A 12-year maturity zero-coupon bond selling at a yield to maturity of 5.25% (effective annual yield) has convexity of 159.9 and modifiedduration of 11.06 years. A 30-year maturity 9.5% coupon bond making annual coupon payments also selling at a yield to maturity of5.25% has nearly identical duration-11.04 years-but considerably higher convexity of 258.4.a. Suppose the yield to maturity on both bonds increases to 6.25 %. What will be the actual percentage capital loss on each bond?What percentage capital loss would be predicted by the duration-with-convexity rule? (Input all amounts as positive values. Do notround Intermediate calculations. Round your answers to 2 decimal places.)ActualPredictedZero Coupon BondCoupon Bond%%%b. Suppose the yield to maturity on both bonds decreases to 4.25%. What will be the actual percentage capital loss on each bond?What percentage capital loss would be predicted by the duration-with-convexity rule? (Input all amounts as positive values. Do notround Intermediate calculations. Round your answers to 2 decimal places.)ActualPredictedZero Coupon BondCoupon Bond96%%

Bond Price Changes with Yield to Maturity ShiftWe can analyze the price changes for both bonds using…

Answered: A 12-year maturity zero-coupon bond…

Essentials Of Investments

11th Edition

ISBN:9781260013924

Author:Bodie, Zvi, Kane, Alex, MARCUS, Alan J.

Publisher:Bodie, Zvi, Kane, Alex, MARCUS, Alan J.

Chapter1: Investments: Background And Issues

Section: Chapter Questions

Problem 1PS

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A 13-year-maturity zero-coupon bond selling at a yield to maturity of 9% (effective annual yield) has convexity of 174.3 and modified duration of 12.06 years. A 30-year-maturity 7% coupon bond making annual coupon payments also selling at a yield to maturity of 9% has nearly identical duration-12.04 years-but considerably higher convexity of 271.1. Required: a. Suppose the yield to maturity on both bonds increases to 10%. What will be the actual percentage capital loss on each bond? What percentage capital loss would be predicted by the duration-with-convexity rule? b. Suppose the yield to maturity on both bonds decreases to 8%. What will be the actual percentage capital loss on each bond? What percentage capital loss would be predicted by the duration-with-convexity rule? Complete this question by entering your answers in the tabs below. Required A Required B Suppose the yield to maturity on both bonds increases to 10%. What will be the actual percentage capital loss on each bond?…
A 9-year-maturity zero-coupon bond selling at a yield to maturity of 7.75% (effective annual yield) has convexity of 169.5 and modified duration of 8.06 years. A 30-year-maturity 7.5% coupon bond making annual coupon payments also selling at a yield to maturity of 7.75% has nearly identical duration-8.04 years-but considerably higher convexity of 257.5. Required: a. Suppose the yield to maturity on both bonds increases to 8.75%. What will be the actual percentage capital loss on each bond? What percentage capital loss would be predicted by the duration-with-convexity rule? b. Suppose the yield to maturity on both bonds decreases to 6.75%. What will be the actual percentage capital loss on each bond? What percentage capital loss would be predicted by the duration-with-convexity rule? Complete this question by entering your answers in the tabs below. Required A Required B. Suppose the yield to maturity on both bonds increases to 8.75%. What will be the actual percentage capital loss on…
A 13.55-year maturity zero-coupon bond selling at a yield to maturity of 8% (effective annual yield) has convexity of 169.0 and modified duration of 12.55 years. A 40-year maturity 6% coupon bond making annual coupon payments also selling at a yield to maturity of 8% has nearly identical modified duration—12.30 years—but considerably higher convexity of 272.9. Required: a. Suppose the yield to maturity on both bonds increases to 9%. What will be the actual percentage capital loss on each bond? What percentage capital loss would be predicted by the duration-with-convexity rule? (Do not round intermediate calculations. Round your answers to 2 decimal places.) b. Suppose the yield to maturity on both bonds decreases to 7%. What will be the actual percentage capital gain on each bond? What percentage capital gain would be predicted by the duration-with-convexity rule? (Do not round intermediate calculations. Round your answers to 2 decimal places.)
A 13.35-year maturity zero-coupon bond selling at a yield to maturity of 8% (effective annual yield) has convexity of 164.2 and modified duration of 12.36 years. A 40-year maturity 6% coupon bond making annual coupon payments also selling at a yield to maturity of 8% has nearly identical modified duration-12.30 years-but considerably higher convexity of 272.9. Required: a. Suppose the yield to maturity on both bonds increases to 9%. i. What will be the actual percentage capital loss on each bond? il. What percentage capital loss would be predicted by the duration-with-convexity rule? (Do not round intermediate calculations. Round your answers to 2 decimal places.) Zero-Coupon Bond Coupon Bond LActual loss Predicted loss b. Suppose the yield to maturity on both bonds decreases to 7%. Show Transcribed Text b. Suppose the yield to maturity on both bonds decreases to 7%. i. What will be the actual percentage capital gain on each bond? ii. What percentage capital gain would be predicted by…
A 9-year maturity zero-coupon bond selling at a yield to maturity of 7.75% (effective annual yield) has convexity of 169.5 and modified duration of 8.06 years. A 30-year maturity 7.5% coupon bond making annual coupon payments also selling at a yield to maturity of 7.75% has nearly identical duration-8.04 years-but considerably higher convexity of 257.5. a. Suppose the yield to maturity on both bonds increases to 8.75% What will be the actual percentage capital loss on each bond? What percentage capital loss would be predicted by the duration-with-convexity rule? (Input all amounts as positive values. Do not round intermediate calculations. Round your answers to 2 decimal places.) Zero Coupon Bond Coupon Bond Actual Predicted
A 10-year maturity bond making annual coupon payments with a coupon rate of 5% andcurrently selling at a yield to maturity of 4% has a convexity of 145.4. a. Compute the Modified Duration of the bond.b. Based on the information above, compute the approximated new price using the Duration& Convexity adjustment if the yield to maturity increases by 75 basis points.c. What is the percentage error?
Suppose you are given the following information about the default-free, coupon-paying yield curve: Maturity (years) Coupon rate (annual payment) YTM a. Use arbitrage to determine the yield to maturity of a two-year zero-coupon bond. b. What is the zero-coupon yield curve for years 1 through 4? Note: Assume annual compounding. a. Use arbitrage to determine the yield to maturity of a two-year zero-coupon bond. The yield to maturity of a two-year, zero-coupon bond is %. (Round to two decimal places.) b. What is the zero-coupon yield curve for years 1 through 4? The yield to maturity for the three-year and four-year zero-coupon bond is found in the same manner as the two-year zero-coupon bond. The yield to maturity on the three-year, zero-coupon bond is %. (Round to two decimal places.) %. (Round to two decimal places.) The yield to maturity on the four-year, zero-coupon bond is Which graph best depicts the yield curve of the zero-coupon bonds? (Select the best choice below.) O A. 8- 7- 6-…
A 12.75-year maturity zero-coupon bond selling at a yield to maturity of 8% (effective annual yield) has convexity of 150.3 and modified duration of 11.81 years. A 30-year maturity 6% coupon bond making annual coupon payments also selling at a yield to maturity of 8% has nearly identical duration—11.79 years—but considerably higher convexity of 231.2.a. Suppose the yield to maturity on both bonds increases to 9%. (i) What will be the actual percentage capital loss on each bond? (ii) What percentage capital loss would be predicted by the duration-with-convexity rule?b. Repeat part (a), but this time assume the yield to maturity decreases to 7%.c. Compare the performance of the two bonds in the two scenarios, one involving an increase in rates, the other a decrease. Based on the comparative investment performance, explain the attraction of convexity.d. In view of your answer to part (c), do you think it would be possible for two bonds with equal duration but different convexity to be…
A 12.75-year maturity zero-coupon bond selling at a yield to maturity of 8% (effective annual yield) has convexity of 150.3 and modified duration of 11.81 years. A 30-year maturity 6% coupon bond making annual coupon payments also selling at a yield to maturity of 8% has nearly identical duration—11.79 years—but considerably higher convexity of 231.2. a. Suppose the yield to maturity on both bonds increases to 9%. What will be the actual percentage capital loss on each bond? What percentage capital loss would be predicted by the duration-with-convexity rule? b. Repeat part ( a ), but this time assume the yield to maturity decreases to 7%. c. Compare the performance of the two bonds in the two scenarios, one involving an increase in rates, the other a decrease. Based on the comparative investment performance, explain the attraction of convexity. d. In view of your answer to ( c ), do you think it would be possible for two bonds with equal duration but different convexity to be priced…
A 30-year maturity bond making annual coupon payments with a coupon rate of 12% has (modified) duration of 11.54 years and convexity of 192.4. The bond currently sells at a yield to maturity of 8%. a) Find the price of the bond if ytm falls to 7% (use financial calculator or spreadsheet). b) What price would be predicted using duration only? c) What price would be predicted using duration and convexity? d) What is the error (in %) for each rule? What do you conclude about accuracy of the two rules? e) Repeat the analysis with yields rising to 9%. Do your conclusions about accuracy hold up?
Suppose the current, zero-coupon, yield curve for risk-free bonds is as follows: Maturity (years) Yield to Maturity 1 4.33% 2 4.64% 3 4.92% 4 5.09% 5 5.30% a. What is the price per $100 face value of a 3-year, zero-coupon risk-free bond? b. What the price per $100 face value of a 4-year, zero-coupon, risk-free bond? c. What is the risk-free interest rate for a 1-year maturity? Note: Assume annual compounding. a. What is the price per $100 face value of a 3-year, zero-coupon risk-free bond? The price is $ (Round to the nearest cent.) b. What is the price per $100 face value of a 4-year, zero-coupon, risk-free bond? The price is $ (Round to the nearest cent.) c. What is the risk-free interest rate for a 1-year maturity? The risk-free rate is %. (Round to two decimal places.)
Consider the zero coupon Treasury bond yield curve. Suppose a 1 year bond has a yield of 2.13%. The yield curve slopes downwards between maturities of 1 year and 3 years, and then slopes upwards. Which of the following must be true? Group of answer choices A) The yield of a zero coupon bond with maturity 5 years is higher than 2.13%. B) A 1 year positive coupon bond must have a lower price than the zero coupon bond with the same maturity. C) Bond purchasers believe the Fed will decrease rates in the short run, and then increase them in the long run. D) The economy will be in a recession within 2 years. E) C and D.

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