Solve the following questions without using Excel. A 5 year bond with a coupon of 7%, that pays interest annually, has its next coupon due in 12 months. It yields 5% per annum. a) compute the duration of the bond. Use this to compute approximately how the price of the bond will change if yields rise to 6%. (b) Compute the convexity of the bond. Use this to obtain a more precise estimate of the change in the price which will occur if the yield rises to 6%.
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- Calculate the modified duration of a bond that pays an annual coupon at a rate of 6% and matures in 2 years. This bond has a face value of 1,000 and is currently selling at a yield of 8%. Show calculations. Using just modified duration, if yield changes by 0.5%, what is the expected change in the price of the bond? Show calculations. Use the timeline method for this. Solving this in a calculator or at some other website that allows you to solve this kind of question and just putting the value is not going to be an acceptable answer.Use a different graph for each one and clearly label the axis and the shifting of curves. Explain clearly (in words and on the graph) whether the price and yield to maturity increased or decreased. You buy a bond that pays annual interest payments of 8% of the bond’s face value of $1000. You initially pay $1050 for the bond. You receive an annual interest payment after one year, then sell the bond for $1010. What is your total rate of return on the investment, expressed as a percentage of the purchase price?Suppose that the interest rate on one-year bonds is currently 4 percent and is expected to be 5 percent in one year and 6 percent in two years. Using the expectations hypothesis, compute the yields on two- and three-year bonds and plot the yield curve.
- Consider a 4-years bond with a 8% annual coupon rate and semi-annual payments. Let us suppose that the zero coupon curve rate today with annual compounding is given by the one in Table 1.(a) Calculate the discount factors for all the previous maturities and then the bond price.(b) Calculate the equivalent continuous compounding rates. What do you expect as result for the bond price with these rates? Should it be lower, higher or equal to the one in part (a)? Why? The equivalent continuous compounding rates should be lower than the annual rates. Why?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.Consider a bond that has just paid a semi-annual coupon and has exactly 2.5 years to maturity and an annual coupon rate of 3.5%. Price the bond with a yield 4.2%. This is an annuity calculation and the stated yield and stated coupon are double the semi-annual yield and coupon. Use Table 6.1. (Do not round Intermediate calculations. Round the final answer to 2 decimal places. Omit $ sign In your response.) Price of the bond $
- Consider a semi-annual bond that has a par value of 100, a 15-year maturity, a 5% coupon rate. Monthly interest rate is 0.412%. (a) What is the price of the bond (without calculation)? And explain why you can determine the price of the bond without calculation? (b) Using answers from (a), calculate the modified duration of this bond. (c) Using answers from (a) and (b), suppose that the bond’s yield to maturity decreases to 3.5%. How much will the bond price increase by applying the duration rule?Consider a semi-annual bond that has a par value of 100, a 15-year maturity, a 5% coupon rate. Monthly interest rate is 0.412%. (a) Calculate the annualized semi-annual compounding yield. (b) What is the price of the bond (without calculation)? And explain why you can determine the price of the bond without calculation? (c) Using answers from (b), calculate the modified duration of this bond. (d) Using answers from (b) and (c), suppose that the bond’s yield to maturity decreases to 3.5%. How much will the bond price increase by applying the duration rule? (e) Do you agree with the following statement, and explain why? “If two bonds have the same duration, then the percentage change in price of the two bonds will be the same for a given change in interest rates.” (f) Discuss the problems with the traditional bond pricing approach by using the yield to maturity. (300 words Maximum)You are considering two bonds. Bond A has a 9% annual coupon while Bond B has a 6% annual coupon. Both bonds have a 7% yield to maturity, and the YTM is expected to remain constant. Which of the following statements is CORRECT? State your reason for the answer. The price of Bond A will decrease over time, but the price of Bond B will increase over time. The price of Bond B will decrease over time, but the price of Bond A will increase over time. The prices of both bonds will remain unchanged. The prices of both bonds will increase by 7% per year. The prices of both bonds will increase by 9% per year.
- Calculate the price of a $1,000, 5% bond with three years to maturity with 7.5% market interest rates. Assume annual coupon payments.What is the duration of this bond?Using the duration price approximation formula, calculate the expected price change in % if interest rates fall to 7.0%. If your answer is negative, don't forget the sign!Assume the pure expectation theory holds: If the return on 6 years maturity treasury bill (TB) is 8%, the return on 1-year maturity TB is 6%, the return on a 2 years maturity (TB) is 7%, X is the return on a 3-year maturity bond. a. Calculate X, the forward rate, the return on a 3-year maturity bond, 3 years from today. b. Graph the yield curve c. Based on the yield curve you just derived, what are your expectations of the future performance of the economy?Suppose that the yield curve shows that the one-year bond yield is 8 percent, the two-year yield is 7 percent, and the three-year yield is 7 percent. Assume that the risk premium on the one-year bond is zero, the risk premium on the two-year bond is 1 percent, and the risk premium on the three-year bond is 2 percent. a. What are the expected one-year interest rates next year and the following year? The expected one-year interest rate next year = The expected one-year interest rate the following year b. If the risk premiums were all zero, as in the expectations hypothesis, what would the slope of the yield curve be? The slope of the yield curve would be (Click to select) % %