A pension fund immunizes a portfolio against an 8-year liability by matching duration to 8 years. Interest rates immediately rise by 2%. What happens to the fund's ability to meet its obligation at year 8?
AThe portfolio market value falls, and the fund will be short at year 8
BThe portfolio market value rises because higher yields increase bond attractiveness
CThe portfolio market value falls, but coupon reinvestment earns more — at the 8-year horizon the two effects approximately offset, leaving terminal value intact
DNothing changes immediately; the impact of rate changes only materializes at maturity
This is the central mechanism of immunization. Higher rates reduce the current market value of the bonds (price effect, via duration) but increase the rate at which coupon cash flows compound when reinvested (reinvestment effect). At a horizon equal to the portfolio's duration, these opposing effects exactly cancel for small parallel rate shifts. The fund's terminal value at year 8 is approximately preserved — that is what 'immunized' means.
Question 2 Multiple Choice
Which of the following statements about immunization is TRUE?
AOnce duration is matched to the liability horizon, no further rebalancing is needed
BDuration matching protects against any yield curve movement, including large nonparallel twists
CA zero-coupon bond maturing exactly at the liability horizon is the simplest immunizing instrument because its duration equals its maturity
DImmunization requires equating the convexity of assets and liabilities but not necessarily duration
A zero-coupon bond has no coupon reinvestment risk — the only cash flow is at maturity — so its duration equals its maturity exactly, and it immunizes perfectly against rate shifts for a single-liability horizon. The other options are false: immunization requires ongoing rebalancing as duration drifts with time and rate changes; duration matching only protects against small parallel shifts (convexity matters for large moves); and duration, not just convexity, must be matched.
Question 3 True / False
A duration-matched portfolio is protected against most interest rate movements, including large rate swings and nonparallel yield curve shifts.
TTrue
FFalse
Answer: False
Duration matching is a first-order (linear) approximation of price sensitivity. It protects against small, parallel shifts in the yield curve. For large rate moves, convexity — the curvature of the price-yield relationship — becomes significant and duration alone is insufficient. For nonparallel shifts (e.g., short rates rise while long rates fall), matching overall duration is not enough; you must match the duration distribution across maturities. Higher-order immunization addresses both issues.
Question 4 True / False
When interest rates rise, the price of a bond portfolio falls, but coupon reinvestment income increases — and these two effects offset each other at the duration horizon.
TTrue
FFalse
Answer: True
This is the fundamental insight behind immunization. Price and reinvestment effects move in opposite directions: a rate increase hurts current portfolio value but benefits future compounding of cash flows. Duration is precisely the time horizon at which these two effects are equal in magnitude and opposite in sign. This is not a coincidence — it is the definition of duration as the weighted average time to receive cash flows.
Question 5 Short Answer
Why does matching a portfolio's duration to the investment horizon protect against parallel yield curve shifts? Explain the two opposing effects and why they cancel at the duration horizon.
Think about your answer, then reveal below.
Model answer: Interest rate changes affect a bond portfolio in two opposing ways: the price effect (higher rates reduce present values, lowering portfolio market value) and the reinvestment effect (higher rates allow coupon payments to compound faster, increasing accumulated income). Duration measures the portfolio's price sensitivity to rate changes. At a holding period equal to duration, the capital loss from higher rates is exactly offset by the additional reinvestment income accumulated by that date — and vice versa for rate decreases. Duration is the 'balance point' where these effects cancel, making the terminal value insensitive to small parallel rate shifts.
The intuition is that short-duration assets are reinvestment-sensitive (lots of near-term coupons to reinvest) while long-duration assets are price-sensitive (distant cash flows discount heavily with rate changes). Matching duration to horizon balances these sensitivities so neither effect dominates at the target date.