive, in addition to their wages, promises of benefits to be paid after retirement. In order to value these benefits, one must first decide what expected future benefits should be recognized today. In the broadest concept, the present value of benefits (PVB), recognizes all future expected benefit payments. This is analogous to accounting, for, the net present value of all of an employee's expected future wages as a current liability, is something that seems unreasonably broad for most of the applications. The public sector commonly recognizes pension liabilities, using a concept called the pension benefit obligation (PBO), or a closely related methodology called the entry age normal (EAN). These account for the future wage growth but not for the future service, and thus, they recognize only a fraction of the PVB. The PBO recognizes the PVB in proportion to the fraction of an employee's service earned to date, relative to the expected total at retirement. The EAN recognizes the PVB in proportion to the fraction of an employee's discounted total wages earned to date relative to the expected total at retirement. The narrowest commonly used liability concept for DB pension plans is the accrued benefit obligation (ABO). This concept only recognizes the benefit payments that are earned to date, and bases projected benefit payments off of an employee's current wage history. It corresponds quite closely to the benefits that a worker would receive if the plan to which they belonged was shut down today, and is thus often called the ‘termination liability’.

Broad measures of pension liabilities that account for wage growth (e.g., the PBO, EAN, or PVB) need to be discounted at higher rates. Wages are exposed to priced risks. Wage growth, the stock market, and the economy more broadly, must all be positively correlated, at least over longer horizons. According to Black (Reference Black1980), ‘stocks go up when it looks like times will be good. In good times, wages and salaries, and benefits all tend to grow faster than usual. Thus the broader your view of the pension liability, the more stocks you will need for hedging’. Lucas and Zeldes (Reference Lucas and Zeldes2006) have developed a framework for estimating appropriate risk-adjusted discount rates for DB pension liabilities, which account for the future pension benefit payments’ exposure to the market through the wage growth channel. These issues are less relevant for the ABO, which are not exposed to wage risk, and the ABO is the most relevant liability concept for the Pension Benefit Guaranty Corporation (PBGC).

Bulow (Reference Bulow1982) argues that ABO is the appropriate liability concept for the corporate plans quite generally, because the broader concepts unreasonably imply ‘an implicit contract under which young workers accept lower total compensation in return for an informal agreement that they will be highly paid later in their career’. This has implications beyond those that are directly related to exactly the benefits that are currently recognized. Bulow (Reference Bulow1982) suggests that, ‘an example of the effect of such an assumption is that many mistakenly believe that if a worker's benefits are tied to final salary, he is protected against inflation until retirement’. The existence (or lack thereof) of inflation protection impacts the appropriate discount rate to use for discounting liabilities, regardless of which exact liabilities are recognized. Bodie (Reference Bodie1990) suggests that the ‘failure of pension funds to show any significant interest in inflation-protected investment products such as CPI-linked bonds is clear evidence that they [the plan sponsors] do not view their liabilities as indexed for inflation’.

Most importantly, under U.S. law, the PBGC's guarantee only extends to benefits accrued prior to a firm's bankruptcy filing. New (insured) accruals thus stop in plan terminations, or even before if bankruptcy predates a plan's termination. The PBGC's liability consequently only extends to the ABO liabilities, making it the most relevant liability concept when valuing DB pension liabilities for PBGC insurance purposes.Footnote ¹

Valuation: promises or expected payments?

The value of the same pension promises may not be the same from the point of view of different stake-holders. For example, retired participants of a plan administrated by a firm near bankruptcy may value their claims under the assumption that they are relatively safe, at least partly because of the existence of the PBGC insurance. The same expected benefit payments may be valued much lower by the firms’ stockholders, who have limited liability. Valuation of DB pension liabilities thus requires a decision, either explicit or implicit, about exactly which payments are being valued. This is basically a question of whether the payments being valued are the promised payments, or the payments that are actually expected to be made.

For the last decade, the Employee Retirement Income Security Act (ERISA) has required private sector firms to discount expected pension payments for reporting and funding purposes using corporate bond rates.Footnote ² These prescribed discount rates implicitly value pension liabilities from the point of view of a firm's equity holders. Corporate bond rates reflect the possibility that firms may default on their debts. These rates thus account for the fact that the expected payments are smaller than the promised payments (because of the possibility of default). They also include a risk premium that arises because, defaults co-vary with priced risks (i.e., because defaults are more likely in bad times, when extra dollars are particularly valuable). ERISA thus prescribes that firm managers value the pension payments that the plan sponsor expects to actually make, not the payments the plan participants expect to receiveFootnote ³.

The distinction arises from limited liability, and from the value of PBGC insurance itself. From the point of view of the plan participants, PBGC insurance is a valuable asset. The insurance makes the future benefit payments (up to a limit) almost risk-free, and thus the stream of payments retirees expect to receive more valuable. From the point of view of the plan sponsor, PBGC insurance is less valuable, because in the event the insurance pays off, it is the participants, and not the sponsor, that receives the payments.Footnote ⁴ For the sponsor, the limited liability essentially acts as a valuable put option, which reduces the value of the stream of benefits it promises. Under certain conditions, a sponsor's liability is limited to the value of a plan's assets, which is economically equivalent to owning an option to deliver the plan's assets in exchange for the value of the plan's liabilities.

Conceptualizing the value of PBGC insurance as a put option allows for its valuation using the no-arbitrage techniques developed to price options (Black and Scholes, Reference Black and Scholes1973).Footnote ⁵ The standard methodology for pricing derivative securities involves constructing the instrument's replicating portfolio (the ‘synthetic’ security), which generates the exact same cash flows at every date in the future in every possible future. Market forces ensure that the price of the derivative security must be close to the price of the hedge portfolio.

Many authors have used this framework to analyze the value of PBGC insurance (e.g., Marcus, Reference Marcus, Bodie, Shoven and Wise1987; Pennacchi and Lewis, Reference Pennacchi and Lewis1994), and particularly the moral hazard arising from the very existence of PBGC insurance. Bodie (Reference Bodie1990) suggests that for underfunded plans ‘… it may be optimal to exploit the put provided by the PBGC insurance through a high-risk investment strategy’.

Insured liability

ERISA (and later the Pension Protection Act of 2006) prescribe that firms account for their pension liabilities using rates that implicitly reflect the possibility of default, yet these rates may not be appropriate for valuing the PBGC's liabilities. The PBGC exists to guarantee pension benefits. Because it will make payments that a plan sponsor cannot, it is inappropriate to use discount rates that reflect the possibility of the sponsor's default when calculating the PBGC's potential liabilities.

The fact that the PBGC's potential liability extends only to the ABO benefits (subject to the payment cap), in conjunction with the fact that the benefits paid by the PBGC are essentially risk-free and make the valuation of these liabilities relatively straightforward. The ABO is not affected by uncertainty about future wages and service, as the cash flows associated with the ABO are based completely on the information known today (plan benefit formulas, current salaries, and current years of service). Mortality is relatively easy to forecast (probabilistically), and the uncertainty in these forecasts is largely idiosyncratic (i.e., uncorrelated with aggregate economic variables that may be related to discount rates).Footnote ⁶ Pension promises related to termination liabilities, which are insensitive to wage risk, should thus be discounted at riskless rates of return (Sharpe, Reference Sharpe1964).

This valuation is most concretely done by simply pricing the defeasance portfolio. A plan's liabilities can be defeated (i.e., made null and void) by delivering a portfolio of securities that generate the income required to make all the future benefit payments. The cost today of buying this replicating portfolio is the value of the liabilities. The defeasance portfolio can most easily be constructed using either true market annuities or default free bonds.

The advantage of defeasing the liabilities using market annuities is that these are already accounted for the impact of mortality on expected payouts, making the construction of the replicating portfolio particularly simple. Defeasing the liabilities in this way yields insurance industry, an annuity pricing of the liabilities. Such pricing may slightly overstate the true cost of liabilities, because the market for these annuities is not as transparent or competitive as the market for the high-quality bonds. That is, an insurance industry's annuity pricing reflects the provider's profit margins, which are likely higher than those enjoyed by the market makers in the bond market.Footnote ⁷ This is likely more than fully offset by the fact that the credit quality of the PBGC is superior to that of even the best annuity providers, which means that the value of an annuity provided by these companies is lower than that of a similar annuity provided by the PBGC. The PIMS model also uses annuity prices that come from surveys, not transactions. Although the American Academy of Actuaries reports only modest differences (3–5%) between the PBGC's survey prices and actual transaction prices, these differences are magnified in firms’ net pension liabilities.Footnote ⁸

The advantage of defeasing the liabilities using default-free bonds is that this may most accurately reflect the true cost of the liabilities provided by the PBGC. This does require forecasting the effects of mortality on expected payments, but this is relatively simple and straightforward. Because the liabilities are basically nominal (i.e., not inflation protected), the bonds employed in the defeasance calculation should themselves be nominal. Using treasuries would almost certainly yield a liability that overstates the liabilities’ true value, because treasuries enjoy a significant liquidity premium (i.e., are expensive) because of their use as a safe-haven asset, and because they have special status as a collateral asset (Longstaff, Reference Longstaff2004; Krishnamurthy and Vissing-Jorgensen, Reference Krishnamurthy and Vissing-Jorgensen2012). The true value of the liabilities is thus probably more accurately reflected by the cost of the defeasance portfolio, constructed using agency securities, which are close to risk-free but do not enjoy the special status of treasuries.

Although there are many subtle issues around the appropriate recognition and valuation of DB pension liabilities, valuing liabilities that the PBGC insures, is ultimately or relatively straightforward. By law, the PBGC's liabilities are limited to the ABO. The only risk the insured ABO cash flows are exposed to is the mortality risk, which is basically unpriced. These liabilities are thus effectively risk-free, and they should therefore be discounted at risk-free rates. These rates are probably best reflected by the yields on agency securities, which are extremely unlikely to default but do not carry the liquidity premium built into treasury yields.

Discounting the distribution of expected future liabilities back to a current ‘value’ is much more difficult. The PIMS User Manual explicitly states that the model should only be used to forecast possible outcomes, and so it cannot be used to calculate the present value of these future liabilities. In practice, however, users of the model seem unable to refrain from doing so. The headline summary statistic that people used to talk about the funding status of the PBGC comes directly from discounting the expected future liability at risk-free rates, which is completely inappropriate. Moreover, this certainly understates the true magnitude of the PBGC underfunding.

Despite the fact that the evolution of the termination liabilities in the PIMS model is driven largely by the interest rate process, the timing and the extent to which the PBGC is forced to assume these liabilities is driven in large part by market and macroeconomic risks. If the PBGC's underfunding is particularly large in 10 years, it will almost certainly be because the U.S. economy has underperformed expectations. This is precisely the time at which any given level of underfunding will be particularly painful, and discounting the models’ forecasted distribution of future underfunding, fails to account for this reality.

Moving towards modeling, the distribution of future liabilities in a manner that accounts for the price risk (i.e., using a ‘risk-neutral’ framework) would allow for calculating the present value of the future liabilities more accurately. This can be an important step for the PIMS system, as it would provide policymakers with information more relevant for decision making. A proper valuation would account for the possibility of painful ‘tail events’, and by doing so in a way that appropriately accounts for the pain associated with these relatively low probability events. This would also permit easier communication of the risks facing the agency with a single univariate statistic.