11 Mar FINC313 Treasury Bonds and Bond Math Project

FINC313 University of Delaware Treasury Bonds and Bond Math Project
FINC 313
Assignment #1 Treasury Bonds and Bond Math
The focus of this assignment is to understand how to construct portfolios of Treasuries and to practice some bond math. Please work on this assignment alone or with a (single) partner. If you work with a partner, you and your partner only need to hand in one copy of your answers. Please show your work and provide explanations where relevant. However, you do not need to print out entire spreadsheets. Your answers should be summarized in a write-up with relevant details of calculations, tables and charts (if applicable), and explanations. The assignment can be turned in during class or via e-mail ([email protected]). If you do submit your assignment via e-mail, please submit it either as a Word document or as a PDF file. In particular, please do not e-mail an Excel spreadsheet – if you feel that the Excel spreadsheet is relevant to providing details of your work, please copy and paste the relevant portions into your Word document. Assume for the purposes of this assignment that you can buy and short fractional units of bonds.
Part 1: Zero Curves and Mispricing Suppose that you observe the following four bonds trading in the market. Bond A B C D Coupon Time-to-maturity Price 0% 0.5 99.01 0% 1 97.07 0% 1.5 94.23 6% 1.5 102.30 Coupons are paid semi-annually. All four bonds have a $100 face value.
1. Calculate zero-coupon yields for maturities of 0.5, 1, and 1.5 years using bonds A, B, and C.
2. Using the yields from (1), calculate the price of bond D if its price were consistent with bonds A, B, and C. Is bond D underpriced or overpriced?
3. Replicate bond D’s cash flows using a portfolio of bonds A, B, and C.
4. Using your results in (3), construct a long-short portfolio that takes advantage of this mispricing. 1
Part 2: Zero Curves and Mispricing Redux Suppose that you observe the following four bonds trading in the market. Bond A B C D Coupon Time-to-maturity Price 5% 0.5 101.99 3% 1 101.49 4% 1.5 102.96 6% 2 108.99 Coupons are paid semi-annually.
1. Calculate zero-coupon yields for maturities of 0.5, 1, 1.5, and 2-years.
2. Calculate the discount factors that the zero-coupon yields imply. Do you see any potential problems? Why?
3. Suppose that you have a technology that allows you to store money for free (a “mattress”) between years 1.5 and 2. That is, if you put $x under your mattress at t = 1.5, you will still have $x at t = 2. Construct a long-short trading strategy using the four bonds that earns you free money today.
Hint: Identify which bond you view as overpriced and start by shorting that bond. Then, use the other bonds to replicate its cash flows. In particular, 1 unit of the “mattress” technology has the following cash flows: Mattress Technology Units 1 t=0 0 t = 0.5 0 t=1 0 t = 1.5 -1 t=1 +1
Part 3: Duration & Convexity Calculations Suppose that a bond has the following terms: • 10-years-to-maturity • $1000 face value • Semi-annual coupons, with an annual coupon rate of 5% Suppose that all discount rates are 7%.
1. Calculate the price of the bond.
2. Calculate the bond’s modified duration.
3. Calculate the bond’s convexity.
4. If discount rates increase to 10%, what is the new price of the bond. Do (i) the actual calculation and (ii) approximate the new bond price using the duration and convexity. How well does the duration and convexity approximation work?