Fixed Income Securities

In class problem on futures pricing

Assume the following Treasury yield curve is in existence.

Time in Years Time in Periods Coupon Rate YTM Price Discount Factor Theoretical Semi-Annual Spot Rate Theoretical Annual Spot Rate Implied Semi-Annual Forward Rates Implied Annual Forward Rates

0.5 1 0.00% 6.00% $97.087 0.97087 3.0% 6.00% 3.250% 6.500%

1 2 0.00% 6.25% 94.031 0.94031 3.125% 6.25% 3.516% 7.032%

Assume that there is a 6-month Treasury bill futures contract in existence.Assume that it is priced to yield 6.6% (BEY).Assume the face value of the contract is $100,000.

a. What is the futures price implied by a BEY of 6.6%?

b. Based on the above curve, what should the BEYof the 6-month Treasury bill futures contract be?

c. What should the priceof the 6-month Treasury bill futures contract be? Round to the nearest dollar.

d. Given this information, is the futures price too high or too low?

e. Given your answer to d above, should you buy the futures contract or should you sell the futures contract (remember: buy low and sell high!)

f. Show that the actual futures price (BEY of 6.6%) is incorrect using a zero-cost investment strategy involving the spot market and the futures market.(Of course, if the futures price is correct, this zero cost strategy will also have zero profit.)Show the actual dollar cash flows at time 0 and at the expiration of the futures contract.