Market pricing of liabilities is central to the financial economics model of pension plans (“pension finance”). A pension liability is valued at the price at which a reference security trades in a liquid and deep market.
Many actuaries question this approach. They observe that pensions do not trade in the financial markets and therefore should not be valued like traded securities. Pension cash flows differ from those of marketable bonds: they are contingent upon future events, such as pay increases and mortality, that do not affect ordinary bonds. This note aims to clarify the application of the pension finance model and respond to the questions.
Application of the ModelThe pension finance model measures economic value, without regard to current accounting or funding rules—though its advocates believe that accounting and funding rules would benefit from closer adherence to financial economics. Economic value is a useful benchmark for exploring a host of pension issues. Examples include the effect of a pension plan on the financial condition of the sponsor, the cost of possible plan improvements, and whether each taxpayer generation pays correctly for public plan pensions earned while it receives governmental services. Economic value is not a termination measure; for example, it uses retirement age assumptions consistent with an ongoing plan. Rather, it measures the consensus value that the capital markets place on the cash flows promised by the plan.
Pension finance treats the ABO as the economic pension liability. The “roll-up” of accrued benefits for pay increases under a final pay plan should be understood as part of the cost of those pay increases. Because future pay increases are not a current economic liability, neither should the pension increases resulting from them. It seems difficult and contradictory to include future pension increases in a definition of economic liability in a way that includes the future pension increases while excluding the pay increases that produce them.
The reference portfolio has cash flows that match the liability in amount, timing, and probability of payment. Amount and timing are clear enough, but the probability of payment is more problematic.
- A riskless reference portfolio should be used to measure the economic liability of very strong sponsors, or sponsors of plans that are well funded and conservatively invested.
- To measure the economic liability of weaker sponsors with plans that carry some default risk, the reference portfolio should carry comparable risk.
- A solvency test or minimum funding target differs from a measurement of economic liability in requiring a riskless reference portfolio for all plans. Only a riskless portfolio can assure payment of all pensions. Any lesser portfolio would pass on either direct costs or risks either to third parties, such as the PBGC for private plans, or to future taxpayer generations for public plans.
The reference portfolio consists of securities that trade in a liquid and deep market. A holder of such securities could either reduce or augment his holdings at about the same price—that is, the bid-ask spread must be small. Recent events remind us that, at least for risky securities, these conditions do not always hold. For some securities at some times, bid-ask spreads may be wide and trading thin. Under these conditions, current transactions may represent special needs of particular investors, rather than an investor consensus of the value of the securities. The pricing of such transactions is not a suitable guide for valuing pension liabilities
Supposing that there is a liquid and deep market, what is the justification for using marketable securities to value nonmarketable pension liabilities? Some actuaries assert that the Law of One Price  cannot apply to pension liabilities, which are not tradable and not subject to arbitrage. The application of bond market pricing to pension valuation, though, is based not on the Law of One Price, but on a simpler notion: Like liabilities have like values. A dollar owed to a pensioner is very like a dollar owed to a creditor, as each must be paid when due. The differing ability of the recipients of those dollars to transfer their rights does not justify a substantial difference in the payer’s assessment of its obligation. Are there other differences that would make these obligations substantially different for the payer? Some actuaries point to demographic contingencies, to which we now turn
Life ContingenciesHow does the traditional actuarial model handle the life contingencies of pension payments? Consider a single payment to a single pensioner: a $1,000 endowment due a few decades hence, with a survival probability of 80 percent. The traditional actuarial model multiplies the $1,000 by 80 percent to arrive at an $800 expected payment. It then discounts this $800 by the selected discount rate. The resulting value is identical to that of an $800 deterministic cash flow. In other words, the traditional model uses the expected payment as a stand-in for the payment probability distribution. Generalizing from an endowment to a group of life annuities, we can say that the traditional model uses demographic assumptions to find an expected payment stream, and then discounts that stream as if no life contingencies were involved. In other words, the traditional model treats the expected cash flows exactly like ordinary, deterministic bond flows. In treating the expected pension cash flow as a deterministic stream, pension finance actuaries only are following long-established actuarial practice
Perhaps supporters of the traditional approach would argue that they reflect the demographic uncertainty by choosing higher discount rates than the market applies to bonds. But from the perspective of a plan sponsor or insurer, the uncertainty would, if anything, make pension obligations more onerous, not less, and would call for a lower discount rate than the bond market suggests.
Both pensions and marketable bonds are made of the same stuff: contractually required cash flows. The contingent nature of pension flows differs from that of bonds. But the major contingency, future pay increases, is not reflected in the pension liabilities that pension finance recognizes. As for demographic contingencies, pension actuaries have always ignored the demographic uncertainty inherent in the expected pension flows. They cannot point to that uncertainty as a problem in the pension finance model without indicting their own practice. Pension finance departs from the traditional model only in asserting that the trillions of dollars of daily trading in Treasuries and similar securities offer a more objective and accurate guide to the economic value of cash flows than the judgments of individual actuaries.
Lawrence N. Bader, FSA, is retired and lives in Cary, N.C. He can be reached at firstname.lastname@example.org.
 See Principle 4 from Reinventing Pension Actuarial Science, Lawrence N. Bader and Jeremy Gold, The Pension Forum, Vol. 14, No. 2, January 2003. A reference security, or a reference portfolio, has cash flows that match the liability in amount, timing, and probability of payment.
 The Law of One Price states that tradeable securities with the same cash flows must have the same price.
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