Finance Quiz: Duration And Price Sensitivity
20 questions · exam conditions
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Duration And Price SensitivityQuestion 1 of 20

A consol bond, which is a type of perpetuity, pays a fixed coupon forever. If such a bond has a yield to maturity of 5%, its Macaulay duration is closest to:

20.0 years.
21.0 years.
25.0 years.
infinity, as the bond never matures.
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Finance Quiz

Finance Quiz: Duration And Price Sensitivity

Practice Duration And Price Sensitivity in Finance with focused quiz questions that help you check what you know, review explanations, and build confidence with test-style prompts.

What this quiz covers

This quiz focuses on Duration And Price Sensitivity, giving you a quick way to practice the rules, question types, and explanations that matter most for Finance.

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Try each quiz question before looking at the correct answer. Use the explanations to review missed ideas, then come back to similar questions until the pattern feels familiar.

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Question 1

A consol bond, which is a type of perpetuity, pays a fixed coupon forever. If such a bond has a yield to maturity of 5%, its Macaulay duration is closest to:

  1. 20.0 years.
  2. 21.0 years. (correct answer)
  3. 25.0 years.
  4. infinity, as the bond never matures.
Explanation: The formula for the Macaulay duration of a perpetuity is DMac=(1+y)/yD_{Mac} = (1 + y) / y, where y is the yield to maturity. Given y = 5% or 0.05: DMac=(1+0.05)/0.05=1.05/0.05=21D_{Mac} = (1 + 0.05) / 0.05 = 1.05 / 0.05 = 21 years. The modified duration would be 1/y=1/0.05=201 / y = 1 / 0.05 = 20 years, a common incorrect choice.

Question 2

A bond with a current market price of $980.00 has a modified duration of 8.2. If the bond's yield to maturity increases by 30 basis points, its new price will be closest to:

  1. $955.71 (correct answer)
  2. $977.54
  3. $1,004.29
  4. $950.00
Explanation: The formula for estimating the percentage price change of a bond using modified duration is: %ΔP≈−Dmod×Δy\% \Delta P \approx -D_{mod} \times \Delta y. First, calculate the estimated percentage price change: %ΔP≈−8.2×0.0030=−0.0246\% \Delta P \approx -8.2 \times 0.0030 = -0.0246 or -2.46%. Next, calculate the dollar price change: \Delta P = -0.0246 \times \980.00 = -$24.108$. Finally, calculate the new estimated price: New Price = \980.00 - $24.108 = $955.892$. The closest answer is $955.71.

Question 3

A bond with a modified duration of 6.5 is initially priced at $1,050. After a shift in the yield curve, the bond's price falls to $1,029. The change in the bond's yield to maturity was most likely a(n):

  1. decrease of 32 basis points.
  2. increase of 32 basis points. (correct answer)
  3. decrease of 20 basis points.
  4. increase of 20 basis points.
Explanation: First, calculate the actual percentage price change: \% \Delta P = (\1,029 - $1,050) / $1,050 = -$21 / $1,050 = -0.02$ or -2.0%. Next, use the duration formula %ΔP≈−Dmod×Δy\% \Delta P \approx -D_{mod} \times \Delta y to solve for Δy\Delta y: −0.02≈−6.5×Δy-0.02 \approx -6.5 \times \Delta y Δy≈−0.02/−6.5≈+0.003077\Delta y \approx -0.02 / -6.5 \approx +0.003077. Converting this to basis points gives 0.003077×10,000≈30.80.003077 \times 10,000 \approx 30.8 basis points. The closest answer is an increase of 32 basis points.

Question 4

A portfolio manager using duration to estimate price changes for a large interest rate shock finds that the actual price decline was larger than predicted. The portfolio most likely contains a significant concentration of:

  1. zero-coupon bonds.
  2. short-term Treasury bills.
  3. callable corporate bonds. (correct answer)
  4. long-term, non-callable government bonds.
Explanation: The standard duration formula assumes positive convexity, where the linear estimate overstates price declines. If the actual price decline is larger than predicted, it implies negative convexity. Negative convexity is a characteristic of bonds with embedded call options, such as callable corporate bonds or mortgage-backed securities. When rates rise, the value of the call option decreases, exacerbating the bond's price decline.

Question 5

A 5-year, non-callable bond and a 15-year callable bond currently have the same modified duration and the same yield. If the yield curve experiences a large, parallel downward shift, which of the following outcomes is most likely?

  1. The prices of both bonds will increase by approximately the same percentage.
  2. The price of the non-callable bond will increase by more than the price of the callable bond. (correct answer)
  3. The price of the callable bond will increase by more than the price of the non-callable bond.
  4. The price of the non-callable bond will increase, but the price of the callable bond will decrease.
Explanation: While both bonds have the same duration, their convexity will differ. The non-callable bond has positive convexity, meaning its price increase will be slightly larger than predicted by duration. The callable bond will exhibit negative convexity as rates fall, because the increasing likelihood of it being called will cap its price appreciation. Therefore, the non-callable bond will experience a larger price increase than the callable bond.

Question 6

An analyst is comparing two bonds, both with a 10-year maturity and a 6% yield to maturity. Bond X has a 4% coupon, and Bond Z has an 8% coupon. Which statement about their price sensitivity to a 1% change in interest rates is most accurate?

  1. Bond X will have greater price sensitivity because its lower coupon rate results in a higher duration. (correct answer)
  2. Bond Z will have greater price sensitivity because its higher coupon payments are more sensitive to discount rate changes.
  3. Both bonds will have identical price sensitivity because they share the same maturity and yield to maturity.
  4. The relative price sensitivity cannot be determined without knowing if the bonds trade at a premium or discount.
Explanation: For two bonds with the same maturity and yield to maturity, the bond with the lower coupon rate will have a higher duration. A higher duration implies greater price sensitivity to changes in interest rates. Therefore, Bond X, with its 4% coupon, will be more price-sensitive than Bond Z, which has an 8% coupon.

Question 7

A security that exhibits negative convexity is characterized by a price-yield relationship where:

  1. price appreciation for a yield decrease is greater than the price depreciation for a yield increase of the same magnitude.
  2. the security's price is largely insensitive to changes in yield.
  3. the security's duration is negative, causing its price to rise as yields rise.
  4. price appreciation for a yield decrease is smaller than the price depreciation for a yield increase of the same magnitude. (correct answer)
Explanation: When analyzing bond price behavior, convexity measures how the price-yield relationship curves. Most bonds exhibit positive convexity, but some securities like callable bonds can show negative convexity under certain conditions. Negative convexity creates an asymmetric price-yield relationship that works against bondholders. When yields fall, the security's price rises, but not by as much as you'd expect. Conversely, when yields rise by the same magnitude, the price falls by a larger amount. This happens because features like call provisions cap the upside potential - if rates drop significantly, the issuer will likely call the bond, limiting price appreciation. However, there's no corresponding floor when rates rise, so the full price decline occurs. Choice D correctly captures this asymmetric relationship where price gains from yield decreases are smaller than price losses from equivalent yield increases. Choice A describes positive convexity, which is the opposite of what we want. This is the normal, beneficial convexity that most straight bonds exhibit. Choice B describes low duration or interest rate insensitivity, which isn't the same as negative convexity - a security can still be sensitive to rate changes while exhibiting negative convexity. Choice C confuses duration with convexity and incorrectly suggests prices rise with yields, which would violate the fundamental inverse relationship between bond prices and interest rates. Remember that negative convexity is bad for investors because it creates "heads I lose a little, tails I lose a lot" price behavior - always look for the asymmetric relationship that favors larger losses.

Question 8

A portfolio's value is allocated as follows: 40% in a bond with a modified duration of 5.0 and 60% in a bond with a modified duration of 10.0. If yields on both bonds are expected to fall by 50 basis points, what is the estimated percentage increase in the portfolio's value?

  1. 3.75%
  2. 4.00% (correct answer)
  3. 7.50%
  4. 8.00%
Explanation: First, calculate the portfolio's modified duration as the weighted average of the individual bond durations: Dp=(w1×D1)+(w2×D2)D_{p} = (w_1 \times D_1) + (w_2 \times D_2) Dp=(0.40×5.0)+(0.60×10.0)=2.0+6.0=8.0D_{p} = (0.40 \times 5.0) + (0.60 \times 10.0) = 2.0 + 6.0 = 8.0 Next, use the duration formula to estimate the portfolio's percentage price change. Note that a fall in yields leads to a price increase. %ΔP≈−Dp×Δy\% \Delta P \approx -D_{p} \times \Delta y %ΔP≈−8.0×(−0.0050)=+0.040\% \Delta P \approx -8.0 \times (-0.0050) = +0.040, or a 4.00% increase.

Question 9

An investor holds a 10-year, 6% annual coupon bond trading at its par value of $1,000. The bond's Macaulay duration is 7.80 years. If the bond's yield to maturity immediately falls by 1%, what is the approximate new price of the bond based on its duration?

  1. $1,078.00
  2. $922.00
  3. $1,073.58 (correct answer)
  4. $926.42
Explanation: First, since the bond trades at par, its yield to maturity (YTM) equals its coupon rate, so YTM = 6%. We need to convert Macaulay duration to modified duration: DMod=DMac/(1+YTM)=7.80/(1+0.06)=7.80/1.06≈7.3585D_{Mod} = D_{Mac} / (1 + YTM) = 7.80 / (1 + 0.06) = 7.80 / 1.06 \approx 7.3585. Next, calculate the estimated percentage price change for a 1% ( -0.01) fall in yield: %ΔP≈−DMod×Δy=−7.3585×(−0.01)=+0.073585\% \Delta P \approx -D_{Mod} \times \Delta y = -7.3585 \times (-0.01) = +0.073585. Finally, apply this percentage change to the initial price: New Price = \1,000 \times (1 + 0.073585) = $1,073.585$. The closest answer is $1,073.58.

Question 10

A 20-year bond is callable in 5 years. The bond's duration-to-maturity is calculated to be 11.5, and its duration-to-call is 4.2. If an analyst expects interest rates to fall significantly, which duration measure is most relevant for assessing the bond's price sensitivity?

  1. Duration-to-maturity, as it reflects the bond's full contractual cash flows.
  2. The average of the two durations, as it balances both potential outcomes.
  3. Duration-to-call, as the issuer is more likely to call the bond in a lower interest rate environment. (correct answer)
  4. Neither, as the bond's convexity would be a more important measure in this scenario.
Explanation: When interest rates fall, the issuer of a callable bond is more likely to exercise the call option to refinance its debt at the new, lower rates. Therefore, the bond's effective maturity is more likely to be the call date than the final maturity date. In this scenario, the duration-to-call becomes the most relevant measure for assessing the bond's price sensitivity.

Question 11

A portfolio's value is allocated as follows: 40% in a bond with a modified duration of 5.0 and 60% in a bond with a modified duration of 10.0. If yields on both bonds are expected to fall by 50 basis points, what is the estimated percentage increase in the portfolio's value?

  1. 3.75%
  2. 4.00% (correct answer)
  3. 7.50%
  4. 8.00%
Explanation: First, calculate the portfolio's modified duration as the weighted average of the individual bond durations: Dp=(w1×D1)+(w2×D2)D_{p} = (w_1 \times D_1) + (w_2 \times D_2) Dp=(0.40×5.0)+(0.60×10.0)=2.0+6.0=8.0D_{p} = (0.40 \times 5.0) + (0.60 \times 10.0) = 2.0 + 6.0 = 8.0 Next, use the duration formula to estimate the portfolio's percentage price change. Note that a fall in yields leads to a price increase. %ΔP≈−Dp×Δy\% \Delta P \approx -D_{p} \times \Delta y %ΔP≈−8.0×(−0.0050)=+0.040\% \Delta P \approx -8.0 \times (-0.0050) = +0.040, or a 4.00% increase.

Question 12

A bond with a modified duration of 6.5 is initially priced at $1,050. After a shift in the yield curve, the bond's price falls to $1,029. The change in the bond's yield to maturity was most likely a(n):

  1. decrease of 32 basis points.
  2. increase of 32 basis points. (correct answer)
  3. decrease of 20 basis points.
  4. increase of 20 basis points.
Explanation: First, calculate the actual percentage price change: \% \Delta P = (\1,029 - $1,050) / $1,050 = -$21 / $1,050 = -0.02$ or -2.0%. Next, use the duration formula %ΔP≈−Dmod×Δy\% \Delta P \approx -D_{mod} \times \Delta y to solve for Δy\Delta y: −0.02≈−6.5×Δy-0.02 \approx -6.5 \times \Delta y Δy≈−0.02/−6.5≈+0.003077\Delta y \approx -0.02 / -6.5 \approx +0.003077. Converting this to basis points gives 0.003077×10,000≈30.80.003077 \times 10,000 \approx 30.8 basis points. The closest answer is an increase of 32 basis points.

Question 13

A portfolio manager using duration to estimate price changes for a large interest rate shock finds that the actual price decline was larger than predicted. The portfolio most likely contains a significant concentration of:

  1. zero-coupon bonds.
  2. short-term Treasury bills.
  3. callable corporate bonds. (correct answer)
  4. long-term, non-callable government bonds.
Explanation: The standard duration formula assumes positive convexity, where the linear estimate overstates price declines. If the actual price decline is larger than predicted, it implies negative convexity. Negative convexity is a characteristic of bonds with embedded call options, such as callable corporate bonds or mortgage-backed securities. When rates rise, the value of the call option decreases, exacerbating the bond's price decline.

Question 14

An analyst is comparing two bonds, both with a 10-year maturity and a 6% yield to maturity. Bond X has a 4% coupon, and Bond Z has an 8% coupon. Which statement about their price sensitivity to a 1% change in interest rates is most accurate?

  1. Bond X will have greater price sensitivity because its lower coupon rate results in a higher duration. (correct answer)
  2. Bond Z will have greater price sensitivity because its higher coupon payments are more sensitive to discount rate changes.
  3. Both bonds will have identical price sensitivity because they share the same maturity and yield to maturity.
  4. The relative price sensitivity cannot be determined without knowing if the bonds trade at a premium or discount.
Explanation: For two bonds with the same maturity and yield to maturity, the bond with the lower coupon rate will have a higher duration. A higher duration implies greater price sensitivity to changes in interest rates. Therefore, Bond X, with its 4% coupon, will be more price-sensitive than Bond Z, which has an 8% coupon.

Question 15

An investor holds a 10-year, 6% annual coupon bond trading at its par value of $1,000. The bond's Macaulay duration is 7.80 years. If the bond's yield to maturity immediately falls by 1%, what is the approximate new price of the bond based on its duration?

  1. $1,078.00
  2. $922.00
  3. $1,073.58 (correct answer)
  4. $926.42
Explanation: First, since the bond trades at par, its yield to maturity (YTM) equals its coupon rate, so YTM = 6%. We need to convert Macaulay duration to modified duration: DMod=DMac/(1+YTM)=7.80/(1+0.06)=7.80/1.06≈7.3585D_{Mod} = D_{Mac} / (1 + YTM) = 7.80 / (1 + 0.06) = 7.80 / 1.06 \approx 7.3585. Next, calculate the estimated percentage price change for a 1% ( -0.01) fall in yield: %ΔP≈−DMod×Δy=−7.3585×(−0.01)=+0.073585\% \Delta P \approx -D_{Mod} \times \Delta y = -7.3585 \times (-0.01) = +0.073585. Finally, apply this percentage change to the initial price: New Price = \1,000 \times (1 + 0.073585) = $1,073.585$. The closest answer is $1,073.58.

Question 16

A 20-year bond is callable in 5 years. The bond's duration-to-maturity is calculated to be 11.5, and its duration-to-call is 4.2. If an analyst expects interest rates to fall significantly, which duration measure is most relevant for assessing the bond's price sensitivity?

  1. Duration-to-maturity, as it reflects the bond's full contractual cash flows.
  2. The average of the two durations, as it balances both potential outcomes.
  3. Duration-to-call, as the issuer is more likely to call the bond in a lower interest rate environment. (correct answer)
  4. Neither, as the bond's convexity would be a more important measure in this scenario.
Explanation: When interest rates fall, the issuer of a callable bond is more likely to exercise the call option to refinance its debt at the new, lower rates. Therefore, the bond's effective maturity is more likely to be the call date than the final maturity date. In this scenario, the duration-to-call becomes the most relevant measure for assessing the bond's price sensitivity.

Question 17

A 5-year, non-callable bond and a 15-year callable bond currently have the same modified duration and the same yield. If the yield curve experiences a large, parallel downward shift, which of the following outcomes is most likely?

  1. The prices of both bonds will increase by approximately the same percentage.
  2. The price of the non-callable bond will increase by more than the price of the callable bond. (correct answer)
  3. The price of the callable bond will increase by more than the price of the non-callable bond.
  4. The price of the non-callable bond will increase, but the price of the callable bond will decrease.
Explanation: While both bonds have the same duration, their convexity will differ. The non-callable bond has positive convexity, meaning its price increase will be slightly larger than predicted by duration. The callable bond will exhibit negative convexity as rates fall, because the increasing likelihood of it being called will cap its price appreciation. Therefore, the non-callable bond will experience a larger price increase than the callable bond.

Question 18

The table below provides details for three option-free bonds from the same issuer.

Based on the table and assuming all three bonds have the same yield to maturity, which of the following correctly ranks the bonds from most sensitive to least sensitive to a small, parallel shift in the yield curve?

  1. M, L, K (correct answer)
  2. K, L, M
  3. M, K, L
  4. L, M, K
Explanation: Price sensitivity is measured by duration. Holding yield constant:
  1. Duration increases with maturity (coupon held constant). Comparing K (10-yr, 5%) and L (20-yr, 5%), Bond L has a longer maturity, so Duration(L) > Duration(K).
  2. Duration decreases with the coupon rate (maturity held constant). Comparing L (20-yr, 5%) and M (20-yr, 3%), Bond M has a lower coupon, so Duration(M) > Duration(L). Combining these facts gives the ranking from highest duration (most sensitive) to lowest duration (least sensitive) as M > L > K.

Question 19

A security that exhibits negative convexity is characterized by a price-yield relationship where:

  1. price appreciation for a yield decrease is greater than the price depreciation for a yield increase of the same magnitude.
  2. the security's price is largely insensitive to changes in yield.
  3. the security's duration is negative, causing its price to rise as yields rise.
  4. price appreciation for a yield decrease is smaller than the price depreciation for a yield increase of the same magnitude. (correct answer)
Explanation: When analyzing bond price behavior, convexity measures how the price-yield relationship curves. Most bonds exhibit positive convexity, but some securities like callable bonds can show negative convexity under certain conditions. Negative convexity creates an asymmetric price-yield relationship that works against bondholders. When yields fall, the security's price rises, but not by as much as you'd expect. Conversely, when yields rise by the same magnitude, the price falls by a larger amount. This happens because features like call provisions cap the upside potential - if rates drop significantly, the issuer will likely call the bond, limiting price appreciation. However, there's no corresponding floor when rates rise, so the full price decline occurs. Choice D correctly captures this asymmetric relationship where price gains from yield decreases are smaller than price losses from equivalent yield increases. Choice A describes positive convexity, which is the opposite of what we want. This is the normal, beneficial convexity that most straight bonds exhibit. Choice B describes low duration or interest rate insensitivity, which isn't the same as negative convexity - a security can still be sensitive to rate changes while exhibiting negative convexity. Choice C confuses duration with convexity and incorrectly suggests prices rise with yields, which would violate the fundamental inverse relationship between bond prices and interest rates. Remember that negative convexity is bad for investors because it creates "heads I lose a little, tails I lose a lot" price behavior - always look for the asymmetric relationship that favors larger losses.

Question 20

For a conventional, option-free 10-year bond, as its yield to maturity decreases, what is the corresponding impact on its price and modified duration?

  1. Price increases; duration increases. (correct answer)
  2. Price increases; duration decreases.
  3. Price decreases; duration increases.
  4. Price decreases; duration decreases.
Explanation: There is a well-established inverse relationship between a bond's price and its yield to maturity; as yield decreases, price increases. There is also an inverse relationship between a bond's yield to maturity and its duration; as yield decreases, the present value of later cash flows (like the principal) increases relative to earlier cash flows, thus increasing the weighted-average time and thereby the duration.