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Difficulty: HardDebt Securities and Bond Structure

A financial advisor is evaluating two corporate debt securities issued by the same firm with identical credit ratings and 10-year maturities: Security A is a 1,000parzero−couponbond,whileSecurityBisa1,000 par zero-coupon bond, while Security B is a 1,000 par bond paying a 5% annual coupon. If benchmark market interest rates decrease by 100 basis points across all maturities, which of the following statements correctly describes the relative price response and sensitivity of these two securities?

  1. Security A will experience a greater percentage price increase than Security B because its duration equals its maturity due to the absence of interim coupon payments.Answer
  2. B
    Security B will experience a greater percentage price increase than Security A because annual coupon payments compound the price gain as market rates fall.
  3. C
    Security A will experience a smaller percentage price increase than Security B because zero-coupon bonds carry higher credit risk, offsetting market price appreciation.
  4. D
    Both securities will experience identical percentage price increases because their maturity dates and credit ratings are identical.

Answer

Security A (the zero-coupon bond) will experience a greater percentage price increase than Security B because its duration equals its maturity due to the absence of interim coupon payments.
Zero-coupon bonds carry maximum interest rate sensitivity for a given maturity because all cash flows are deferred until maturity. When interest rates decline, a zero-coupon bond appreciates at a higher percentage rate than a coupon-bearing bond of identical maturity, whose interim coupon payments shorten its duration.

Step-by-Step Solution

1
Analyze the relationship between coupon rate, duration, and price sensitivity.
Lower coupon bonds have longer durations and higher price volatility when interest rates change.
Duration measures a bond's price sensitivity to interest rate movements based on the weighted average time until cash flows are received.
2
Compare the duration of Security A (zero-coupon) and Security B (5% annual coupon).
Security A has a duration of exactly 10 years, whereas Security B has a duration of less than 10 years due to interim annual interest cash flows.
Because zero-coupon bonds pay no interest prior to maturity, 100% of their cash flow occurs at year 10, maximizing duration.
3
Determine the impact of a 100 basis point decline in market interest rates on price.
Bond prices move inversely to interest rates; the security with the longer duration (Security A) will appreciate by a larger percentage.
Percentage price change is approximately equal to negative duration multiplied by the change in yield.

Key Concept

Bond Duration and Price Sensitivity of Zero-Coupon vs. Coupon Bonds
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Topics

Debt Securities and Bond Structure

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