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Home / Financial Tools / Pension Funding Stress-Test & Longevity/Discount-Rate Risk Simulator

Graduate-Level Modeling · Actuarial & Pension ALM

Pension Funding Stress-Test & Longevity/Discount-Rate Risk Simulator

A pension plan's biggest risk usually isn't the market crashing. It's rates falling at the same time, inflating the liability just as the assets are getting hit too.

How To Use This Model

Reading This Tool

Enter the plan's assets and liability, split assets between growth and fixed income, and set liability duration and asset duration.

Then stress discount rates, equity markets and longevity assumptions together, the combined-shock scenario every pension actuary actually has to plan around, and see whether the plan's funded status holds up or breaks.

Baseline Plan Position

Asset Allocation & Hedging

Stress Scenario

Fixed income assets move opposite the discount rate shock at their own duration, exactly like the liability, this is the mechanism behind liability-driven investing (LDI): the closer fixed income duration sits to liability duration, the more rate risk cancels out.

Stressed Funded Status

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Stressed Funded Ratio

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Stressed Assets

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Stressed PBO

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Surplus / (Deficit)

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Funded Ratio Across A Range Of Rate Shocks (Current Equity Shock Held Fixed)

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Why Falling Rates Are A Pension Plan's Silent Enemy

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The Duration-Matching Logic Behind LDI

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Why A Single Extra Year Of Life Expectancy Matters So Much

A defined benefit promise is paid for as long as the retiree lives, so any systematic increase in life expectancy across the whole membership compounds across every future payment. That's why even a seemingly small longevity assumption change can move the liability by a meaningfully larger percentage than the assumption change itself.

Funded Ratio Grid: Rate Shock × Equity Shock

Actuarial & Pension ALM Stress Testing

The Core Formulas

Stressed PBO = PBO × (1 − Liability Duration × ΔRate) × (1 + Longevity Years × 3.5%)
Stressed Fixed Income Assets = FI Assets × (1 − FI Duration × ΔRate)
Stressed Equity Assets = Equity Assets × (1 + Equity Shock)
Stressed Funded Ratio = Stressed Assets / Stressed PBO

When To Actually Use This Model

  • Teaching pension asset-liability management and the rationale for liability-driven investing in an actuarial science or pension finance course.
  • Building board-level intuition for why a plan's funded status can swing sharply even when nothing "went wrong" operationally, rates and markets moved.
  • Illustrating the combined, correlated nature of real stress scenarios, rates and equities often move together in a crisis, not independently.

Key Assumptions & Limitations

  • Uses linear duration approximations for both assets and liabilities, ignoring convexity, which understates the impact of very large rate moves in either direction.
  • The 3.5% PBO increase per extra year of life expectancy is an illustrative rule of thumb, the real sensitivity depends heavily on the plan's specific age and benefit distribution.
  • A real actuarial valuation revalues the liability cash flow by cash flow against a full yield curve, rather than applying a single duration multiplier to a single PBO figure.

Foundational Reference

CPA Canada Handbook, Section 3462, Employee Future Benefits. Society of Actuaries research on liability-driven investment strategies for defined benefit pension plans.

Need the periodic pension cost expense mechanics too?

Open The Net Periodic Pension Cost Model →