Question

signment 0 Saved Help Save & 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. Time 6 months 12 months 18 months 24 months EAR 3.80% 4.24 4.92 5.64 a. What is the forward price of this contract? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g.. 32.16.) b. Suppose shortly after you purchased the forward contract all rates increased by 40 basis points. For example, the six-month rate increased from 3.80 percent to 4.20 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.) a. Forward price b. Forward price

Answer 1

Solution :-

(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,

Now Price of Bond Today

Current price of the bond = $1000 /(1 + 0.0492)^(3/2)

= $1,000 / 1.0747 = $930.49

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 = 930.49 * (1.0380)^1/2 = $930.49 * 1.0188

= $948.01

(b)

All rates increase by 40 basis point, each rate increases by 0.004. So, the new price of the bond today is

New body price = $1000 / (1 + 0.0492 + 0.004)^3/2

= $1,000 / 1.0753

= $929.96  

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 = $929.96 * ( 1 + 0.0380 + 0.004 )^6/12

= $929.96 * 1.02078

= $949.288

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