FRM Exam Part I · Insurance Companies and Pension Plans

Pension Plan Funding, Liabilities and Sponsor Risk

Updated 11 October 2026 · Fact-checked

A defined benefit plan is underfunded when the present value of promised benefits exceeds plan assets. Liabilities are discounted at a high-quality corporate bond rate. Funded status equals assets minus liabilities. A deficit is a claim on the sponsor, and a failed sponsor passes losses to a guarantee fund such as the PBGC.

Understand Pension Plan Funding, Liabilities and Sponsor Risk

A defined benefit (DB) plan promises a pension based on salary and years of service. The sponsoring company, not the employee, carries the investment risk. If assets fall short of promises, the sponsor must make up the gap.

To compare promises with assets, you convert future benefit payments into a present value. This is the pension liability. The payments are long dated, often 20 to 50 years, and they are partly uncertain because of salary growth, longevity and retirement age. You discount them at a rate that reflects the safety of the promise. The common convention is a high-quality (AA) corporate bond yield. Some regulators and risk managers argue for a government or swap curve instead. Lower discount rates raise the liability.

Funded status is plan assets minus the present value of liabilities. A negative number means the plan is underfunded. A positive number means it is overfunded. The funded ratio is assets divided by liabilities.

The key risk is asset-liability mismatch. Liabilities behave like a long-duration bond, so they rise when rates fall. Assets are often heavy in equities, with much shorter interest rate duration. When rates fall and equities drop together, liabilities rise as assets fall, and the deficit widens quickly. Inflation-linked benefits and rising life expectancy also push liabilities up.

This creates sponsor risk. A deficit is like debt owed by the company. It can require cash contributions, depress earnings, and weaken credit quality. The risk is worst when the sponsor is weak at the same time the plan is underfunded. If the sponsor fails, a guarantee fund steps in. In the US this is the Pension Benefit Guaranty Corporation (PBGC), which insures private DB plans, takes over terminated underfunded plans and pays benefits up to legal limits. It is funded by premiums from sponsors. Because premiums may not match the risk, the guarantee creates moral hazard: a weak sponsor can take more risk with plan assets, since losses fall partly on the insurer.

Key formulas to remember

Funded status: Funded status = Plan assets − PV of pension liabilities; Negative means underfunded (a deficit). Positive means overfunded (a surplus).
Funded ratio: Funded ratio = Plan assets ÷ PV of liabilities; Below 1 means underfunded. Above 1 means overfunded.
Present value of liabilities: PV = Σ Bₜ ÷ (1 + r)ᵗ; Bₜ is the expected benefit paid at time t. r is the discount rate, usually a high-quality corporate bond yield.
Liability sensitivity to rates: ΔL ≈ −D × L × Δr; D is the modified duration of the liabilities. A fall in rates raises L.
Change in funded status: ΔSurplus = ΔA − ΔL; Compare asset change with liability change. Use each side's own duration.

How to solve Pension Plan Funding, Liabilities and Sponsor Risk questions

Use this sequence for any question on pension funding, discounting or sponsor risk.

1Identify the plan type. Only DB plans leave funding risk with the sponsor. In a DB plan the employer bears the risk. In a DC plan the employee does.
2Find the liability. Discount expected benefit payments at the stated rate, or use the given PV.
3Compute funded status as assets minus liabilities, and the funded ratio if asked.
4Check the discount rate direction. A lower rate gives a higher liability, and the effect is larger for longer duration.
5For rate or market shocks, calculate the change in assets and the change in liabilities separately, then net them.
6Link the result to the sponsor: a deficit is a debt-like claim, it may need cash contributions, and it matters most if the sponsor is weak.
7If a guarantee fund is mentioned, state its role: it covers benefits up to limits when a sponsor fails, and it raises moral hazard.

Quickest way: Duration gap shortcut

When to use it: Use it when a question gives a rate move and asks about the change in funded status or surplus.

Write the asset and liability values.
Multiply each by its duration and by the rate change to get ΔA and ΔL.
Remember that a fall in rates raises both, but liabilities usually rise more when assets are short-duration or equity-heavy.
Surplus change = ΔA − ΔL. Pick the option with the right sign and size.

Common mistakes in Pension Plan Funding, Liabilities and Sponsor Risk

Discounting liabilities at the expected return on plan assets.
It feels natural to use the return the plan hopes to earn.
Fix: Discount at a rate matching the risk of the promise, typically a high-quality corporate bond yield. A high asset return assumption understates liabilities.
Thinking a rate fall helps the plan because bond assets rise.
Students look only at the asset side.
Fix: Liabilities have long duration and rise more than typical assets. Always compute both sides.
Treating funded status as assets divided by liabilities.
Funded ratio and funded status are confused.
Fix: Status is a currency amount (A − L). Ratio is A ÷ L.
Applying pension funding risk to defined contribution plans.
Both are called pension plans.
Fix: In a DC plan the employee bears investment risk and there is no promised benefit to fund.
Assuming the guarantee fund removes all loss for members.
The word guarantee sounds absolute.
Fix: Guarantees are capped by legal limits and funded by sponsor premiums. They also create moral hazard.
Ignoring non-rate drivers of liabilities.
Questions focus on discounting.
Fix: Salary growth, inflation indexation and longevity also raise the PV of liabilities.

Worked examples

Example 1

A DB plan has assets of $850 million and the present value of liabilities is $1,000 million. Find the funded status and funded ratio. If the discount rate falls and liabilities rise by 8%, assets are unchanged, what is the new funded ratio?

Show the solution

Funded status = 850 − 1,000 = −$150 million, so the plan is underfunded.
Funded ratio = 850 ÷ 1,000 = 0.85, or 85%.
New liabilities = 1,000 × 1.08 = $1,080 million.
New funded ratio = 850 ÷ 1,080 = 0.787, or about 78.7%.
New funded status = 850 − 1,080 = −$230 million.

Answer: Funded status is −$150 million with a ratio of 85%. After the rate fall the ratio is about 78.7% and the deficit is $230 million.

Example 2

A plan has assets of $2,000 million with duration 5 and liabilities of $2,000 million with duration 15. Rates fall by 50 basis points across the curve. Ignoring convexity, what is the change in surplus?

Show the solution

Change in assets ≈ +D × A × |Δr| = 5 × 2,000 × 0.005 = +$50 million.
Change in liabilities ≈ +15 × 2,000 × 0.005 = +$150 million.
Change in surplus = ΔA − ΔL = 50 − 150 = −$100 million.
Surplus was zero, so the plan moves to a deficit of $100 million.

Answer: Surplus falls by about $100 million, leaving a deficit of about $100 million, because liability duration exceeds asset duration.

Exam tips

Expect conceptual questions on why falling rates hurt DB plans. Always reason with duration on both sides.
If the question names the discount rate convention, use it. If not, assume a high-quality corporate bond yield.
Link underfunding to sponsor credit risk and to the PBGC role, including moral hazard.
Do the arithmetic with care on ratio versus amount. Check the sign of your answer.

Practice questions from Insurance Companies and Pension Plans

Pension Plan Funding, Liabilities and Sponsor Risk: frequently asked questions

How are pension liabilities discounted?

Expected future benefit payments are discounted to present value. A high-quality corporate bond yield is the common rate, since the promise is fairly safe. A lower rate gives a larger liability.

Why does a fall in interest rates hurt a pension plan?

Liabilities are long-dated and have high duration, so their present value rises sharply. Assets, especially equities or short bonds, usually rise less. The deficit widens.

What does the Pension Benefit Guaranty Corporation do?

It is the US agency that insures private defined benefit plans. If a sponsor fails with an underfunded plan, it takes over the plan and pays benefits up to legal limits. Sponsors pay premiums for this cover.

What is the risk to the sponsoring company of an underfunded plan?

The deficit acts like debt. The company may have to make extra cash contributions, report lower earnings and suffer weaker credit quality. The risk is greatest when the sponsor is already financially weak.