. 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.)
To calculate the gain or loss on the futures contract, you need to determine the change in price resulting from the increase in interest rates.
Here's how to calculate it step by step:
Step 1: Convert the quoted price to a decimal.
The quoted price 80-07 can be converted to a decimal by dividing the number after the dash by 32 and adding it to the number before the dash. In this case, it becomes 80 + 7/32 = 80.21875.
Step 2: Calculate the contract value.
The contract value can be calculated by multiplying the quoted price by the par value. Since the par value is given as $1,000, the contract value would be 80.21875 * 1000 = $80,218.75.
Step 3: Calculate the change in price.
To calculate the change in price, you need to multiply the change in interest rates by the price factor. The price factor is determined by the conversion factor of the futures contract.
Step 4: Determine the price factor.
To find the price factor, you can use the relationship between the futures contract and the underlying Treasury bond. The formula for the price factor is:
Price factor = (1 + (Annual interest rate / 2))^(-n)
In this case, the annual interest rate has increased by 1.00 percentage point, so the new interest rate would be the current rate plus 1.00. Assuming the original interest rate is r, the new interest rate would be r + 1.00.
Step 5: Substitute the values and calculate the change in price.
Using the formula from step 4, plug in the values to calculate the price factor. The exponent (n) represents the number of periods until the futures contract expires. Assuming it is one year until expiration, you can set n = 2 (since CBOT Treasury bond futures contracts have quarterly expiration cycles).
Let's assume a constant annual interest rate of 5.00% for the original interest rate:
Price factor = (1 + (0.05 / 2))^(-2) ≈ 0.95123
Now, let's calculate the change in price:
Change in price = (New price factor - Original price factor) * Original price
= (New price factor - 0.95123) * $80,218.75
Step 6: Calculate the gain or loss.
The gain or loss on the futures contract is given by the change in price.
If the change in price is positive, it means there is a gain. If it is negative, it means there is a loss. Round the gain or loss to the nearest whole dollar.
By following these steps, you should be able to calculate the gain or loss on the futures contract based on the given information.