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2. Assume that Treasury Securities with 10 years to mature, a face value of $100,000 and annual coupon payments = 4% of face value are selling today for $100,000 value in the spot market Assume that the price of a 3 - month futures contract based on a $100,000 Face Value 10 year T note with a 4% coupon is $101,500. Finally, assume that it is possible for well-collateralized institutions to either borrow or lend money for 3 months at periodic interest rate of .5%. Explain in detail what you would do to exploit the risk free arbitrage opportunity that exists at these spot and future prices. You may ignore transactions costs such as brokers fees. 4pts. a) b) What would your abtrage poit per contract he as long as the purchases and sales you used to set up your arbitrage position did not change the futures price or the underlying T-Note price? 2pts Explain why the futures price and underlying price in the T-Note and T-Note would not remain at their current levels for long? 4pts c)Explanation / Answer
(a) 10 Year T-Note Futures Price = $ 101500 and current price of 10 Year T-Note = $ 100000.
Peiodic Interest Rate =0.5%
Using , the cost of carry model, expected future spot price = Current Spot Price x (1.005) = $100500
Since the current spot price is below the expected future price, the market is in contango (wherein the future/forward price is greater than the expected future spot price) and a cash and carry arbitrage can be executed to generate riskless profit as given below:
- Borrow $ 100000 at the periodic (3-month) interest rate of 0.5%.
- This borrowing would become a liability worth (100000 x 1.005) = $ 100500 after three months
- With the borrowing purchase one 10 year T-Note and sell one 10 year T-Note future contract with maturity of 3 months
- The T-Note purchased at $100000 can be sold under the 3 month futures contract at the futures price of $101500.
Thereby this purchase and subsequent sale 3 months later will generate a profit = 101500 - 100000 = $1500
The investor will have to pay a portion of this profit to cover the interest on the initial borrowing of $100000 (made to purchase the T-Note). Interest on the initial borrowing = 0.005 x 100000 = $ 500
Therefore, riskless arbitrage profit generated = Profit made from purchase and sale - Interest on Initial Borrowing
= 1500 - 500 = $1000
(b) The arbitrage profit per contract will be equal to $1000 as demonstrated in part (a)
(c) As more and more people start buying the T-Note using borrowed money, its demand will increase and so will its price. Similarly, as more people start selling the T-Note futures its supply will increase and price will fall. The two prices will soon converge to eliminate the opportunity of generating riskless arbitrage profit through execution of a cash and carry arbitrage.
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