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Q: Finance ( Answered 5 out of 5 stars,   0 Comments )
Subject: Finance
Category: Business and Money > Finance
Asked by: sophisticated1-ga
List Price: $20.00
Posted: 12 Oct 2006 19:27 PDT
Expires: 11 Nov 2006 18:27 PST
Question ID: 773073
I need "EITHER" a Discussion "OR" mathamatical calculations for this
particular question.

If I entered into a forward contract to buy a 10 year, zero coupon
bond that will be issdued in one year. The face value of the bond is
$1000, and the 1 year and 11 year spot interest rates are 4% per annum
and 9%, respectiviely. Both of these interest rates are expressed as
effective annual yields (EAYs).
(Calculations would be to answer A and B)
A. What is the forward price of your contract?
B. Suppose both the spot rates unexpectively shift downward by 1%,
what would be the price of a forward contract identical to mine?


(A discussion would be to answer the following questions.)
1.What financial concept or principle is the problem inquiring about?
2. With the context of the problem in mind, what are some business
decisions that a manager would be able to make with solving this
3. Is there any additional information that would enhance the decision
making process within this questions?
4. Without showing any math calculations, in writing how would this
problem be solved?
Subject: Re: Finance
Answered By: elmarto-ga on 13 Oct 2006 06:46 PDT
Rated:5 out of 5 stars
I will give you the mathematical calculations you need in order to
solve this problem.

Part A
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.

Best wishes!
sophisticated1-ga rated this answer:5 out of 5 stars
Thanks alot for everything, the info for research on this problem is
excellent just as the mathmatical solution!!

There are no comments at this time.

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