What is the Modified duration of a portfolio with one 2-year 10% semi-annual coupon bond and three 3-year 10% semi-annual bond when the required yield is 10%? Answer: - - - Both bonds are trading at par, so their prices are equal (to par value) and portfolio weights are (1/4, 34) From Example 3.2 and Exercise 3.1, the modified durations of these two bonds are 1.77 and 2.54, respectively Modified Duration of this portfolio:

What is the Modified duration of a portfolio with one 2-year 10% semi-annual coupon bond and three 3-year 10% semi-annual bond when the required yield is 10%? Answer: - - - Both bonds are trading at par, so their prices are equal (to par value) and portfolio weights are (1/4, 34) From Example 3.2 and Exercise 3.1, the modified durations of these two bonds are 1.77 and 2.54, respectively Modified Duration of this portfolio:

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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Given a bond with a coupon rate of 10% semi-annual interest, if the YTM is 11%, which statement is true about this security? A. This bond is trading at a Discount B. This bond is trading at Par. C. This bond is trading at a Premium D. Non of the above.
不 Which of the bonds A to D is most sensitive to a 1%drop in interest rates from Consider the following bonds: 6.5% to 5.5% Which bond is least sensitive? Bond Data table is most sensitive. (Select from the drop-down menu.) (Click on the following icon in order to copy its contents into a spreadsheet.) Bond A BC D Coupon Rate (annual payments) 0.0% 0.0% 4.3% 7.7% Print Done Maturity (years) 10 15 15 10
The following information about bonds A, B, C, and D are given. Assume that bond prices admit noarbitrage opportunities. What is the convexity of Bond D?Cash Flow at the end ofBond Price Year 1 Year 2 Year 3A 91 100 0 0B 86 0 100 0C 78 0 0 100D ? 5 5 105
(PLEASE READ THIS DIRECTION)Rules for Bond Valuation Problem Solving:a. For the "PV FACTOR in computing the PV of the coupon and PV for the maturity value/ principal use until 8-9th decimal place" before multiplying the coupon payment or future value.Example: ___x 2.123456789 or 22.12345678b. For "COMPOUNDED RATES" include all decimals in the rate (do not round off).Example semi-annual: 13%/2 =0.065c. For the "VALUE OF THE BOND/ PRICE OF THE BOND" round off your answers and final answers into whole numbers.Example: 824.59= 825 1. A bond issued by Delta Corporation matures in 12 years. It has a 12.5 percent annual coupon rate and a face value of P10,000. The bond has a discount rate to maturity of 9.5 percent. What is the price of Omega's bond today?
20. Assume there are two bonds in a bond portfolio. Bond 1 has a price of R₁, a Macaulay duration of MacD₁, a dollar duration of SD, and a modified duration of ModD, and a weight of w, in the portfolio. Bond 2 has a price of P₂, a Macaulay duration of MacD₂, a dollar duration of SD₂ and a modified duration of ModD, and a weight of w, in the portfolio. Assuming the yield curve is flat, and that the portfolio has a Macaulay duration of MacD Portfolio a dollar duration of SD Porfolio and a modified duration of ModD which of the following statements is incorrect? A. MacD Portfolio =W₁MacD₁+w₂MacD₂ B. ModD Portfolio = W₂ModD₂ +w₂ModD₂ C. SD Portfolio = ₁ SD + ₂D₂ $D₂ + $D₂ D. ModDp R₁ + P₂ dP dP₂ + dy dy Portfolio E. ModD Portfolio = = P₁+P₂ Portfolio
Yield to maturity The relationship between a bond's yield to maturity and coupon interest rate can be used to predict its pricing level. For the bond listed below, state whether the price of the bond will be at a premium to par, at par, or at a discount to par. Coupon interest rate Yield to maturity 10% 8% What is the price of the bond in relation to its par value? (Select the best answer below.) O A. The bond sells at a discount to par. OB. The bond sells at par. OC. The bond sells at a premium to par.
Unlike the coupon interest rate, which is fixed, a bond's yield varies from day to day depending on market conditions. To be most useful, it should give us an estimate of the rate of return an investor would earn if that investor purchased the bond today and held it for its remaining life. There are three different yield calculations: Current yield, yield to maturity, and yield to call. A bond's current yield is calculated as the annual interest payment divided by the current price. Unlike the yield to maturity or the yield to call, it does not represent the actual return that investors should expect because it does not account for the capital gain or loss that will be realized if the bond is held until it matures or is called. This yield was popular before calculators and computers came along because it was easy to calculate; however, because it can be misleading, the yield to maturity and yield to call are more relevant. The yield to maturity (YTM) is the rate of return earned on a…
Consider the following two-bond portfolio of option-free bonds; Bond A Bond B Years to maturity 5 years 10 years Coupon rate 5% 5% Par value 1000 1000 Yield to maturity 8% 6% Par amount owned R3,45 million R2 million Market value R30 367.59 (in 000’s) R18 528 (in 000’s) Assuming that Bond A is an option-free bond, calculate the bond’s modified duration using Macauly’s Duration.
Consider the characteristics of two annual pay bonds from the same issuer with the same priority in the event of default: You also observe the following spot interest rates from the current yield curve: Par value Coupons Maturity Coupon rate Yield to maturity Price Bond A $100 Annual 3 yrs 8% 10.25% 94.43 1 2 3 Bond B $100 Annual 3 yrs 4% 10.35% 84.31 Term (yrs) Spot Rates (zero coupon, %) 4% 7 10 Neither bond's price is consistent with the spot rates. Using the information in these displays, recommend either Bond A or Bond B for purchase. Justify your choice. Do not round intermediate calculations. Round your answers to the nearest cent. The non-arbitrage price of Bond A: $ The non-arbitrage price of Bond B: $ -Select- ✓ appears to be the better purchase.
Consider a portfolio of bonds that have an average default rate of 1%. The correlation between normalized default times for these bonds is 0.14. What is the 99.9% worst-case default rate for this bond portfolio? Note: Your answer must be expressed in percentage terms and accurate to within 0.16.
13. Consider a coupon bond with coupon payment=4.25, M=100, and n=2. Suppose ?1 = 4% and ?2 = 4.24%. Consider a forward contract for the delivery of the coupon bond in one period from today. Calculate the forward price using the following two approaches: 1) use the forward rate to price the forward contract; 2) use the cost of carry approach: spot-forward parity adjusted for the coupons.

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