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Use at least four decimal places for those questions that require a numerical answer

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Use at least four decimal places for those questions that require a numerical answer. Please show all work on the exam. Failure to show all work will result in zero credit. Please remember to write your name on your solutions and submit a PDF copy to Blackboard.

1. A Treasury bond reaches maturity in 9 months. Assume that the Treasury bond has a coupon of 3% and the current price of the bond is $99,500.

a. Estimate the bond’s yield to maturity (based on continuous compounding) using an iterative procedure and a starting value of 0.04.

b. Verify that your estimate for the yield to maturity produces a bond value that is within $10 of the current market price.

2. Explain why the price of an expiring futures contract must be approximately equal to the spot price of the asset underlying the future’s contract. Provide two examples that show why your explanation makes sense using the wheat futures contract.

3. One month ago, an investor entered into a forward agreement to sell a bond in three months’ time at a price of $100. The current spot price for the bond is $101.50. Suppose the term structure of interest rates is such that the 1-month spot rate is 2%, the 2-month spot rate is 4% and the 3-month spot rate is 6%. Assume all interest rates are based on continuous compounding.

a. Given the above information, what is the value of the investor’s position assuming the bond does not pay a coupon?

PV = 101.5 * e^(-2%/12) = 101.3310

b. Suppose instead the bond pays a 5% coupon and the next coupon payment is one month from today and that the following coupon payment will be in seven months. In that event, what is the value of the investor’s position?

1st month cashflow = 5%*100 =5

2nd month cashflow = 5%*100=5

3rd month cashflow = 5%*100+100=105

PV = 5e^(-2%/12)+5e^(-4%/6)+105e^(-6%/4)=113.3952

4. Some time ago a swap dealer entered into a Forward Rate Agreement (FRA) that has a notional value of $25,000,000. The swap dealer agreed to pay 4.96% based on quarterly compounding and receive Libor. Libor zero rates (based on continuous compounding are given below.

a. What is the value of the FRA to the swap dealer assuming it begins in 9 months and lasts for 3 months?

b. Provide an example which shows exactly how the swap dealer can hedge its position in the FRA.

Maturity (months) Zero Rate (%)

3 4

6 4.5

9 5

12 5.5

15 6

5. Use the following information to determine the value of a currency swap in US dollars. Under the terms of the agreement payments are exchanged on a quarterly basis and the US based swap dealer pays 2% in pounds and receives 4% in US dollars (both rates are per annum based on quarterly compounding). The current exchange rate is $1.3 USD for each UK pound. The term structure of interest rates in the United States and the UK is flat and the interest rate (based on continuous compounding) in both countries is currently 5% per annum. The principals in the two countries are $100 million dollars and 80 million pounds. Assume that the next exchange of payments is in 3 months and that the swap will last one more year from today.

6. A trader has decided to roll a short hedge forward until December to hedge a long position in corn inventory. The schedule below shows the dates on which trades are made and the prices.

a. Determine the effective price at which the corn was sold on December 12.

b. Explain whether the trader would have made more (or less) profit if it had not hedged its inventory position.

Date Action Price

February 6 Sell March Futures $5.73

March 15 Buy March Futures $6.20

March 15 Sell May Futures $5.90

May 16 Buy May Futures $5.10

May 16 Sell July Futures $5.30

July 22 Buy July Futures $5.70

July 22 Sell September Futures $6.20

September 17 Buy September Futures $6.90

September 17 Sell December Futures $6.95

December 12 Buy December Futures $6.50

December 12 Sell Cash Inventory $6.45

7. The table below provides information about treasury bonds.

Bond Number Bond Principal ($) Time to Maturity (months) Annual Coupon (%) Market Price ($)

1 100 6 3 98

2 100 12 5 97

3 100 18 0 85

a. Calculate zero rates (based on continuous compounding) for 6, 12, and 18 months and graph the treasury yield curve and provide your answers in the following table:

b. Estimate the price of an 18-month Treasury bond that pays a coupon of 6%.

Bond 1 Zero Rate