Without doing any math, rank the following bonds in descending order from highest to lowest duration.

1. A bond with a coupon rate of 5% and a maturity of 12 years.
2. A bond with a coupon rate of 7% and a maturity of 12 years.
3. A bond with a coupon rate of 5% and a maturity of 4 years.
4. A bond with a coupon rate of 7% and a maturity of 4 years.

Question

Without doing any math, rank the following bonds in descending order from highest to lowest duration.

1. A bond with a coupon rate of 5% and a maturity of 12 years.
2. A bond with a coupon rate of 7% and a maturity of 12 years.
3. A bond with a coupon rate of 5% and a maturity of 4 years.
4. A bond with a coupon rate of 7% and a maturity of 4 years.

BlackTom AI · Accepted Answer

Question restatement: You need to rank four bonds from highest to lowest duration without performing any calculations. The bonds are: 1) 12-year maturity, 5% coupon; 2) 12-year maturity, 7% coupon; 3) 4-year maturity, 5% coupon; 4) 4-year maturity, 7% coupon.

Key concepts to apply:
- All else equal, longer maturity generally means longer duration.
- For bonds with the same maturity, a higher coupon lowers duration (because more of the present value is in smaller, nearer cash flows).

Now evaluate each option in detail:
Option A: "2, 3, 4, 1". This sequence places the 12-year, 7% bond first. Since it has the same 12-year maturity as bond 1 but a higher coupon, its duration should be shorter than the 12-year, 5% bond. However, placing it ahead of bond 3 (4-year, 5%) and bond 4 (4-year, 7%) ignores the general rule that the longer maturity tends to dominate duration. The result would imply the 12-year, 7% bond has a greater duration than the 4-year bonds, which is inconsistent with standard duration behavior.
Option B: "4, 3, 2, 1". This starts with the 4-year, 7% bond and ends with the 12-year, 5% bond. The order would imply that the 4-year, 7% has the longest duration and the 12-year, 5% has the shortest, which contradicts both the effect of longer maturity and the effect of higher coupon on shortening duration. The culprit is misplacing the 12-year bonds ahead of the 4-year ones in terms of duration despite distinct coupon and maturity interactions.
Option C: "3, 4, 1, 2". Here, the 4-year bonds come first, with 4-year, 5% before 4-year, 7%, suggesting the 4-year, 5% has a longer duration than the 4-year, 7%. While this matches the coupon effect for equal maturities, it still places both 4-year bonds ahead of the 12-year bonds, which is incorrect because the 12-year bonds typically have longer duration than any 4-year bond regardless of coupon. This option undervalues the impact of maturity.
Option D: "1, 2, 3, 4". In this arrangement, the bond with 12-year maturity and 5% coupon leads, followed by the 12-year, 7% bond, then the 4-year, 5% bond, and finally the 4-year, 7% bond. This ordering reflects the intuitive and well-supported rules: the longest-maturity bond (12 years) tends to have the longest duration, and within the same maturity, a lower coupon bond (5%) has a longer duration than a higher coupon bond (7%). Consequently, the 12-year, 5% bond comes before the 12-year, 7% bond, and both of these precede the 4-year bonds, with the 4-year, 5% bond ahead of the 4-year, 7% bond. This aligns with the general duration principles across the four scenarios.

In summary, the reasoning shows how maturity dominates duration across these options, while coupon differences modulate duration within the same maturity. The comparison demonstrates why swapping the positions in Options A, B, or C creates inconsistencies with either the maturity effect or the coupon effect on duration, whereas Option D preserves the expected hierarchy based on both factors.

25751 Financial Institution Management - Spring 2025 Week 5 Quiz

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