Based on a modified duration of 4.1141, the price of the bond should increase by approximately 4.1141% in response to a 1.00% increase in yield-to-maturity (YTM). Select one: True False
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Based on a modified duration of 4.1141, the price of the bond should increase by approximately 4.1141% in response to a 1.00% increase in yield-to-maturity (YTM).
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- Explain what you see from the pricing calculations. How do the two bonds differ? Bond C Bond Price = PV(rate,nper,pmt,fv) Given: n = Period which takes values from 0 to the nth period = 0,1,2,3 & 4 Cn = Coupon payment in the nth period = 10%*$1,000 = $100 YTM = interest rate or required yield = 9.6% P = Par Value of the bond = $1,000 Bond Z Bond Price = PV(rate,nper,pmt,fv) Given: n = Period which takes values from 0 to the nth period = 0,1,2,3 & 4 Cn = Coupon payment in the nth period = 0%*$1,000 = $0.00 YTM = interest rate or required yield = 9.6% P = Par Value of the bond = $1,000 years Bond A Bond Z 4 $1,012.79 $693.04 3 $1,010.02 $759.57 2 $1,006.98 $832.49 1 $1,003.65 $912.41 0 $1,000.00 $1,000.00Suppose the current price of the bond is $95, the YTM is 4%, and the duration of the bond is 9. If YTM decrease from 4% to 3.9%, approximate the change in price using duration of the bond. Price would increase by ____%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.
- Suppose that y is the yield on a perpetual government bond that pays interest at the rate of $1 per annum. Assume that y is expressed with simply com- pounding, that interest is paid annually on the bond, and that y follows the process dy = a(y0 −y)dt + oydWt, where a, y0, and o are positive constants and dWt is a Wiener process. (a) What is the process followed by the bond price? (b) What is the expected instantaneous return (including interest and capital gains) to the holder of the bond?5. Manually compute the modified duration for the following bond: Maturity Date: 04/20/2017 Settlement Date: 02/05/2016 Coupon Rate: 10% Coupon Frequency: Semiannual Yield-to-Maturity: 12% Day Count Convention: 30/360 (European) For the bond in question 5, find the modified duration using Excel, and please show your input For the bond in question 5, find the convexity for a 50-bps change in yield-to-maturity (Ai= 0.5%).3) Consider a bond selling at par with modified duration of 10.6 years and convexity of 210. A 2% decrease in yield would cause the price to increase by 21.2% according to the duration rule. What would be the percentage price change according to the duration-with-convexity rule? A) 21.2% B) 25.4% C) 17.0% D) 10.6%
- 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 сGive typing answer with explanation and conclusion 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.7. Plot the (positive) prices (Y axis) of a new 10-year, 10% bond and a new 2-year, 10% bond against r (X axis), using r = market interest rate = 0%, 2%, 5%, 8%, 10% 12%, 15%, 20%, 25%, 30%, and 45%. Note that two curves should be in one chart (See Slide 5.47). Comment on the results. Turn in the Excel file (use the required file name) with the chart and calculations. Can use Excel functions to make it efficient.
- 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…еВook Problem Walk-Through Last year Carson Industries issued a 10-year, 13% semiannual coupon bond at its par value of $1,000. Currently, the bond can be called in 6 years at a price of $1,065 and it sells for $1,200. a. What are the bond's nominal yield to maturity and its nominal yield to call? Do not round intermediate calculations. Round your answers to two decimal places. YTM: % YTC: % Would an investor be more likely to earn the YTM or the YTC? -Select- -Select- ent yield and to Table 7.1) Round your answer to two decimal places. b. Since the YTM is above the YTC, the bond is likely to be called. Since the YTC is above the YTM, the bond is likely to be called. Since the YTM is above the YTC, the bond is not likely to be called. Since the YTC is above the YTM, the bond is not likely to be called. Since the coupon rate on the bond has declined, the bond is not likely to be called. I. If the bond is called, the capital gains yield will remain the same but the current yield will be…(3) Use a 1 bps shock to compute duration and convexity (using approximating measures for duration and convexity, respectively) for the following bond as of the origination date. Origination Date Maturity Date 12/31/2021 12/31/2023 $100 Par Value Annual Coupon Rate 2.00% Рayment frequenсy Quarterly Assume the applicable zero rates for this bond are the following on 12/31/2021 Date Zero rate 12/31/2021 3/31/2022 0.18% 6/30/2022 9/30/2022 0.42% 0.64% 12/31/2022 0.84% 3/31/2023 6/30/2023 9/30/2023 12/31/2023 1.06% 1.24% 1.35% 1.42%