10.3 Valuation of pension liabilities and assets

Pension liability valuation

Pension liability valuation is about estimating the present value of all future benefits a plan has promised to its participants. Getting this number right drives every downstream decision: how much the sponsor contributes, how assets are invested, and whether the plan can meet its obligations. Actuaries combine benefit formulas, demographic projections, and economic assumptions to arrive at a single liability figure that represents a complex stream of future cash flows.

Pension asset valuation, the other side of the equation, determines what the plan actually holds to pay those benefits. Together, liabilities and assets define the plan's funded status, which is the central metric for regulators, auditors, and plan sponsors alike.

Accrued vs. projected benefits

These two measures frame how much the plan "owes," but they answer slightly different questions.

• Accrued benefits reflect what participants have earned based on service and salary to date. Think of it as the liability if the plan froze right now.
• Projected benefits look forward, incorporating expected future service and salary growth until each participant's assumed retirement age.

The distinction matters because projected benefits will always be larger than accrued benefits for active employees. Accounting standards (like FASB ASC 715) use the Projected Benefit Obligation (PBO), while funding rules sometimes reference the accrued measure. Which one you use changes both the size and the timing of recognized liabilities.

Actuarial cost methods

A cost method answers: How do we spread the total cost of a participant's pension over their working career? Different methods produce different contribution patterns, even when the total lifetime cost is the same.

• Entry Age Normal (EAN): Assigns a level percentage of salary (or level dollar amount) from hire date to retirement. Produces stable annual costs and is the most common method for U.S. public plans.
• Projected Unit Credit (PUC): Attributes a unit of benefit to each year of service based on the projected final salary. Costs tend to increase as participants age because the discounting period shrinks. This is the required method under IAS 19.
• Traditional Unit Credit (TUC): Similar to PUC but uses current salary rather than projected salary. Costs are lower early on but rise steeply near retirement.

The choice of method doesn't change the total benefit paid; it changes when the cost hits the books and how much the sponsor contributes each year.

Actuarial assumptions

Every liability calculation rests on two categories of assumptions:

• Demographic assumptions project who will receive benefits and when: mortality, retirement, termination, disability, and marital status.
• Economic assumptions project how much those benefits will cost in present-value terms: the discount rate and the salary scale.

Small changes in assumptions can move liabilities by large amounts. A 25-basis-point drop in the discount rate, for example, can increase a mature plan's liability by 3–5%. That sensitivity is why assumption-setting is one of the most consequential tasks an actuary performs.

Discount rates

The discount rate converts future benefit payments into a present value. It's the single most influential economic assumption.

• Under U.S. GAAP (ASC 715), the discount rate is based on yields of high-quality corporate bonds (typically AA-rated) with durations matching the plan's expected cash flows.
• Under IAS 19, the same high-quality corporate bond approach applies, though in markets without a deep corporate bond market, government bond yields may be used.
• For U.S. public plans, the discount rate is often set equal to the expected return on assets, which is a fundamentally different (and debated) approach.

The inverse relationship is critical: lower discount rates produce higher liabilities, and higher discount rates produce lower liabilities. This is straightforward time-value-of-money mechanics, but it has enormous practical consequences when market rates shift.

Mortality rates

Mortality assumptions determine how long the plan expects to pay benefits. Actuaries rely on published mortality tables and apply projection scales to account for future improvements in life expectancy.

• In the U.S., the Society of Actuaries publishes tables like the Pri-2012 base table with MP-2021 (or later) improvement scales.
• Generational mortality tables, which project continued improvement year by year, produce higher liabilities than static tables because they assume each successive cohort lives longer.
• Even a one-year increase in average life expectancy can raise liabilities by roughly 3–4% for a typical plan.

Salary scale

For plans with benefits tied to final average salary, the salary scale assumption projects how participants' pay will grow over their careers. It typically includes three components:

• Inflation (general wage growth)
• Productivity gains (economy-wide real wage increases)
• Merit and promotion increases (individual career progression, usually highest at younger ages)

A higher salary scale means higher projected final salaries, which means higher projected benefits and larger liabilities. Actuaries calibrate this assumption using the sponsor's historical compensation data and broader economic forecasts.

Termination rates

Termination (or withdrawal) rates estimate the probability that an active participant leaves employment before retirement.

• Rates are typically highest for young, short-service employees and decline with age and tenure.
• A participant who terminates before vesting forfeits their benefit entirely, reducing plan liabilities.
• Even vested terminators often receive smaller benefits (a deferred annuity based on salary at termination rather than projected final salary).

Higher assumed termination rates therefore reduce liabilities, sometimes substantially for plans with younger workforces.

Retirement rates

Retirement rate assumptions specify the probability that a participant retires at each eligible age.

• Plans with early retirement subsidies (e.g., unreduced benefits at age 55 with 30 years of service) need careful modeling because early retirees collect benefits for more years.
• Earlier assumed retirement ages increase liabilities for two reasons: benefits start sooner, and they're paid over a longer period.
• Actuaries build retirement rate tables from the plan's own historical experience when credible data exists.

Disability rates

Disability rates capture the probability that a participant becomes disabled and qualifies for a disability benefit under the plan.

• These rates vary significantly by age, gender, and occupation (blue-collar workers typically have higher disability incidence).
• Disability benefits often begin immediately and may be calculated differently from normal retirement benefits.
• Higher disability rates increase liabilities, though for most plans the impact is smaller than mortality or retirement assumptions.

Marital status

Many pension plans provide joint and survivor benefits, which continue paying a reduced benefit to the participant's spouse after the participant dies.

• Actuaries assume a percentage of participants will be married at retirement (often 80–85% for male participants, somewhat lower for female participants).
• The assumed age difference between spouses also matters, since a younger spouse extends the expected payment period.
• Higher assumed marriage rates and larger spousal age gaps both increase liabilities.

Funding requirements

Pension plans must meet minimum funding standards set by law. In the U.S., the key framework is ERISA as amended by the Pension Protection Act of 2006 (PPA).

• Plans must maintain a minimum funded percentage (generally 80–100% on a PPA basis) or face restrictions on benefit improvements and lump-sum payments.
• Shortfall contributions are required when assets fall below the funding target.
• Contribution requirements create a floor, but sponsors can (and often do) contribute more than the minimum to build a funding cushion.

Amortization of unfunded liability

When liabilities exceed assets, the resulting unfunded actuarial liability (UAL) must be paid down over time through additional contributions.

• Under PPA rules for single-employer plans, the shortfall is generally amortized over 7 years.
• Public plans often use longer amortization periods (15–30 years), which reduces annual payments but increases total interest cost.
• The amortization method (level dollar vs. level percentage of payroll) and whether payments are calculated on an open or closed basis significantly affect the contribution schedule.

Pension asset valuation

While liabilities represent what the plan owes, asset valuation determines what it has. The gap between the two is the funded status, and the way you measure assets can make that gap look very different.

Fair market value

Fair market value (FMV) is the price plan assets would fetch in an orderly transaction between willing parties on the measurement date.

• For publicly traded securities, FMV is straightforward: it's the closing market price.
• For illiquid holdings (real estate, private equity), FMV requires appraisals or model-based estimates.
• FMV is the required basis for balance-sheet reporting under ASC 715 and IAS 19.

The downside of FMV for funding purposes is volatility. A sharp equity decline can suddenly make a well-funded plan appear underfunded, triggering large contribution swings.

Actuarial vs. market value

To dampen that volatility, actuaries often use an actuarial value of assets (AVA) for funding calculations.

• The AVA smooths investment gains and losses over a period (commonly 3–5 years) so that a single bad year doesn't dominate the funding picture.
• Accounting standards require FMV on the balance sheet, but funding rules in many jurisdictions permit or require smoothed values.
• The AVA will lag behind FMV in both rising and falling markets, which is the intended trade-off: less accuracy in exchange for more stability.

Asset smoothing methods

Two common smoothing approaches:

• Weighted average method: Blends the current market value with prior years' actuarial values. A typical 5-year smoothing recognizes 20% of each year's gain or loss per year.
• Corridor method: Constrains the AVA to stay within a corridor (e.g., 80–120%) of the FMV. If the smoothed value drifts outside the corridor, it's reset to the boundary.

Both methods reduce contribution volatility but can mask the true economic position of the plan.

Expected return on assets

The expected return on assets (EROA) is the long-term rate of return the plan assumes its investments will earn.

• EROA is built from the plan's target asset allocation and capital market assumptions for each asset class. For example, a 60/40 equity/bond portfolio might assume 7% equities and 4% bonds, yielding a blended EROA of roughly 5.8%.
• Under ASC 715, the EROA offsets pension expense: a higher assumed return means lower reported cost.
• Setting EROA too aggressively creates a risk of persistent actuarial losses when actual returns fall short.

Asset allocation strategies

Asset allocation is the primary driver of both expected return and investment risk.

• Equities offer higher expected returns but with greater volatility. A large equity allocation can improve long-term funded status but increases short-term contribution risk.
• Fixed income provides more predictable cash flows and, when duration-matched to liabilities, can hedge interest rate risk.
• Real estate and alternatives (hedge funds, private equity, infrastructure) can add diversification and potentially higher returns, but they introduce illiquidity, complexity, and valuation uncertainty.

The right allocation depends on the plan's funded status, liability profile, sponsor's risk tolerance, and time horizon.

Equities vs. fixed income

This is the core allocation decision for most pension plans.

• A growth-oriented plan (e.g., 70% equities / 30% bonds) seeks to grow assets faster than liabilities but accepts higher funded-status volatility.
• A liability-hedging plan (e.g., 30% equities / 70% long-duration bonds) prioritizes stability of funded status over asset growth.
• Many plans adopt a glide path: as funded status improves, they shift from equities toward fixed income, locking in gains and reducing risk.

Alternative investments

Alternatives can play a role in pension portfolios, but they come with trade-offs:

• Hedge funds may offer lower correlation to public markets, but fees are high and performance dispersion is wide.
• Private equity has historically delivered a return premium over public equities, though with significant illiquidity (capital can be locked up for 7–10 years).
• Real assets (real estate, infrastructure, commodities) can provide inflation protection and diversification.

Due diligence and governance are especially important for alternatives because of their complexity and reduced transparency.

Funding policy

A funding policy is the sponsor's strategic framework for contributions. It balances three goals:

• Benefit security: Maintaining enough assets to pay promised benefits.
• Contribution stability: Avoiding large year-to-year swings in required payments.
• Intergenerational equity: Ensuring that the cost of benefits is borne by the generation of stakeholders that benefits from the employees' service.

A well-designed funding policy specifies a target funded ratio, a contribution strategy (e.g., always contribute at least the normal cost plus a margin), and triggers for adjusting the approach.

Contributions vs. benefit payments

The plan's cash flow equation is simple in concept:

$\text{Ending Assets} = \text{Beginning Assets} + \text{Contributions} + \text{Investment Returns} - \text{Benefit Payments} - \text{Expenses}$

• When benefit payments exceed contributions (common in mature or closed plans), the plan is in negative cash flow and depends on investment returns to maintain funded status.
• Negative cash flow plans face greater liquidity risk and may need to hold more liquid assets, potentially sacrificing return.

Cash flow projections

Cash flow projections model future contributions and benefit payments year by year, typically over a 20–30 year horizon.

• Projections rely on the same actuarial assumptions used for the liability valuation.
• They help the plan assess liquidity needs (can the plan pay benefits without forced asset sales?) and inform the investment strategy.
• Sensitivity testing under different economic scenarios (e.g., rising rates, falling equity markets) is standard practice.

Pension expense

Pension expense is the cost of providing pension benefits as recognized in the sponsor's financial statements. It doesn't necessarily equal the cash contribution; accounting expense and funding contributions follow different rules.

Service cost

Service cost is the present value of the additional benefits participants earn during the current period.

• It's calculated using the plan's actuarial cost method (PUC under IFRS, typically PUC or EAN under U.S. GAAP).
• Service cost is the only component of pension expense classified as an operating cost under ASC 715 (post-2018 guidance).

Interest cost

Interest cost reflects the growth of the liability due to the passage of time. It's calculated as:

$\text{Interest Cost} = \text{Discount Rate} \times \text{Beginning-of-Year PBO}$

As participants move one year closer to retirement, their discounted liability increases. Higher discount rates produce larger interest cost in dollar terms, but they also produce a smaller starting PBO, so the net effect depends on the plan's maturity.

Expected return on assets

In the pension expense calculation, the EROA is applied to the market-related value of assets (which may be a smoothed value) to produce an offset against expense:

$\text{Expected Return Component} = \text{EROA} \times \text{Market\text{-}Related Value of Assets}$

This component reduces pension expense. The difference between the expected return and the actual return becomes an actuarial gain or loss.

Amortization of gains/losses

When actual experience deviates from assumptions (e.g., actual investment return differs from EROA, or mortality experience differs from the table), the difference is an actuarial gain or loss.

• Under ASC 715, gains and losses are accumulated in Accumulated Other Comprehensive Income (AOCI) and amortized into expense only when the net cumulative amount exceeds a corridor of 10% of the greater of the PBO or plan assets.
• The excess is amortized over the average remaining service period of active participants.
• This corridor approach delays recognition, smoothing expense but potentially building up large unrecognized amounts.

Amortization of prior service cost

When a plan amendment retroactively increases (or decreases) benefits, the change in PBO is called prior service cost.

• Prior service cost is recognized in AOCI at the amendment date and amortized into expense over the average remaining service period of employees expected to benefit from the change.
• For a plan with an average remaining service of 12 years, a $12 million prior service cost would add roughly $1 million per year to pension expense.

Net periodic pension cost

Net periodic pension cost (NPPC) is the sum of all components:

$\text{NPPC} = \text{Service Cost} + \text{Interest Cost} - \text{Expected Return on Assets} + \text{Amortization of Losses} - \text{Amortization of Gains} + \text{Amortization of Prior Service Cost}$

Under current U.S. GAAP, only service cost appears in operating income. The remaining components are reported below the operating line (in "other income/expense") unless the entity elects a different presentation.

Accounting standards

Two primary frameworks govern pension accounting:

• FASB ASC 715 (U.S. GAAP): Requires recognition of the funded status (PBO minus fair value of assets) on the balance sheet. Uses the corridor approach for gain/loss amortization.
• IAS 19 (IFRS): Also requires balance-sheet recognition of the net defined benefit liability (or asset). Remeasurements (actuarial gains/losses and return differences) go directly to Other Comprehensive Income and are never recycled to profit or loss, unlike the U.S. corridor method.

The key practical difference: under IFRS, pension expense is more volatile in OCI but smoother in profit or loss. Under U.S. GAAP, the corridor method delays recognition but eventually flows gains and losses through the income statement.

Pension risk management

Sponsoring a defined benefit pension plan exposes the organization to a range of interconnected risks. Effective risk management doesn't eliminate these risks but identifies them, quantifies their impact, and deploys strategies to keep them within acceptable bounds.

Interest rate risk

Interest rate movements affect both sides of the balance sheet, but not symmetrically.

• A 100-basis-point decline in rates can increase a plan's PBO by 10–15% for a plan with a liability duration of 12–15 years.
• Plan assets invested in bonds also increase in value when rates fall, but only to the extent that asset duration matches liability duration.
• The mismatch between asset duration and liability duration is the primary source of interest rate risk.

Longevity risk

If participants live longer than the mortality tables predict, the plan pays benefits for more years than expected.

• Longevity risk is systematic: it affects all participants in the same direction and can't be diversified away within the plan.
• A one-year increase in life expectancy at age 65 can raise liabilities by approximately 3–4%.
• This risk is particularly significant for plans with large retiree populations.

Inflation risk

Inflation erodes the real value of fixed-dollar benefits, but plans that provide cost-of-living adjustments (COLAs) face direct inflation exposure.

• Even plans without formal COLAs may face pressure to grant ad hoc increases during high-inflation periods.
• Inflation-linked bonds (like TIPS in the U.S.) can partially hedge this risk, though the market for long-duration inflation-linked securities is limited.

Investment risk

Investment risk is the possibility that actual asset returns fall short of the assumed EROA.

• A plan assuming 7% returns that earns only 4% over a decade will see its unfunded liability grow substantially.
• Diversification across asset classes reduces but doesn't eliminate this risk.
• Risk budgeting allocates the plan's total risk tolerance across asset classes and strategies, ensuring that no single bet dominates the portfolio.

Funding risk

Funding risk is the risk that the sponsor cannot or will not make required contributions.

• This risk is highest when the sponsor's financial health deteriorates at the same time as the plan's funded status (a common correlation, since economic downturns hurt both).
• Credit rating agencies and regulators monitor pension funded status as a factor in assessing sponsor creditworthiness.
• Conservative funding policies (contributing above the minimum) build a buffer against this risk.

Regulatory risk

Changes in legislation or regulation can alter funding requirements, tax treatment, or benefit rules.

• The Pension Protection Act of 2006 significantly tightened funding rules for U.S. single-employer plans.
• IFRS changes (e.g., the 2011 revision to IAS 19 eliminating the corridor option) have affected how pension costs appear in financial statements globally.
• Sponsors manage regulatory risk by staying engaged with legislative developments and maintaining flexible plan designs.

Risk mitigation strategies

The main tools for managing pension risk include:

• Liability-driven investing (LDI): Aligns asset duration and cash flows with liabilities to reduce interest rate mismatch.
• Annuity purchases (buy-outs and buy-ins): Transfer some or all liabilities to an insurer, eliminating longevity and investment risk on the transferred portion.
• Lump sum windows: Offer terminated vested participants a one-time cash payment, removing their liability from the plan.
• Plan design changes: Freezing accruals, closing the plan to new entrants, or shifting to a cash balance formula can reduce future liability growth.

Each strategy involves trade-offs in cost, complexity, and participant impact.

Liability-driven investing

LDI is the most widely adopted risk management framework for pension plans.

1. Measure the plan's liability duration and cash flow profile.
2. Construct a fixed-income portfolio with similar duration and cash flow characteristics.
3. Allocate remaining assets to a "return-seeking" portfolio (equities, alternatives) sized to the plan's risk budget.
4. As funded status improves, shift more assets from the return-seeking portfolio into the liability-hedging portfolio (the glide path).

A well-implemented LDI strategy means that when rates fall and liabilities rise, the hedging portfolio rises by a similar amount, stabilizing funded status.

Annuity purchases

Annuity purchases transfer pension obligations to an insurance company.

• In a buy-out, the insurer takes over the obligation entirely and pays benefits directly to participants.
• In a buy-in, the plan purchases an annuity policy as a plan asset; the plan still pays participants, but the insurer reimburses the plan.
• Pricing depends on the insurer's own assumptions (mortality, discount rates, expenses), and the cost typically exceeds the plan's accounting liability, resulting in a settlement charge.

Lump sum offerings

Lump sum windows give terminated vested participants the option to take a one-time payment instead of a future annuity.

• The lump sum is calculated using IRS-prescribed interest rates and mortality tables (Section 417(e) rates), not the plan's own assumptions.
• Participants who expect to live longer than average may prefer the annuity; those who don't (or who value liquidity) may take the lump sum. This creates adverse selection risk: if mostly short-lived participants take the lump sum, the remaining population is longer-lived, increasing per-capita liability.
• Despite this risk, lump sum offerings are popular because they permanently remove liabilities and reduce administrative costs.