Hi bluesteel!
The fair value of a futures contract should be given by the following formula:
F = S*(1+r)^t
where F is the futures contract value, S is the spot value of the
underlying asset (in this case, the value of the note), r is the
risk-free interest rate, and t is the time to maturity (in this case
it will be 1/4, assuming that the 1.75% rate is annual, expiration is
1/4 of a year from now).
We'll see the rationale for this formula in a moment. In your case:
S = 115
r = 0.0175
t = 0.25
so the futures contract should be valued at 115*(1.0175)^(0.25) =
115.5, or 115-16 in 32nds. Since the futures contract is valued at
115-18, there is an arbitrage opportunity (ignoring, of course,
transaction costs).
In order to take advantage of the opportunity, you should:
1. Sell the futures contract, and buy the note, borrowing $115.
2. On the expiration date, hand over your treasury note, receiving $115-18
3. At the same time, repay your $115 debt. You will owe
115*(1.0175)^(0.25)=115-16. You have thus realized a 2/32 ($0.0625)
risk-free profit
Now the reason for the fair value formula shoud be clear. When the
futures contract is valued above it, there exists, as we've just seen,
an arbitrage opportunity. Similarly, if the futures contract is priced
below the fair value, again an arbitrage opportunity exists, buying
the futures contract, shorting the note and lending the $115 proceeds
of this sale at the risk-free rate.
For more details, you may want to go to the following links
Rational Pricing (go to Futures section)
http://www.answers.com/topic/rational-pricing
Futures Arbitrage
http://pages.stern.nyu.edu/~adamodar/New_Home_Page/invfables/futurearb.htm
Google search terms
futures pricing arbitrage
://www.google.com/search?hl=en&lr=&q=futures+pricing+arbitrage
I hope this helps! If you have any doubts regarding my answer, please
don't hesitate to request clarification before rating it; otherwise I
await your rating and final comments.
Best wishes!
elmarto |
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