Pension and OPEB Sensitivity Analysis: Stress-Testing Hidden Duration

Key Takeaways

• Turn footnote inputs into a sensitivity table by using liability duration to translate discount rate moves into percent and dollar changes in projected benefit obligation.
• Estimate liability duration from either actuarial disclosures or a cashflow reconstruction to convert rate shocks into balance sheet impact and funded ratio changes.
• Project cash contributions by combining service cost, interest cost, expected return on assets, and assumed contribution policy to model future funding drains.
• Run scenario matrices for discount rate, asset return, and mortality shocks to capture hidden leverage and one-time actuarial losses that drive contributions.
• Compare scenarios for 100 basis point and 300 basis point shocks, and quantify impact on free cash flow, covenant ratios, and recapitalization needs.
• Use sensitivity outputs to stress-test companies with large pension or OPEB exposure, such as $BA or $PG, and embed results into valuation or credit models.

Introduction

Pension and OPEB sensitivity analysis is the process of converting the assumptions described in a company's footnotes into quantitative scenarios that show how liabilities and employer cash contributions change when key assumptions move. This matters because pension and OPEB plans often contain hidden duration and leverage that can crystallize as large balance sheet swings or cash drains under stressed conditions.

You'll learn how to read actuarial footnotes, estimate liability duration, build a sensitivity table for discount rate changes, and project expected employer contributions across scenarios. I will show you practical calculations, templates, and a worked example so you can replicate this in your models.

By the end you'll be able to answer questions like, what happens to the funded ratio if rates fall 100 basis points, or how much additional cash contribution might a company need if asset returns underperform for three years. Ready to quantify the risk under the hood?

1) Reading Pension and OPEB Footnotes: Key inputs and where to find them

Start with the plan footnote, usually labeled pensions and postretirement benefits. Extract the projected benefit obligation or accrued benefit obligation, plan assets at fair value, the discount rate, expected long term return on plan assets, service cost, interest cost, employer contributions, and demographic assumptions such as mortality and turnover.

Commonly reported items you'll need include PBO or ABO, fair value of assets, net periodic benefit cost split into service cost and interest cost, and a reconciliation of the beginning and ending obligations that shows actuarial gains and losses. For OPEB, benefits are often smaller but discount rate sensitivity and pay-as-you-go cash needs can be material.

Footnotes sometimes disclose a sensitivity to 1 percentage point change. If they do, that number provides a check. If not, you'll build your own sensitivity using duration approximations and cashflow reconstructions.

2) Estimating Liability Duration and Sensitivity

Duration is the key link between interest rate moves and liability changes. Liability duration measures the weighted average time until plan benefits are paid and can be approximated without full cashflows. Once you have duration, a small change in discount rate translates into a percentage change in liability using the modified duration formula.

Simple duration approximation

If actuarial cashflows are not disclosed, use plan age profile and average participant age to estimate duration. Typical corporate pension durations range from 8 to 18 years. Mature plans with many retirees have longer durations near 12 to 16 years. Younger plans skew shorter.

Modified duration rule of thumb

Approximate percentage change in liability = -Duration * change in rates in decimal form. For example, if Duration = 12 and rates fall 1 percentage point or 0.01, liability increases about 12%.

This linear approximation is reliable for small shocks. For larger moves apply a convexity correction or reprice cashflows using present value calculations. Convexity typically reduces the true increase slightly versus the linear estimate.

3) Building a Discount Rate Sensitivity Table

Create a matrix that shows liability, plan assets, funded ratio, and net liability under a range of discount rate scenarios. Use baseline PBO and assets from the balance sheet and apply the duration-based percent change to the PBO for each rate move.

1. Record baseline PBO, assets, funded ratio, and net liability.
2. Choose rate shocks: for example -300 bps, -100 bps, baseline, +100 bps.
3. For each shock compute percent change in PBO = -Duration * delta rate. Then compute new PBO = baseline PBO * (1 + percent change).
4. Assume plan assets move with market values. For short run stress you can keep assets constant or apply the same rate shock to asset discount yields which may change fair value.
5. Compute new funded ratio and net liability = new PBO - new assets.

Example sensitivity outputs should include absolute dollar changes and percent changes so you can see both balance sheet and relative funded status impact.

4) Projecting Employer Cash Contributions

Contributions are driven by the employer's funding policy plus actuarial service cost and interest cost less expected return on assets. In many cases companies set contributions to meet regulatory minimums or to close funding gaps over time. Model the mechanics explicitly.

Core projection formula

Estimated Employer Contribution in year t = Targeted contribution policy amount plus any additional catch-up required by funding rules. A simplified projection uses.

• Start with beginning of year net liability
• Add service cost and interest cost
• Subtract expected return on assets
• Adjust for assumed employer contribution policy and regulatory minimums

Interest cost = beginning PBO * discount rate. Expected return = beginning assets * expected long term return assumption. Service cost is provided in the footnote and usually escalates with salary growth. If a company targets steady funded ratio improvement, include a planned catch-up payment each year equal to a percentage of the shortfall.

Real-World Example: Hypothetical $BA-style Plan

Assume a company reports PBO 20 billion, plan assets 15 billion, so net liability 5 billion and funded ratio 75 percent. Discount rate is 4.5 percent, expected asset return 6.0 percent, service cost 0.6 billion, and employer cash contributions last fiscal year were 0.4 billion. You estimate liability duration of 12 years.

Shock: rates fall 100 basis points to 3.5 percent. Percent change in PBO ≈ -Duration * delta rate = -12 * -0.01 = +12 percent. New PBO = 20bn * 1.12 = 22.4bn. Plan assets if unchanged stay 15bn. New funded ratio = 15 / 22.4 = 67 percent. Net liability = 7.4bn, a 48 percent rise from 5bn.

Now project contributions for year 1. Interest cost = beginning PBO * discount rate = 20bn * 4.5% = 0.9bn. Expected return = 15bn * 6% = 0.9bn. Net interest on liability after expected return is neutral in this simplified case. Service cost is 0.6bn. If the sponsor decides to make a catch-up payment to improve funded ratio by 2 percent of PBO, that is roughly 0.4bn to 0.45bn extra. Under the rate shock the sponsor faces a larger shortfall and may choose a 1bn catch-up, raising total contributions to 1.6bn from 0.4bn previously.

This example shows how a 100 basis point decline can change contributions materially and how you should model both the one-time actuarial loss and the multi-year cash contribution response.

5) Modeling Multiple Scenarios and Mortality Sensitivity

Discount rate and asset return are the dominant variables. Mortality improvements and other demographic changes are second order but still schedule risk. A shift to slower mortality improvements increases liabilities because benefits are expected to be paid longer.

To include mortality, use the footnote's sensitivity if disclosed. If not, a rough rule is that a standard longevity improvement shock of 10 percent more life expectancy might increase liabilities 1 to 3 percent depending on plan demographics. Combine this with rate shocks using additive or multiplicative adjustments to liability totals.

Run scenario matrices, for example:

• Base case: reported assumptions
• Adverse rates: -100 bps to discount rate and -200 bps to expected return for 3 years
• Severe stress: -300 bps discount rate, -300 bps expected return, mortality worse by 5 percent

For each scenario report projected PBO, assets under return assumptions, funded ratio, net liability, and cash contributions for 3 to 5 years. This gives you a time path of both balance sheet and cash drain.

Common Mistakes to Avoid

• Using duration without checking plan maturity. How to avoid it: verify duration against disclosed age and pension payment profiles or run a simple cashflow reconstruction.
• Keeping assets fixed in multi-year projections. How to avoid it: project asset returns under scenario assumptions and apply market-to-market effects if you model fair value changes.
• Ignoring employer contribution policy or regulatory minimums. How to avoid it: read the footnote for contribution guidance and incorporate company stated policy into the cash model.
• Failing to include convexity for large rate moves. How to avoid it: apply a convexity adjustment or reprice cashflows for shocks larger than 100 basis points.
• Overlooking OPEB pay-as-you-go cash drains. How to avoid it: model explicit cash outflows for OPEB in each year instead of folding them into a single liability number.

FAQ

Q: How accurate is the duration approximation for pension liabilities?

A: Duration is a simple and useful first-order tool. It works well for small rate moves, especially under 100 basis points. For larger shocks you should reconstruct cashflows and price them exactly to capture convexity. Use any disclosed sensitivity as a cross-check.

Q: Should I adjust plan assets when discount rates change?

A: Yes, if you are projecting beyond a single reporting date you should project asset market returns and mark-to-market. In a short-term sensitivity you can hold assets constant to isolate liability effects but be explicit about that assumption.

Q: How do mortality assumption changes compare to discount rate shifts in magnitude?

A: Mortality shifts are usually a second-order effect. A modest longevity improvement might move liabilities by 1 to 3 percent, while a 100 basis point discount rate move often shifts liabilities 8 to 15 percent depending on duration.

Q: Where do I find the actuarial assumptions I need in filings?

A: Look in the pension and postretirement footnotes of the annual report. Key sections include the reconciliation of benefit obligation, the net periodic benefit cost table, and a section labeled actuarial assumptions where discount rate, expected return, salary growth, and mortality tables are listed.

Bottom Line

Pension and OPEB sensitivity analysis is a high-impact exercise that turns qualitative footnote assumptions into quantitative scenarios you can use in valuation and credit work. You should estimate liability duration, build a discount rate sensitivity table, and project cash contributions under plausible scenarios.

Start by extracting PBO, assets, discount rate, expected return, and service cost from the footnote. Then estimate duration and run scenario matrices that combine rate moves, asset underperformance, and mortality shocks. Use the outputs to measure hidden leverage and to stress-test free cash flow and covenant headroom. At the end of the day these analyses help you quantify funding risk and make better informed investment and risk decisions.