I will give you the mathematical calculations you need in order to
solve this problem.
In order to get the price of the contract, we should first find the 1
year forward 10-yr interest rate. That is, we need to find what is the
expected spot 10-yr rate one year from today. This value can be found
using arbitrage arguments. The 11-yr rate today is 9%. Therefore, an
11-year investment of $1 today would return
1.09^11 = 2.5804...
in 11 years. This investment is equivalent to investing $1 today for 1
year (at the spot 1-yr rate) and then, at the end of the 1st year,
reinvest it for 10 years, at whatever spot rate that holds at that
time. That rate is the 1 year forward 10-yr rate, and should be such
that the returns from both investments are equal. The return from this
investment would be:
Therefore, the forward 10-yr rate comes from this equation
1.09^11 = 1.04*(1+r)^10
(1+r )^10 = (1.09^11)/1.04
r = ((1.09^11)/1.04)^(1/10) - 1 = 0.09513...
So the 1 year forward 10-yr rate is approximately 9.51%. So the
present value of an investment that returns $1,000 in 10 years,
discounted at this rate, would be:
1000/(1.09513)^10 = 403.03
Therefore, in one year you would pay $403.03 for the 10-yr bond.
That's exactly the forward price of the contract.
b. We must recalculate the 1 year forward 10-yr rate. Using the same
reasoning as before, we find that it will be:
r = ((1.08^11)/1.03)^(1/10) - 1 = 0.08513...
The forward rate will thus fall to 8.51%. So the forward price of the
contract will be:
1000/(1.08513)^10 = $441.75
As you can see, since the forward rate falls as a result of the
decrease in the spot rates, this will cause the price of the bond to
You can find a summary on bond pricing methods in the PowerPoint
presentation at the following link:
A Primer on Bond Pricing
Google search terms
bond foward pricing
I hope this helps! If you have any doubt regarding my answer, please
don't hesitate to request clarification before rating it. Otherwise, I
await your rating and final comments.