Q4. A newly issued bond has a maturity of 8 years and pays a 5% coupon rate (with coupon payments coming once annually). The bond sells at par value. a) Compute the convexity and the modified duration of the bond. b) Find the actual price of the bond assuming that its yield to maturity immediately increases from 5% to 6% (with maturity of still 8 years). c) What price would be predicted by the duration rule for one percentage price change? What is the percentage error of that rule? d) What price would be predicted by the duration-with-convexity rule for one percentage price change? How does it differ with the actual price of the bond?

Q4. A newly issued bond has a maturity of 8 years and pays a 5% coupon rate (with coupon payments coming once annually). The bond sells at par value. a) Compute the convexity and the modified duration of the bond. b) Find the actual price of the bond assuming that its yield to maturity immediately increases from 5% to 6% (with maturity of still 8 years). c) What price would be predicted by the duration rule for one percentage price change? What is the percentage error of that rule? d) What price would be predicted by the duration-with-convexity rule for one percentage price change? How does it differ with the actual price of the 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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The YTM on a bond is the interest rate you earn on your investment if interest rates don't change. If you actually sell the bond before it matures, your realized return is. known as the holding period yield (HPY). (Round the final answers to 2 decimal places.) a. Suppose that today you buy an 9.5% annual coupon bond for $ 1,210. The bond has 19 years to maturity. What rate of return do you expect to earn on your investment? Expected rate of return % b-1. Two years from now, the YTM on your bond has declined by 1%, and you decide to sell. What price will your bond sell for? (Omit $ sign in your response.) Bond price $ b-2. What is the HPY on your investment? HPY%
A newly issued bond with 1 year to maturity has a price of $1,000, which equals its face value. The coupon rate is 15% and the probability of default in 1 year is 35%. The bond’s payoff in default will be 65% of its face value. a. Calculate the bond’s expected return. b. Use a data table to show the expected return as a function of the recovery percentage and the price of the bond. Please show how you got part B using all functions.
You have a bond with the following features: - Semi-annual coupon payments. - Coupon rate 7.60%. - Face value $1,000. - 3.5 years to maturity. - Current market price $1,130. Requirements (A, B, and C are independent): 1. Calculate the duration and modified duration for this bond. Duration ___ Mduration ___ 2. Now, let’s assume the modified duration of this bond is 3 years. If the yield increases by 30 bps (basis points), what will the new price of the bond using modified duration? 3. If the yield drops by 75 bps, what is the actual new price of the bond?
← Suppose a seven-year, $1,000 bond with an 8.4% coupon rate and semiannual coupons is trading with a yield to maturity of 6.65%. a. Is this bond currently trading at a discount, at par, or at a premium? Explain. b. If the yield to maturity of the bond rises to 7.05% (APR with semiannual compounding), what price will the bond trade for? a. Is this bond currently trading at a discount, at par, or at a premium? Explain. (Select the best choice below.) O A. Because the yield to maturity is less than the coupon rate, the bond is trading at a premium. B. Because the yield to maturity is greater than the coupon rate, the bond is trading at par. OC. Because the yield to maturity is greater than the coupon rate, the bond is trading at a premium. D. Because the yield to maturity is less than the coupon rate, the bond is trading at a discount.
Suppose you are given the following information about the default-free, coupon-paying yield curve: Maturity (years) Coupon rate (annual payment) YTM 1 0.00% 2.587% 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. 2 11.00% 4.008% 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.) The yield to maturity on the four-year, zero-coupon bond is %. (Round to two decimal places.) Which graph best depicts the yield curve of the zero-coupon bonds? (Select the…
Consider a bond with a face value of $1,000 that sells for an initial price of $700. It will pay no coupons for the first nine years and will then pay 11% coupons for the remaining 29 years. Choose an equation showing the relationship between the price of the bond, the coupon (in dollars), and the yield to maturity. O A. B. O C. O D. 700 = 700 = 700 = 700 = 110 110 9 (1+i)⁹ (1+i)⁹+1 + 110 + i) ⁹ + 1 (1 + 1,000 (1+i) 29-9 1,000 (1 + i) 9 +29 + +...+ 110 (1+i) 9+2 + 110 (1 + i)9+29-1 110 + (1 + i) ⁹ + 110 (1+i)9 +29 9+29-1 + 110 (1 + i)9 +29 + 1,000 (1+i) 9+29
Duration1. A zero coupon bond with 3 years to maturity has an annualized yield to maturity of 3%. A 3-year maturity annual-pay coupon bond has a face value of $1000 and a 5% coupon rate. The coupon bond is also currently trading at a 3% yield. (a) Please calculate the duration of each bond. Which bond has the lower duration? Provide some intuition for this result. (b) Using the formula that approximates bond price change as a function of its duration, please calculate the approximate price change of both bonds if yields increase from 3% to 4%.
Consider a bond with a coupon of 7 percent, five years to maturity, and a current price of $1,025.30. Suppose the yield on the bond suddenly increases by 2 percent. a. Use duration to estimate the new price of the bond. (Do not round intermediate calculations. Round your answer to 2 decimal places.) Price b. Calculate the new bond price using the usual bond pricing formula. (Do not round intermediate calculations. Round your answer to 2 decimal places.) Price
A general power bond varies a coupon rate of 9.2%, has 9 years until maturity, and sells at a yield to maturity of 8.2%. a. Wage interest payments do bond holders receive each year? b. At what price does the bond sell? c. What will happen to the bond price if the yield to maturity falls to 7.2%?d. If the yield to maturity falls to 7.2%, will the current yield be less, or more, than the yield to maturity, and by what percent?
Suppose a 10-year, $1,000 bond with an 8.6% coupon rate and semi-annual coupons is trading for a price of $1,035.22. a. What is the bond's yield to maturity (expressed as an APR with semi-annual compounding)? b. If the bond's yield to maturity changes to 9.3% APR, what will the bond's price be? **** a. What is the bond's yield to maturity (expressed as an APR with semi-annual compounding)? The bond's yield to maturity is%. (Round to two decimal places.)
Question A .Consider a 2-year, risk-free bond with a coupon rate of 6% (annual coupons) and a face value of $1,000. If the yield on the above bond is 6%: a. What is the Macaulay duration of this bond? b. If the yield increases to 7% immediately, what does the duration approximation predict will be the percentage change in the bond price? c. If the yield decreases to 5% instead, what is the approximate percentage change in the bond price implied by the bond’s duration? d. After receiving the first coupon payment in year 1, the yield increases to 7% and you decide to sell the bond. What is your annualized HPR? Full explain this question and text typing work only We should answer our question within 2 hours takes more time then we will reduce Rating Dont ignore this line
Suppose that your firm issued a bond with 10 years until maturity, a face value of $1000, and a coupon rate of 7% (annual payments). The yield to maturity on this bond when it was issued was 6%. For questions e-g, assume that this bond DOES NOT pay any coupon a) What was its price when it was issued? b) For this zero-coupon bond, suppose it is actually sold for $500, what should the YTM be?

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