How does duration matching work for immunizing a liability, and what are the conditions for it to work?

Duration matching (immunization) is a fundamental portfolio management technique. You're right that the concept sounds simple, but proper implementation requires meeting several conditions.

The Core Idea:

When interest rates change, bond portfolios face two opposing effects:

1. Price effect: Rate increases reduce bond prices (bad for the portfolio)
2. Reinvestment effect: Rate increases allow coupons to be reinvested at higher rates (good for the portfolio)

At the duration point, these two effects exactly offset each other. So if your liability is due in exactly the duration-matched period, you're protected.

Classical Immunization Conditions:

Condition 1: Duration Match

The Macaulay duration of the asset portfolio must equal the investment horizon (time until the liability is due).

Condition 2: Present Value Match

The present value of the assets must equal (or exceed) the present value of the liability.

Condition 3: Convexity Minimization

The convexity of the asset portfolio should be minimized (just above the liability's convexity) to reduce exposure to non-parallel yield curve shifts.

Worked Example:

Pacific Pension Fund has a single liability of $12M due in 7 years. Current interest rate: 5%.

PV of liability: $12M / (1.05)^7 = $8.53M

The fund must build a bond portfolio worth at least $8.53M with a Macaulay duration of exactly 7 years.

Option A: Single 7-year zero-coupon bond (perfect match)

Option B: Mix of 3-year and 12-year bonds with portfolio duration = 7 years

Both have duration = 7, but Option A is a perfect immunization (no reinvestment risk, no convexity mismatch). Option B has higher convexity, which introduces risk from non-parallel shifts.

Why Convexity Matters:

Limitations of Classical Immunization:

1. Assumes parallel yield curve shifts — If short rates rise while long rates fall, a barbell portfolio will not be immunized even with correct duration
2. Requires rebalancing — As time passes and rates change, duration drifts and must be re-matched periodically
3. Single liability only — For multiple liabilities, you need cash flow matching or multifunctional duration matching
4. No default risk — Assumes the bonds will pay as promised

Exam Tip: Know all three conditions (duration match, PV match, minimize convexity). A common exam question presents two portfolios with the same duration and asks which is better for immunization — choose the one with lower convexity.

Practice immunization problems in our CFA Level I question bank.