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Difficulty: Very hardDebt Securities and Bond Structure

An investor is comparing two investment-grade corporate bonds that both mature in 15 years. Bond X is a zero-coupon bond, whereas Bond Y pays a 7% annual coupon. If prevailing market interest rates decline by 150 basis points across all maturities, which of the following best describes the relative price response and structural interest rate risk of these two bonds?

  1. Bond X will experience a larger percentage price appreciation than Bond Y because bonds with lower coupon rates have higher duration and greater price sensitivity to interest rate changes.Answer
  2. B
    Bond Y will experience a larger percentage price appreciation than Bond X because its periodic cash flows can immediately be reinvested at higher effective yields during rate declines.
  3. C
    Both bonds will experience an identical percentage price increase because interest rate sensitivity depends exclusively on maturity length and credit quality.
  4. D
    Bond X will decrease in market value while Bond Y increases in market value because zero-coupon bond prices move inversely to interest rate shifts while coupon bond prices move directly with interest rates.

Answer

Bond X will experience a larger percentage price appreciation than Bond Y because bonds with lower coupon rates have higher duration and greater price sensitivity to interest rate changes.
Bond price volatility (interest rate risk) is inversely related to coupon rate. Because Bond X is a zero-coupon bond, its payment stream is concentrated entirely at maturity, giving it the maximum possible duration for a 15-year bond. Bond Y returns capital earlier via annual coupon payments, which lowers its duration. Consequently, when market interest rates fall, the price of Bond X increases by a larger percentage than the price of Bond Y.

Step-by-Step Solution

1
Analyze the general relationship between interest rates and bond prices.
Bond prices move inversely to market interest rates. When rates fall by 150 basis points, the market value of both bonds increases.
Existing bond yields must adjust to match lower prevailing market rates, driving secondary market prices up.
2
Evaluate the structural impact of coupon rate on duration and interest rate risk.
A zero-coupon bond (Bond X) pays no cash flows prior to maturity, so its full payment occurs at maturity, maximizing its duration. Bond Y pays annual coupons, returning cash flow earlier and shortening its duration.
Duration measures price sensitivity to rate movements; lower coupon rates yield higher duration for equivalent maturities.
3
Compare the expected percentage price appreciation between the two bonds.
Because Bond X has a higher duration than Bond Y, a 150 basis point rate decline causes a larger percentage price increase in Bond X.
Higher duration directly translates to greater volatility and percentage price movement for a given change in yields.

Key Concept

Bond Duration and Coupon-Price Volatility Relationship
Estimated Time:1m 40s
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Topics

Debt Securities and Bond Structure

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