A pension plan owes $50M in 8 years. A municipal sinking fund owes $10M every year for 20 years. Both face the same question: how should fixed-income assets be structured against known cash outflows? The exam tests whether you can pick the right strategy and explain what breaks it.
Four strategies dominate.
Buy a zero-coupon bond. A zero matching the liability date and amount eliminates reinvestment risk and price risk. If Treasury zeros of the right maturity exist, this is the cleanest hedge. Limit: zeros for very long maturities (20+ years) are scarce and may not match the exact dollar need.
Cash flow matching with coupon bonds. Buy a coupon bond (or strip) whose principal-plus-coupon stream covers the liability. Slightly less precise than a zero but more available.
Duration matching (immunization). Build a portfolio of coupon bonds whose Macaulay duration equals the liability horizon and whose PV equals (or exceeds) the liability PV. Price risk from rate changes offsets reinvestment risk because the two move in opposite directions at the duration horizon.
Common mistakes
- Treating duration matching as sufficient against any rate change. The match is exact only for small parallel shifts at the liability horizon. Trap: assuming a duration match immunizes against curve twists.
- Forgetting convexity minimization. A duration-matched portfolio with excessive convexity has high structural risk under twists. Trap: choosing the highest-convexity barbell when curve twists are the dominant scenario.
- Using a market index as the LDI benchmark. A pension plan should be benchmarked against its liability return, not the Bloomberg Aggregate. Trap: reporting a 4% Aggregate beat while surplus fell 6%.
Bottom line
- Single-liability immunization requires PV assets ≥ PV liability, asset duration (or BPV) matched to the liability, asset convexity ≥ liability convexity, and convexity minimized to cap structural risk
- Single-liability approaches span zero-coupon match (cleanest), duration matching, and contingent immunization (active management until a trigger forces lock-in)
- Multiple-liability strategies use cash flow matching, BPV matching across the curve, or a derivatives overlay (futures, swaps) to adjust duration without trading the cash bonds
- Cash flow matching is curve-shape immune but expensive; duration matching is cheaper but exposed to non-parallel shifts (structural risk), which minimizing convexity reduces
Exam shortcut
If the vignette names a single horizon date and a known dollar amount, the default answer is a zero-coupon match or, when zeros are unavailable, duration matching with minimized convexity. Convexity minimization is the structural-risk hedge. For multiple liabilities, the trade-off is cost vs. curve risk. Cash flow matching wins on curve immunity. Duration matching wins on cost. Derivatives overlay wins on flexibility when the cash book is constrained.
The full lesson (about 2,993 words, 20 min read) adds 2 worked examples, all 6 common mistakes, a self-check, free in the app.
Learning objectives
- ldi strategies
- yield curve strategies
- credit strategies
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