See attached. I want Shakeel. He completed assignments 75117 and 76124.
COURSE OUTLINE 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 you derived 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. · Please submit your assignment in one excel document with a tab for each question providing supporting documentation that show all your backup data, calculations, and formulas. 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)? 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. 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? 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. (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 3? (Part II) At time 1, the spot price of $1 par of a zero maturing at time 2 is 0.97 and the spot price of $1 par of a zero maturing at time 3 is 0.93. a. At time 1, what is the forward price an investor could lock in to pay, at time 2, for $100,000 par of a zero maturing at time 3? b. What is the value, at time 1, of Investor A’s position in the forward contract from Part I?