Duration

Q: Olivia, a bond portfolio manager, expects interest rates to rise significantly over the next 12 months. She currently holds four corporate bonds with similar credit ratings and wants to minimize potential price declines. Which bond should she favor in her portfolio to reduce interest rate risk?

**D is correct.** When expecting rising interest rates, investors should shorten portfolio duration to minimize price declines. The 5-year bond with 8% coupon has the shortest duration (4.3 years), meaning it will experience the smallest percentage price decline if rates rise. For every 1% increase in yields, this bond would lose approximately 4.3% of its value. A (duration 16.8 years) would suffer the largest price decline, losing approximately 16.8% for each 1% rate increase. B (duration 10.2 years) has intermediate risk, losing approximately 10.2% per 1% rate increase. C (zero-coupon with 10-year duration) would lose approximately 10% per 1% rate increase and lacks the cash flow cushion from coupon payments that helps reduce volatility.

Q: Which statement about duration is accurate?

**C is correct.** For coupon-paying bonds, duration is always shorter than maturity because interim coupon payments reduce the weighted average time to receive cash flows. Only zero-coupon bonds have duration equal to maturity since all cash flow occurs at maturity. A is incorrect because duration equals maturity only for zero-coupon bonds, not all bonds. B is incorrect; higher coupon rates result in SHORTER duration (inverse relationship) because more cash is returned earlier through coupon payments. D is incorrect; duration measures price sensitivity to interest rate changes (risk measure), not total return.

Q: A corporate bond has a modified duration of 8.5 years. If market yields increase by 0.75%, what is the approximate percentage change in the bond's price?

**A is correct.** Calculate using the formula: Price Change ≈ -Modified Duration × Yield Change. Price Change ≈ -8.5 × 0.75% = -6.375%. The negative sign indicates a price decline, which is expected when yields rise (inverse relationship). B incorrectly shows a price increase; when yields rise, bond prices fall, not rise. C (11.33%) incorrectly divides duration by yield change (8.5 ÷ 0.75) instead of multiplying. D (8.50%) uses only the duration without multiplying by the 0.75% yield change. Remember: modified duration directly estimates the percentage price change, with the negative sign indicating the inverse relationship between price and yield.

Q: All of the following statements about bond duration are accurate **EXCEPT**

**C is correct (the EXCEPT answer).** Duration does NOT increase as bond yields increase; in fact, duration DECREASES as yields rise. Higher yields mean faster payback through the yield component, which shortens the effective maturity (duration). This is an inverse relationship. A is accurate: longer maturity bonds generally have longer duration because cash flows are spread further into the future. B is accurate: higher coupon rates return more cash earlier, reducing the weighted average time to receive cash flows and shortening duration. D is accurate: zero-coupon bonds have no interim cash flows, so all return comes at maturity, making duration exactly equal to maturity.

Q: An investor is comparing four bonds with the same 15-year maturity and similar credit quality. Which of the following statements about these bonds are accurate? 1. A zero-coupon bond will have duration equal to 15 years 2. A bond with a 10% coupon will have longer duration than a bond with a 5% coupon 3. The bond with the highest duration will experience the greatest percentage price change if interest rates change 4. All four bonds will have the same duration since they have the same maturity

**B is correct.** Statements 1 and 3 are accurate. Statement 1 is TRUE: Zero-coupon bonds have duration equal to maturity because all cash flow occurs at maturity. A 15-year zero-coupon bond has a duration of exactly 15 years. Statement 2 is FALSE: A bond with a 10% coupon will have SHORTER duration than a bond with a 5% coupon, not longer. Higher coupon rates mean more cash is returned earlier, reducing the weighted average time to receive cash flows. This is an inverse relationship. Statement 3 is TRUE: Duration directly measures price sensitivity to interest rate changes. The bond with highest duration will experience the greatest percentage price change (modified duration estimates this change). Statement 4 is FALSE: Bonds with the same maturity have different durations based on their coupon rates. Only zero-coupon bonds have duration equal to maturity; coupon-paying bonds always have duration shorter than maturity, with the amount depending on the coupon rate.

Investment Vehicles High Relevance

A measure of a bond's price sensitivity to interest rate changes, expressed in years. Macaulay duration measures the weighted average time to receive all cash flows, while modified duration measures the approximate percentage price change for a 1% change in yield. Duration increases with longer maturity and decreases with higher coupon rates. For zero-coupon bonds, duration equals maturity; for coupon-paying bonds, duration is always shorter than maturity.

Example

A 10-year Treasury bond with a 6% coupon has a modified duration of approximately 7.4 years. If interest rates rise 1%, the bond's price will fall approximately 7.4%. A zero-coupon bond maturing in 10 years has a duration of exactly 10 years, making it more price-sensitive than the coupon bond with the same maturity.

Common Confusion

Students often confuse duration with maturity (they are different except for zero-coupon bonds), forget that higher coupon rates shorten duration (inverse relationship), or miss that modified duration directly estimates percentage price changes while Macaulay duration measures time.

How This Is Tested

Comparing bonds to identify which has the longest duration based on coupon rates and maturities
Understanding that modified duration estimates percentage price change for a 1% yield change
Recognizing that zero-coupon bonds have duration equal to maturity
Identifying that higher coupon rates result in shorter duration (inverse relationship)
Using duration to assess which bond has greater interest rate risk and price volatility

Example Exam Questions

Test your understanding with these practice questions. Select an answer to see the explanation.

Question 1

Olivia, a bond portfolio manager, expects interest rates to rise significantly over the next 12 months. She currently holds four corporate bonds with similar credit ratings and wants to minimize potential price declines. Which bond should she favor in her portfolio to reduce interest rate risk?

Question 2

Which statement about duration is accurate?

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Question 3

A corporate bond has a modified duration of 8.5 years. If market yields increase by 0.75%, what is the approximate percentage change in the bond's price?

Question 4

All of the following statements about bond duration are accurate EXCEPT

Question 5

An investor is comparing four bonds with the same 15-year maturity and similar credit quality. Which of the following statements about these bonds are accurate?

1. A zero-coupon bond will have duration equal to 15 years
2. A bond with a 10% coupon will have longer duration than a bond with a 5% coupon
3. The bond with the highest duration will experience the greatest percentage price change if interest rates change
4. All four bonds will have the same duration since they have the same maturity

💡 Memory Aid

Think of duration as how long your money is tied up on average. Higher coupons = Cash back faster = shorter duration. Zero-coupon bonds = All cash at the end = duration equals maturity. Modified duration = Price swing percentage: 8 years duration = approximately 8% price change for each 1% rate move. Remember: "Duration Down when Coupons go UP" (inverse relationship).