- Consider again these same three markets with today?s market values of their respective prices. A mortgage lender has just originated a twenty year, interest-only Canadian mortgage with a balance of $500,000.00 and an announced annual mortgage coupon rate, ?, of 6%. He offers to sell either you or your classmate, today, a security composed of a single three-month coupon plus a single six-month coupon, each of which could be traded on an individual basis in these markets.1
- What should you offer to pay for this security today?
- What would your classmate offer to pay for this same security if he used the announced annual coupon rate of 6% to calculate its present discounted value?2
- To whom would the lender sell the security?
- If your classmate buys the security at the price he calculates for its present discounted value, how much does he gain or lose (in dollars today) relative to what he would have paid by using the market prices in the three coupon markets above?
- Since you can trade in today?s markets for three-month and six-month coupons, you decide you can make an arbitrage profit from your classmate?s purchase by offering to trade each of the three- month and six-month coupon payments composing the security he now owns. Assuming you and he limit your trading to just one coupon of each maturity, determine (i) how much of a profit you could make and (ii) whether you buy or sell the three-month coupon you trade with him and, analogously, whether you buy or sell the six-month coupon you trade with him.
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