Which of the following bonds will most likely have the largest decrease in price if interest rates increase in Year 1 of the life of the bonds?

Question

BlackTom AI · Accepted Answer

To assess which bond experiences the largest price decrease when interest rates rise in Year 1, we need to compare their price sensitivity, i.e., their duration (and to some extent convexity), given the remaining characteristics of each bond.

Option 1: An option free 11-year 9% coupon bond selling at a discount.
- This bond has a long remaining maturity (11 years) and a relatively high coupon (9%), which tends to lower duration compared with a zero-coupon bond of the same maturity because coupon payments reduce the effect of a rate move over time. However, because it is 11 years out and not zero coupon, its modified duration will still be substantial, but typically not as high as a 10-year zero-coupon bond. Since it is selling at a discount, its yield-to-maturity is higher than its coupon rate, and price sensitivity to rate increases will be pronounced but moderated by the coupon cash flows catching up to maturity.
- In short, this bond has significant duration due to the long horizon, but the presence of coupons reduces its effective duration relative to a pure zero-coupon, making its price drop large but not necessarily the largest among the options.

Option 2: A 10-year 5% coupon bond that is callable at 104 in three years.
- Calls reduce a bond’s effective duration because the issuer can redeem the bond earlier if rates decline or stay favorable for the call. Here, the call at 104 in three years provides an early exercise option that dampens price sensitivity to rate changes beyond that horizon. Moreover, the coupon rate (5%) is moderate, which also lowers duration compared with higher-coupon bonds. So, while there is still interest-rate risk, the call feature and moderate coupon reduce how much price would move for a given rate shift in Year 1.
- Therefore, this bond’s price would typically respond less to an immediate rise in rates than an equivalent non-callable, longer-maturity instrument.

Option 3: A 7-year 4% coupon bond that is puttable after two years.
- The puttable feature provides the holder with a way to sell the bond back to the issuer at a stated price if rates rise, which can cap duration. When rates rise, the investor is more likely to exercise the put, which effectively shortens the horizon over which the bond’s cash flows are exposed to rate changes. The relatively short remaining maturity (7 years) and the low coupon (4%) yield a lower baseline duration, and the put option further reduces sensitivity to rate increases.
- Consequently, this bond tends to have a lower price sensitivity to an immediate rate hike in Year 1 compared with longer, non-puttable instruments.

Option 4: A 10-year zero coupon bond.
- A zero-coupon bond has no interim coupon payments; its entire value comes from the single payment at maturity. Therefore, its duration equals its time to maturity (approximately 10 years here). When rates rise, the present value of that single future payment drops by a larger proportional amount than for bonds with coupons that provide cash flows sooner and hence reduce duration.
- Among the listed options, the 10-year zero-coupon bond typically exhibits the largest duration and thus the largest price decrease in response to an increase in interest rates in Year 1. The lack of coupons means there are no cash flows to cushion the impact of rate changes in the near term, amplifying price sensitivity.

In summary, while the other bonds have features (callability, putability, coupons) that dampen their duration and price reactions to a rate increase, the 10-year zero-coupon bond’s pure, long-duration exposure without any coupon cash flows makes it the most sensitive to higher rates in Year 1.

Which of the following bonds will most likely have the largest decrease in price if interest rates increase in Year 1 of the life of the bonds?

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