Suppose that the term structure of interest rates is: t 0.5 1 1.5 2 r 1% 1.2% 1.4% 1.8% Interest rates are annual interest rates that are semi-annually compounded. 1. Calculate the price and modified duration of a 1-year bond with a 6% coupon rate, with coupons paid semi-annually. The bond has a face value of 100.0 2. Calculate the price and modified duration of a 2-year bond with a 10% coupon rate, with coupons paid semi-annually. The bond has a face value of 100.0 3. Compare your results from 1 and 2 above. Which bond is more sensitive to changes in interest rates?

Suppose that the term structure of interest rates is: t 0.5 1 1.5 2 r 1% 1.2% 1.4% 1.8% Interest rates are annual interest rates that are semi-annually compounded. 1. Calculate the price and modified duration of a 1-year bond with a 6% coupon rate, with coupons paid semi-annually. The bond has a face value of 100.0 2. Calculate the price and modified duration of a 2-year bond with a 10% coupon rate, with coupons paid semi-annually. The bond has a face value of 100.0 3. Compare your results from 1 and 2 above. Which bond is more sensitive to changes in interest rates?

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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Suppose a 10% 3years bond with a FV of $1000 Spot rates r1= 10%, r2= 12%, r3=13%. Calculate the forward rate required to calculate the bond price using the forward rate 1f2
Consider the following: Price Yield to maturity Periods to maturity Modified duration Fixed-rate Bond Fixed-rate Note 107.18 5.00% 18 6.9848 100.00 5.00% 8 3.5851 a. For an increase in interest rates of 100 basis points, determine the change in value for the fixed-rate note. Show your work. b. For an increase in interest rates of 100 basis points, determine the change in value for the fixed-rate bond. Show your work. c. Which of the two fixed-rate securities are more sensitive to increases interest rates? Why? d. What would be the most appropriate course of action to take given interest rates are expected to rise? Explain carefully.
Consider the following scenario: A bond has a price of $95 (Par Value 100). It matures in 7 years and pays coupons semi-annually. Find the coupon rate of the bond (in annual terms) that would yield a duration of 5.5.
Assume that the real risk free rate is 2% and the average expected inflation rate is 3% for each future year. The default risk premium and the liquidity premium for bond x are each 1% and the applicable Maturity Risk premium is 2% what is bond x’s interest rate. Round to 2 decimal places
Bond A makes semi-annual interest payments of $30. Bond B makes an annual payment of $50. All else equal, which one has the lower coupon rate? Select one: a. B b. A=B c. A
Consider a bond paying a coupon rate of 9.5% per year quarterly when the market interest rate is 5.25% per half-year. The bond has four years until maturity. a. Find the bond’s price today and nine months from now. b. What is the total rate of return on the bond?
Consider two bonds, a 3-year bond paying annual coupons at 5% and a 10-year bond also paying annual coupons at 5%. Coupons are paid annually (not semiannually). Both are currently trading at par (i.e., price = face value). A. What must be the current discount rate for these bonds? B. Suppose that the discount rate for these bonds suddenly rise to 9%. What is the new price of the 3-year bond? What is the new price of the 10-year bond? C. Compare the price changes (i.e., the current price of $1,000 vs. the new bond price from Part B) of two bonds. Determine whether long-term or short-term bonds are more sensitive to interest rate fluctuation.
Suppose that you want to construct a 2-year maturity forward loan commencing in 3 years. The face value of each bond is $1,000. Maturity (Years) 1 2 3 4 5 Price $ 996.04 895.89 833.92 772.80 675.18 Required: a. Suppose that you buy today one 3-year maturity zero-coupon bond with face value $1,000. How many 5-year maturity zeros would you have to sell to make your initial cash flow equal to zero (specifically, what must be the total face value of those 5-year zeros)? b. What are the cash flows on this strategy in each year? c. What is the effective 2-year interest rate on the effective 3-year-ahead forward loan? d. & e. Confirm that the effective 2-year forward interest rate equals (1 + f4) ×(1 + f5)-1. You therefore can interpret the 2-year loan rate as a 2-year forward rate for the last two years. Alternatively, show that the effective 2-year forward rate equals (1 + y5) 15 + (1+y3) ³. - 1
Provide table solutions
K Assume that a bond will make payments every six months as shown on the following timeline (using six-month periods): Period 0 2 Cash Flows $19.12 $19.12 a. What is the maturity of the bond (in years)? b. What is the coupon rate (as a percentage)? c. What is the face value? a. What is the maturity of the bond (in years)? The maturity is years. (Round to the nearest integer.) 39 $19.12
Consider a bond (with par value = $1,000) paying a coupon rate of 10% per year semiannually when the market interest rate is only 4% per half-year. The bond has three years until maturity. Required: a. Find the bond's price today and six months from now after the next coupon is paid. b. What is the total (6-month) rate of return on the bond? Complete this question by entering your answers in the tabs below. Required A Required B Find the bond's price today and six months from now after the next coupon is paid. Note: Round your answers to 2 decimal places. Current price Price after six months $ $ 1,052.42 1,044.52
Suppose the current interest rate on a one-year bond is 2% and the current interest rate on a two-year bond is 4%. The term premium on a two-year bond is 1%. According to the expectations hypothesis, what interest rate should we expect on a one-year bond next year? Answer as a percentage to one decimal place and do not include symbols (e.g. $, %, commas) in your answer. Answer:

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