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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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- 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…After recently receiving a bonus, you have decided to add some bonds to your investment portfolio. You have narrowed your choice down to the following bonds (assume semiannual payments): a. Using the PRICE function, calculate the intrinsic value of each bond. Is either bond currently undervalued? How much accrued interest would you have to pay for each bond? b. Using the YIELD function, calculate the yield to maturity of each bond using the current market prices. c. Calculate the duration and modified duration of each bond.d. Which bond would you rather own if you expect market rates to fall by 2% across the maturity spectrum? What if rates will rise by 2%? Why?6. Assume that the formula for the coupon rates of a floater and an inverse floater are: Floater coupon rate: reference rate + 1.5% Inverse floater co upon rate: 12% - reference rate Answer the following questions: (A) What is the coupon rate of the fixed rate collateral for these two floating rate bonds? (B) Suppose the floor for the inverse floater is 1%. What would be the cap of the floater?
- Which of the following is correct? O If you pay a price above its face value to buy a bond, your return will be higher than its coupon rate. O When market rate is greater than coupon rate, the bond has a price below its face value. O When determining the value of a bond that payments semi-annual payments, one need to use semi-annual coupon rate to determine the coupon payments and semi-annual market rate as discount rate.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?For the yield-to-maturity (YTM) to qual the actual compound return an investor realizes on an investment in a coupon bond, we must assume: O A. cash flows will be paid as promised. B. The bond will be held until maturity. C. cash flows will be reinvested at the YTM rate. D. All of the above.
- Suppose that, in each period, the cost of a security either goes up by a factor of 2 or goes down by a factor of 1/2 (i.e. u=2, d=1/2). If the initial price of the security is 100, determine the no-arbitrage cost of a call option to purchase the security at the end of two periods for a price of 150.Suppose you are given the following information about the default-free, coupon-paying yield curve: Maturity (years) Coupon rate (annual payment) YTM a. Use arbitrage to determine the yield to maturity of a two-year zero-coupon bond. b. What is the zero-coupon yield curve for years 1 through 4? Note: Assume annual compounding. a. Use arbitrage to determine the yield to maturity of a two-year zero-coupon bond. The yield to maturity of a two-year, zero-coupon bond is %. (Round to two decimal places.) b. What is the zero-coupon yield curve for years 1 through 4? The yield to maturity for the three-year and four-year zero-coupon bond is found in the same manner as the two-year zero-coupon bond. The yield to maturity on the three-year, zero-coupon bond is %. (Round to two decimal places.) %. (Round to two decimal places.) The yield to maturity on the four-year, zero-coupon bond is Which graph best depicts the yield curve of the zero-coupon bonds? (Select the best choice below.) O A. 8- 7- 6-…The forward rate f(t1,12) of a bond, is the implicit interest rate in a future period between time t1 and t2. For example, assuming continuous time returns, if the discount rate from period 0 to t1 is: exp(-r t1), and from period 0 to 12 (greater than t1) is: exp(-r t2), then the forward rate f from t1 to t2 maintains the following no arbitrage relationship: exp(-r t1) exp(-f (t2-t1) exp(-r t2)). Suppose we observe the prices of a 14-year zero-coupon bond (with a face value of $93.31), where P(t1,t2) regans the price of the bond between t1 and 12, and a year 7-to-14 forward rate as follows:P(0.14) - $86.5496905000 and f(7,14) - 0.6074704253 %. Calculate the price of a 7-year zero-coupon, with face value $99.27: $82.9604 $96.0778 ✓(25 %) $96.2349 $82.1804
- Suppose that you have calibrated both HL and BDT models to the yield curve and are trying to price a forward contract on a 5 year treasury note (Note: a forward contract is an obligation to buy a 5y treasury not at a predetermined date in the future at a predetermined price). Which of the two models will assign a higher price to this forward contract? a. HL price will be higher b. HL and BDT prices will be equal c. BDT price will be higher Explain why.Calculate YTC using a financial calculator by entering the number of payment periods until call for N, the price of the bond for PV, the interest payments for PMT, and the call price for FV. Then you can solve for 1/YR YTC. Again, remember you need to make the appropriate adjustments for a semiannual bond and realize that the calculated 1/YR is on a periodic basis so you will need to multiply the rate by 2 to obtain the annual rate. In addition, you need to make sure that the signs for PMT and FV are identical and the opposite sign is used for PV; otherwise, your answer will be incorrect. A company is more likely to call its bonds if they are able to replace their current high-coupon debt with less expensive financing. A bond is more likely to be called if its price is above par-because this means that the going market interest rate is less than its coupon rate. Quantitative Problem: Ace Products has a bond issue outstanding with 15 years remaining to maturity, a coupon rate of 8.4%…Consider a 1-factor parallel yield shift model with a flat structure of interest rates and consider two bonds with the same maturity time T but with different coupon rates. Which bond has a higher duration? A) The bond with a lower coupon rate B) The bond with a higher coupon rate C) The Durations of these two bonds are the same