# Homework: Zero Coupon Bond Assignment

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Calculate the yield to maturity (I. E. , the AIR) of bonds A and B assuming they trade at the prices quoted in part B. Which bond has a higher yield to maturity at these prices? Compare these to the yields of the various zero coupon bonds. E. Based on your answers to parts B and D above, does yield to maturity give you a guide as to possible misprinting in the market? Can you think about why this might be the case? (Hint: how would your answer to all the parts above change if the term structure or yield curve was flat at, say, 13%? ) Question 2: Bond arbitrage Suppose that the current term structure is given by: 2. 5% 2. 70% 2. 79% 2. 98% Year(n) 0. 5 1. 5 1 . Price zero coupon bonds for each maturity (be sure to write down the general formula) 2. Price a 5% (annulled coupon rate) coupon bonds for each maturity. 3. Suppose the two-year 5% coupon bond is trading for 103. 414 dollars. Is there an arbitrage? If so, explicitly construct a trade that delivers a risk-less profit of \$50,000. This means, write down the entire portfolio with initial cost and final payoffs at each time. Question 3: Bloomberg some feel for the market. Go to one of Bloomberg terminals in the Library.

You do not want to wait to do this assignment until Monday evening, as you will see lots of your classmates sitting there with you! The point of this exercise is to remind of the institutional details we sometimes glaze over in class. At any point in time, to return to the previous screen, hit the menu key. Follow these steps: Type in the letter t, hit the GO key and then hit GO. In front of you will see the complete list of U. S. Treasury bills, notes and bonds outstanding. I want you to find the 4% Treasury note expiring on 2/15/14. To scroll up or down at any point in time, hit page back or forward.

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The maturity date is the column with dates in it. To select the bond, click on it with the mouse. From now on we will refer to this screen as the Main Screen. 1 . What is its price? When was it issued and how large was the issuance? To figure this out, click on item Security Valuation/Scofflaws. After clicking on this, click on Description. A screen with a lot of information will pop-up. The amount issued will be under Security Information. Click the MENU key twice. 2. What is the yield to maturity of the bond? From the Main Screen, click on Yield and AS Analysis and then click on WAY Yield Analysis. Report the street convention yield. . Find the appropriate spot rates for discounting the scofflaws. To do this, go to the Main Screen of this security, click on Security Valuation/Scofflaws and then click on Scofflaws Analyzer. (Hint: the Scofflaws Column provides what in class notation is C/2. ) Print or write down the spot rates and scofflaws. 4. For the rest of the question, you do not need to be in front of the Bloomberg terminal, but you need to have in hand the prices, scofflaws and spot rates. A. Compute yield using the formulas from class with the observed market price. You are owing to recognize an immediate problem: timing of the coupons.

To get over this problem, compute the yield under 2 alternative scenarios: rounding back to the last coupon date and rounding forward to the next coupon date. In both cases use the same price. Is the bond yield the same as in part 2? The answer is typically no. B. Using the scofflaws and spot rates, compute the price using semi-annual compounding. Is this the same as the observed price? Again, it probably won’t be. Question 4 a) Suppose an investor has access to two bonds, one with a duration of 1. 8 and the other with a duration of 4. You are approached to construct a portfolio of these bonds that has a duration of 7.

What percentages of the investor’s portfolio should go into bonds 1 and 2 to achieve this target duration? These durations are modified durations. B) One of these weights is negative. What does this mean in terms of the What problems might there be in implementing your recommendation (e. G. , costs, liquidity, etc. )? Question 5 Portfolio X consists of a I-year zero-coupon bond with a face value of \$2,000, and a 10-year zero-coupon bond with a face value of \$5000. Portfolio Y consists of a 5. 63 year correction with a face value of \$5000. The current yield on all the bonds considered is 10% per annum, and compounding happens semi-annually.

What is the modified duration of the two portfolios? Ii Use modified duration to estimate the impact of a decrease in the yield from 10% to 9. 5% on the percentage price change of the two portfolios. Question 6: Bond price volatility Access the data in the file EYE-Assigns-data. XSL. The first and second worksheets in this file provide zero coupon bond yields for ten-year and six-month maturities observed at weekly frequency. 1 . Compute percentage changes in yields and compute the annulled standard aviation of the yield changes (to do this, compute the standard deviation and multiply by sort(52)). . Compute zero coupon bond prices for both maturities. Be careful to get the compounding correct.

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