2. Assume that Treasury Securities with 10 years to mature, a face value of $100
ID: 2803630 • Letter: 2
Question
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 man 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 norths at a 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. What would your arbitrage profit per contract be 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 a) b) c)Explanation / Answer
The $ 100,000 face value bond has annual coupon of 4%, maturity of 10 years and spot sale price of $ 100,000 - this means that the ytm is equal to the coupon rate. Hence, in 3 months the value of this bond should increase by interest accrual which shall (100,000 * 4% / 4) = $ 1000. Hence the expected price of the bond should be $ 101,000 after 3 months. Since the borrowing or lending rate for 3 months is given as 0.50%, if one was to borrow and invest in this bond, then the pay of holding the bond for 3 months would be (101000 - (100,000*(1+0.50%)) = $ 500.
However we are given that the 3 months future contract is available with similar charecteristic bond for $ 101,500, thus we can use the different future and spot prices as below:
(i) First borrow $ 100,000 at 0.50% for 3 months, and purchase the bond in sport market. (ii) Sell the same bond in the futures market at the current future price of $ 101,500 (iii) At the end of 3 months, give the delivery of the bond to the buyer of the futures contract and receive the sale consideration of $ 101,500 (iv) Use part of these sale proceeds to pay off the debt taken to purchase the bond. The balance left over shall be the risk free arbitrage profit.
The risk free arbitrage (assuming that the spot & futures prices do not change and ignoring the transaction costs) pay off shall be below:
(a) Cost of borrowing $ 100,000 at 0.5% for 3 months = (100000*0.50%) = $ 500
(b) Profit on sale of bond (locked in by selling in futures) = $ 1500
(c) Hence arbitrage pay off = $ 1000
However, this cannot continue forever since as more and people spot this opportunity, they will sell in the futures and push the price down and at the same time, purchase in spot and push the price of bond in spot up. Eventually the arbitrage will be finished
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