Suppose the September CBOT Treasury bond futures contract has a quoted price of 89-09. What is the implied annual interest rate inherent in this futures contract? Assume this contract is based on a 20 year Treasury bond with semi-annual interest payments. The face value of the bond is $1000, and the semi-annual coupon payments are $30. The annual coupon rate on the bonds is $60 per bond (or 6%). The futures contract has 100 bonds.
N: 40
PV = (0.89+0.09/32) × $1,000 = -$892.81
FV = $1,000
PMT = $30
I/YR = 3.5%
Annual rate: I/YR × 2 = 7.00%
1-Suppose the September CBOT Treasury bond futures contract has a quoted price of 89-09. What is the implied annual interest rate inherent in this futures contract?
a. 6.32%
b. 6.65%
c. 7.00%
d. 7.35%
e. 7.72%
2-Suppose the December CBOT Treasury bond futures contract has a quoted price of 80-07. What is the implied annual interest rate inherent in the futures contract?
a. 6.86%
b. 7.22%
c. 7.60%
d. 8.00%
e. 8.40%
3-Suppose the December CBOT Treasury bond futures contract has a quoted price of 80-07. If annual interest rates go up by 1.00 percentage point, what is the gain or loss on the futures contract? (Assume a $1,000 par value, and round to the nearest whole dollar.)
a. -$78.00
b. -$82.00
c. -$86.00
d. -$90.00
e. -$95.00
3 is d
I think 3 is loss of $78
To calculate the implied annual interest rate inherent in the futures contract, you need to consider the relationship between the quoted price of the futures contract and the cash flows from the underlying Treasury bond.
The quoted price of the futures contract is expressed in 32nds of a point. In this case, the quoted price is 89-09, which means the price is 89 and 9/32nds of a point.
To start, convert the quoted price to a decimal. Divide the 32nds by 32 and add it to the whole number part of the quote. In this case, the decimal price would be 89 + (9/32) = 89.28125.
Next, calculate the total market value of the underlying bond. Multiply the face value of the bond ($1000) by the decimal price. In this case, the market value would be $1000 * 89.28125 = $89281.25.
Since the bond pays semi-annual coupon payments of $30, there are two coupon payments per year. The annual coupon payment for one bond would be $30 * 2 = $60.
To calculate the implied annual interest rate, divide the annual coupon payment by the market value of the bond and multiply by 100. In this case, the implied annual interest rate would be ($60 / $89281.25) * 100 = 0.0672, or 6.72%.
Therefore, the implied annual interest rate inherent in this futures contract is 6.72%.