Question 1
 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? 
 Question 2 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? 
 Question 3 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)? 
 Question 4 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 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. Question 5 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 Duration #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. Question 6 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. 
 Question 7 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? 
 Question 8 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?