The Bond That Looks Safe Until You Look at Duration
A wealth manager holds a $10 million position in a 30-year, 3.0% coupon corporate bond trading at par (yield 3.0%). The client is nervous about rising rates and asks whether to switch into a 5-year, 4.5% coupon bond also trading near par. The manager argues: 'The 5-year bond has a higher coupon, so it pays more income and is safer.' The client's liability is a single $10 million payment due in 5 years. The 30-year bond has a modified duration of 19.8; the 5-year bond has a modified duration of 4.6. Credit spreads are expected to widen by 50 bps over the next year for both issuers.
1. Evaluate the manager's claim that the 5-year bond is 'safer.' Which bond better matches the client's liability, and why?
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The manager's reasoning is wrong on two counts.
- 'Higher coupon = safer' conflates income with risk. Price risk is driven by duration, not coupon. The 30-year bond has modified duration 19.8 - a 100 bp rise in yield costs roughly 19.8% of price (~$1.98M on $10M). The 5-year bond's duration of 4.6 means
4.6% ($460K). For price volatility, the 5-year is far less exposed. - But the client has a 5-year liability. The correct frame is immunization / duration matching: the portfolio's duration should equal the horizon of the liability. The 5-year bond (duration 4.6 ≈ 5-year horizon) is the natural match; the 30-year bond's duration of 19.8 is wildly mismatched and exposes the client to large price swings exactly when the $10M is due.
Conclusion: The 5-year bond is the better liability match - but for the duration reason, not the coupon reason. The manager reached a defensible conclusion via indefensible logic, which matters because the logic would fail in other cases.
2. How does the expected 50 bp spread widening affect each bond, and does it change the recommendation?
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Spread widening hits both, but asymmetrically:
- 30-year bond: ΔP ≈ −D × Δy × P = −19.8 × 0.005 × $10M ≈ −$990K (≈ −9.9%).
- 5-year bond: ΔP ≈ −4.6 × 0.005 × $10M ≈ −$230K (≈ −2.3%).
The long bond absorbs roughly 4.3x the spread loss. This reinforces the switch: the client cannot afford a ~10% drawdown a year before a fixed $10M obligation.
Does it change the recommendation? No - it strengthens it. But note the nuance: if the client were not liability-driven and instead believed spreads would widen, the analysis would be about relative value and credit quality, not just duration. Here the liability anchor settles it. The manager should also consider that a 5-year bond maturing at the liability date eliminates reinvestment risk entirely, whereas a duration-matched portfolio still carries some.