Economics Help?

Question

Assume that a Treasury Security with 10 years to mature and annual coupon payments = 6% of its face value is selling today at its face value in the spot market. Assume that the price of a 10 year T- Note futures contract due to expire in 6 months is $98,500 per 100,000 of face value. Finally, assume that it is possible for well-collateralized institutions to either borrow or lend money for 6 months at an annualized interest rate of 5 %. Is there an opportunity for risk free arbitrage here? If so, explain what you would do to exploit it. If not, explain why not. You may ignore transactions costs such as brokers’ fees.

Answer 1

Ok, assuming the Treasury Security is a T-Note, I would:

1) shortsell the T-Note at $100,000 face value today and receive $100,000 now.

2) Lend this money for 6 months at the annualized interest rate of 5%, so that in 6 months I would receive 100,000*(1+0,05/2)=$102,500.

3) Buy the T-Note futures contract (for $100,000 of face value) now. That means that in 6 months, I would be able to buy the T-Note I need to fulfill my obligation from shortselling at $98,500 plus $3,000 accrued interest, i.e. for a total price of $101,500.


Hence, my cash flow today would be $0:
+100.000 from shortselling
-100.000 from lending
= 0

In 6 months, my cash flow would be $1,000:
+102,500 from the 100,000 lent plus interest
-101,500 from paying for the T-Note under the futures contract
=1,000

These $1,000 in 6 months would be my profit from exploiting the risk free arbitrage opportunity.

Answer 2

ummmm, y did u ask this question 5 times...