Treasury Bill Forward Contracts

FI 4000

Sample Problems

Fall 2000

Example 1. The price of a T-Bill with three months (91 days) to maturity is 95 (as a percentage of par). Similarly, the price of a T-Bill with six months (181 days) to maturity is 90, and the price of a T-Bill with nine months (272 days) to maturity is 85.

a. What is the annualized yield on a bank discount basis (expressed as a decimal) for each of these T-Bills?

b. What is the dollar discount on each of these T-Bills if the face value is $1 million.

c. What is the forward price today for delivery in three months of a $1 million face value T-Bill with three months to maturity? How would this forward price differ from the corresponding futures price?

d. What is the forward price today for delivery in six months of a $1 million face value T-Bill with three months to maturity? How would this forward price differ from the corresponding futures price?

e. Describe how to borrow at the three month forward rate three months hence.

Example 2. Suppose the theoretical spot rates three months (91 days), six months (182 days), and nine months (272 days) to maturity are 8.91%, 11.56%, and 12.16%, respectively.

a. What is the price today of a T-Bill with three months, six months, and nine months to maturity, respectively, if the face value of each bill is $1 million?

b. What is the annualized yield on a bank discount basis (expressed as a decimal) for each of these T-Bills?

c. Suppose the forward price today for delivery in three months of a $1 million face value T-Bill with three months to maturity is $869,565. How can you take advantage of this?

e. Describe how to lend at the three month forward rate six months hence.

Example 3. The price of a T-Bill with three months (91 days) to maturity is 86.96 (as a percentage of par). Similarly, the price of a T-Bill with six months (182 days) to maturity is 82.64, and the price of a T-Bill with nine months (272 days) to maturity is 80.50.

a. What is the annualized yield on a bank discount basis (expressed as a decimal) for each of these T-Bills?

b. What is the forward price today for delivery in three months of a $1 million face value T-Bill with three months to maturity?

c. What is the forward price today for delivery in six months of a $1 million face value T-Bill with three months to maturity?

d. If the forward price today for delivery in three months of a $1 million face value T-Bill with three months to maturity is $953,289, how would you take advantage of this?

e. If the forward price today for delivery in six months of a $1 million face value T-Bill with three months to maturity is $966,180, how would you take advantage of this?

f. Describe how to lend at the three month forward rate three months hence.

g. Describe how to borrow at the three month forward rate six months hence.