Course: Fixed Income Instruments. Complete each of the questions. Attached are the readings for the course. The assignment is due on March 4, 2021 at 2359 EST.
COURSE OUTLINE 1 of 5 PRE-MODULE ASSIGNMENT Module 2: Fixed Income Instruments and Markets Prof Jennifer Carpenter March 10-13, 2021 (Wed – Sat) Academic Honor Code By agreeing to complete the assignment / exam, you pledge your honor that you would not receive or give help for this assignment / exam, nor have you seen this assignment / exam prior to it being taken by you. You also certify that you will not divulge the contents of this assignment / exam to anyone. Additionally, you pledge to complete the assignment / exam within the agreed upon time constraints, and not use solutions to these questions from other sources. You agree not to seek an unfair advantage over other students, including, but no limited to giving or receiving authorized aid during completion of academic requirements. Besides, you will act truthfully and honestly in your academic pursuit, and acquaint yourself with the University’s policy on academic integrity and discipline. If there are any direct quotations in your submission (including material cut and pasted from websites), they must be clearly identified and immediately attach the citation that indicates the source of the quote. Any plagiarism (including copy and paste from a website without proper referencing) and any violation of the best practice for a direct quote of someone else’s work or writing is a serious violation of the Honor Code. Sanctions will be imposed if students are found to have violated the regulations governing academic integrity and honesty. I, (Name: ), certify that I have read, understood, and agreed to comply with the Academic Honor Code of the HKUST-NYU Stern MS in Global Finance Program. MS in Global Finance | Fixed Income Instruments and Markets Prof Jennifer Carpenter | Pre-Module Assignment 2 of 5 Assessment Scheme Pre-Module Assignment 20% In-Class Participation and Problems 20% Final Take-Home Exam 60% Deadline 6 March 2021 (Saturday) 2359 hours (NY Time) IMPORTANT! Late submissions will not be accepted and will result in zero mark. Pre-Module Assignment Submission: Please submit your assignment in PDF format ONLY via HKUST Canvas and ensure that your name appears on all attachments. No submissions will be accepted via email. If you would like to provide supporting documentation to show backup data / calculations, please submit the file via HKUST Canvas. If you would like to replace the submitted assignment with a revised version before the deadline, please do so via HKUST Canvas. This is an individual assignment. You must work alone and cannot seek guidance or advice from any other person. The teaching assistant will answer clarifying questions only. Enquiry If you have any questions, please contact our Teaching Assistant, Franz Hinzen at fhinzen@stern.nyu.edu. MS in Global Finance | Fixed Income Instruments and Markets Prof Jennifer Carpenter | Pre-Module Assignment 3 of 5 Important Notes Please round to four decimals after the comma. There won’t be any deductions for rounding errors as long as they can be clearly identified as those. Round prices as x.xxxx and rates as x.xxxx%. Be explicit about how exactly how you derive the solution, i.e., show all steps that lead to the solution. If you cannot make transparent how you derive your solution, you won’t get full points. Make explicit which formulas you are using and how you manipulate them to arrive at your numerical answer. Pre-Module Assignment Assume all rates are annualized with semi-annual compounding unless otherwise noted. 1. Assume all rates are annualized with semi-annual compounding. Please be explicit about how you derive your results and round to four decimals after the comma. $100 par of a 0.5-year 12%-coupon bond has a price of $104. $100 par of a 1-year 14%-coupon bond has a price of $108. a. What is the price of $1 par of a 0.5-year zero? b. What is the price of $1 par of a 1-year zero? c. Suppose $100 of a 1-year 10%-coupon bond has a price of $99. Is there an arbitrage opportunity? If so, how? d. What is the 0.5-year zero rate? e. What is the 1-year zero rate? f. What is the 1-year par rate, i.e., what coupon rate would make the price of a 1-year coupon bond equal to par? g. Considering the shape of the yield curve, should the yield on the 1-year 14%-coupon bond be higher or lower than the 1-year par rate? 2. Suppose the yield curve is upward-sloping and there is no arbitrage. Two ordinary fixed coupon bonds, bond A and bond B, have the same maturity, but bond A has a higher yield. Which bond has the higher coupon? 3. Assume all rates are annualized with semi-annual compounding. Please be explicit about how you derive your results and round to four decimals after the comma. Suppose that at time 0 you buy a 10%-coupon 20-year bond priced at par, and at time 0.5 you sell this bond at a yield of 12%. a. What is your time 0.5 payoff per $1 of initial investment? b. What is the rate of return on your investment (annualized, with semi-annual compounding)? (Cont’d next page) 4. Assume all rates are annualized with semi-annual compounding. Please be explicit about how you derive your results and round to four decimals after the comma. MS in Global Finance | Fixed Income Instruments and Markets Prof Jennifer Carpenter | Pre-Module Assignment 4 of 5 The 0.5-year zero rate is 7% and the 1-year zero rate is 9%. a. What is the price of: i. $1 par of a 0.5-year zero? ii. $1 par of a 1-year zero? iii. $100 par of a 1-year 10%-coupon bond, in the absence of arbitrage? b. What is the dollar duration of: i. $1 par of a 0.5-year zero? ii. $1 par of a 1-year zero? iii. 100 par of a 1-year 10%-coupon bond? c. What is the duration of: i. $1 par of a 0.5-year zero? ii. $1 par of a 1-year zero? iii. $100 par of a 1-year 10%-coupon bond? d. Use dollar duration to estimate the change in value of $1,000 par of the 1-year 10%- coupon bond if all zero rates rise 100 basis points. 5. Your liabilities have a market value of $1,120,000 and a duration of 7.5. You want to immunize your position by constructing a portfolio of two assets below that has the same market value and duration as your liabilities. Asset Market Value Duratio n #1 600 10 #2 200 3 a. Write down equations that determine the number of units of each asset in the portfolio. Use notation N1 and N2 to represent the number of units of asset #1 and #2, respectively. b. Solve the equations for N1 and N2. 6. Suppose you have a short position in a 30-year 5%-coupon bond and a long position in a zero- coupon bond with exactly the same market value and duration. If all zero rates fall by 25 basis points, will your net position rise or fall in value? Explain. 7. Assume all rates are annualized with semi-annual compounding. Please be explicit about how you derive your results and round to four decimals after the comma. The current price of $1 par of a zero maturing at time 2 is $0.97 a. What is the 2-year spot rate? b. What is the dollar duration of $1 par of the 2-year zero? The current price of $1 par of a zero maturing at time 3 is $0.92 c. What is the 3-year spot rate? d. What is the dollar duration of $1 par of the 3-year zero? You can enter into a forward contract today to buy, at time 2, $1 par of a zero maturing at time 3. The price you would pay at time 2 is the forward price. The cost today of entering into this contract is zero. e. Construct a portfolio of 2- and 3-year zeroes that synthesizes this forward contract. f. What is the no arbitrage forward price? g. What is the dollar duration of the forward contract? (Cont’d next page) 8. Assume all rates are annualized with semi-annual compounding. Please be explicit about how you derive your results and round to four decimals after the comma. MS in Global Finance | Fixed Income Instruments and Markets Prof Jennifer Carpenter | Pre-Module Assignment 5 of 5 (Part I) At time 0, Investor A enters into a forward contract, at no cost, to buy, at time 2, $100,000 par of a zero maturing at time 3. The forward price this investor locks in to pay at time 2 is $93,000. a. What forward rate does this investor lock in at time 0, through this forward contract, for lending from time 2 to time