This morning you agreed to buy a one-year Treasury bond in six months. The bond
ID: 2745828 • Letter: T
Question
This morning you agreed to buy a one-year Treasury bond in six months. The bond has a face value of $1,000. Use the spot interest rates listed here to answer the following questions.
Suppose shortly after you purchased the forward contract all rates increased by 30 basis points. For example, the six-month rate increased from 3.71 percent to 4.01 percent. What is the price of a forward contract otherwise identical to yours given these changes? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.)
Time EAR 6 months 3.71 % 12 months 4.15 18 months 4.83 24 months 5.55
Explanation / Answer
a.
The forward price of an asset with no carrying costs or convenience value is:
Forward Price = S0 (1+R)
Since, You will receive the bond’s face value of $1000 in 18 months, we can find the price of the bond today
Current price of the bond = $1000 /(1.0483)^(3/2)
Current price of the bond is 931.69.
Since the forward contract differs delivery of the bond for 6 months. The Appropriate interest rate to use in the forward pricing equation is the six month EAR. Then the forward price is
Forward Price = 931.69 (1.0371) ^ (1/2) = $948.8155.
b.
It is important to remember that 100 basis points equal 1 percent and one basis point equals 0.01%.
Therefore, if all rates increase by 30 basis point, each rate increases by 0.003. So, the new price of the bond today is
New body price = $1000 / (1+0.0483+0.003)^(3/2) = $927.7052.
Since, the forward contract differs delivery of the bond for six months, the appropriate interest rate to use in the forward pricing equation is the six month EAR.
Forward Price = $927.7052 (1+0.0371+0.003)^(1/2) = $946.1229.
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