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 term structure for zero-coupon bonds is currently: Maturity (Years) YTM (%) 1 5.2% 2 6.2 3 7.2 Next year at this time, you expect it to be: Maturity (Years) YTM (%) 1 6.2% 2 7.2 3 8.2 Required: What do you expect the rate of return to be over the coming year on a 3-year zero-coupon bond? Under the expectations theory, what yields to maturity does the market expect to observe on 1- and 2-year zeros at the end of the year? Is the market's expectation of the return on the 3-year bond greater or less than yours?
A General Power bond carries a coupon rate of 9.7%, has 9 years until maturity, and sells at a yield to maturity of 8.7%. (Assume annual interest payments.) a. What interest payments do bondholders receive each year? b. At what price does the bond sell? Note: Do not round intermediate calculations. Round your answer to 2 decimal places. c. What will happen to the bond price if the yield to maturity falls to 7.7%? Note: Do not round intermediate calculations. Round your answer to 2 decimal places. a. Interest payments b. Price c. Price will by rise fall
There are three bonds that mature at the same time, have the same par value, and are expected to pay their first annual coupon 1 next year. The bonds are detailed in the below table. Bond A B с PV PV PV Present Value B ? ? ? PV B If ca r, then what can we say about the prices of the bonds today? (Enter >, <, or ?) PV C PV Yield to Maturity C r rb Coupon Rate ca с с
A newly issued bond pays its coupons once a year. Its coupon rate is 4.7%, its maturity is 15 years, and its yield to maturity is 7.7%. a. Find the holding-period return for a one-year investment period if the bond is selling at a yield to maturity of 6.7% by the end of the year. (Do not round intermediate calculations. Round your answer to 2 decimal places.) Holding-period return % b. If you sell the bond after one year when its yield is 6.7%, what taxes will you owe if the tax rate on interest income is 40% and the tax rate on capital gains income is 30%? The bond is subject to original-issue discount (OID) tax treatment. (Do not round intermediate calculations. Round your answers to 2 decimal places.) Tax on interest income $ Tax on capital gain $ Total taxes $ c. What is the after-tax holding-period return on the bond? (Do not round intermediate calculations. Round your answer to 2 decimal places.)…
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%.
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?
4. (i) A forward contract written on a bond has 10 months remaining until maturity. The face value of the bond is $1000, and it pays a 7% coupon every 6 months. The final coupon is due immediately prior to the maturity of the forward. The relevant riskless rate of interest is 5%. If the bond is trading at $1025, calculate the theoretical forward price and initial value of the forward contract and explain the forward pricing relationship. (ii) Provide numerical examples of arbitrage strategies for situations where a broker offers a price above, and below the theoretical forward price.

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