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Find the Macaulay duration and the modified duration of a 15-year, 7.5% corporate
According to the modified duration of this bond, how much of a price change would this bond incur if market yields rose to 6.5%? Using annual compounding, calculate the price of this bond in one year if rates do rise to 6.5%. How does this price change compare to that predicted by the modified duration? Explain the difference.
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- Consider a bond with a duration of 8.8 years priced at $1,100. If market interest rates were to increase by 0.25%, what would be the predicted new bond price according to duration?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) % %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.
- Suppose you can observe that 1-year bond interest rate is 4%, 2-year bond interest rate is 8%, and 3-year bond interest rate is 10% at time t. It is also known that the term premium on a 2-year bond is 1% and the term premium on a 3-year bond is 1.5%. a) What are the market's expected 1-year bond interest rates for the next two years from time t? b) How to interpret those expected short-term interest rates? (what would be the "possible" economic meanings in the expected short- term interest rates?) Discuss as least two "candidates" to explain them.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?Consider a 10-year bond with current price of $98.4 and a duration of 9.1 years. Suppose the yield on the bond is 9.6% per year with continuous compounding. What is the predicted change in the price (in dollars) of the bond if the yield increases by 0.4%? (required precision: 0.01 +/- 0.01)
- (i) If investors have demanded an interest rate of 5 percent on the bond investment, what is the maximum prices to pay for the 1-year bond and 30-year bond? (ii) Suppose that the interest rate has increased to 20%, calculate the values of the 1-yearbond and 30-year bond.(iii) Based on the calculations in parts (b) (i) and (ii) above, explain with reasons thefundamental relationship between interest rates and bond maturity. (iv) Briefly explain the meaning of the terms “bond’s coupon rate”, “current yield”, and“yield to maturity”. (v) Explain why bonds have protective covenants.Assuming that the expectation theory is the correct theory of the term structure, calculate the interest rates in the terms structure for maturities of on to five years, and plot the resulting yield curves for the following series of one-year interest rates over the next five year. how would your yield curves change if people preffered shorter-term bonds over longer-term bonds? i) 5%, 4%，4%， 4%， 4%1. Consider two bonds with a similar credit rating and pay the same coupon rate per annum. The terms to maturity for Bond A and Bond B are 5 years and 10 years respectively. If inflation rate is expected to increase in the near future and therefore leads to an increase in interest rate, what is the effect on the bond prices? Which bond is likely to experience a larger effect due to the increase in interest rate? Briefly explain your answer.
- 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%.Using the information from the prior problem, what rate (in %s) do you expect a 5-year bond to have? From Prior: You observe that there is a one-year Treasury bond with a yield of 3.0%. You also assume that rates will increase and that the one-year bond will increase by 1.0% each year. For example, you expect the one-year bond in year 2 will be 4.0% and 5.0% in year 3.What is the Macaulay duration of a semi-annual bond with a coupon rate of 7 percent, five years to maturity, and a current price of $959? What is the modified duration? Duration is __. years. Modified duration is __ years.