How do I duration-match for a single future liability?

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AcadiFi · Accepted Answer

Duration-matching a single liability (a single outflow at a future date) is the cleanest immunization case. Steps: Step 1: DEFINE THE LIABILITY. $5M due in 6 years. Current risk-free yield for 6-year zeros: 4.5%. PV of liability = $5M / 1.045⁶ = $3.842M. This is the minimum you must invest. Step 2: SELECT BOND UNIVERSE. Pick investment-grade bonds with sufficient maturity dispersion. Step 3: BUILD PORTFOLIO WITH DURATION = 6.0. Step 4: ENSURE CONVEXITY >= LIABILITY CONVEXITY. A bullet (single 6-year bond) has convexity ≈ 42, close to the liability's ≈ 42. A barbell (mix of short + long) has higher convexity but more structural risk under twists. Aim for BULLET or slight bullet-leaning. Step 5: CHECK PV SUFFICIENCY. PV of assets >= $3.842M. Step 6: REBALANCE. Concrete example: Coralglen Foundation has the $5M / 6-year liability. It buys $3.90M face of Harborfern Corp 5.2% coupon bond maturing in 7.5 years, priced at 99.5 (YTM 5.3%), Macaulay duration 6.4. Too long. Adds $0.25M of 2-year Treasury at duration 1.9. Weighted average duration = (3.88/4.13)·6.4 + (0.25/4.13)·1.9 ≈ 6.13. Close to 6.0 but slightly long — swap into a bit more of the 2-year to get to exactly 6.0. Rebalancing: after 1 year, liability horizon falls to 5.0. But portfolio duration (due to aging bonds) falls less — maybe to 5.4. Must sell some long bonds and add short ones to realign. Rebalance quarterly or when duration gap exceeds 0.25 years. ```mermaid flowchart TD A[Liability 6yr] --> B[Build Port
D=6] B --> C[Convexity check] C --> D[Rebalance
quarterly] D --> E[Horizon] ``` Risk: non-parallel shifts and credit events can still create shortfalls. Conservative approach: 103-105% funded and high-quality bonds only.

How do I duration-match for a single future liability?

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