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# In this question all quoted yields and coupon rates are rates per annum, payable semi-annually

1. ### In this question, all quoted yields and coupon rates are rates per annum, payable semi-annually.

A borrower is about to issue a security with a face value of \$500,000,000. It is an unusual security that features a payment holiday for 9 months. The borrower will receive the proceeds from issuing the amortizing note on 1 November 2017. The first payment of interest and principal will be made nine months later, on 1 August 2018, with subsequent equal payments being made each February 1 and August 1 up to and including 1 August 2028 (i.e. all payments after the holiday period will be the same size; there is no bullet maturity). Hereafter this security will be referred to as the “amortizing note” or the “amortize.”

Given the borrower’s credit rating and the general level of interest rates, the note will be priced to yield 5% per year compounded semi-annually. That is, the fixed interest rate used to compute the payment amount will be 5% per year payable semi-annually. The price at this yield will be par (i.e. 100% of principal value) on 1 Nov 2017.

A) Under the above terms, how much are the payments the borrower must make on each payment date from 1 Aug 2018 through 1 Aug 2028? Note that this is a bit more complicated than it appears at firstglance, given the first period (Nov 1 – Feb 1) is a “stub” period. You may assume that this period is exactly 0.25 years.

B) Given the payment size computed in A, make an amortization schedule for the security. (An amortization schedule is a table that breaks the payments into their principal and interest components and shows the remaining principal balance after each payment. If carried out through the final payment, the schedule should reveal a remaining balance of zero, assuming your answer to part A is correct.)

C) Suppose you are the underwriter of this deal and you are going to buy the entire amount of the amortizing note on 1 November 2017 and then sell it to investors. Because this security is non-standard, you think it will take several days to be sold. Consequently, you want to hedge your interest rate exposure on the transaction.

You have identified four government bonds that are candidates for use as a hedging bond. The candidates have the following characteristics:

 Coupon Maturity YTM Bond 1 5.50% 1-Jun-18 3.25% Bond 2 6.00% 1-Dec-21 3.50% Bond 3 6.00% 1-Jun-24 3.65% Bond 4 5.00% 1-Dec-26 4.00%

Which of one these four bonds has an interest rate risk profile that most closely resembles that of the amortizing note? Why? You may find Excel functions like DURATION and M DURATION useful here. Just keep in mind that the functions work for standard issues (semi-annual pay coupon with face value paid at maturity). The amortizing note is NOT standard, but the above bonds are standard. Assume the day count convention used is Canadian convention and that the settlement date for all transactions is 1 November 2017.

D) What is the par value of the hedge bond you chose in part C that must be sold to offset the interest rate risk of the investment dealer will face by purchasing the \$500MM position in the amortizing note? Assume the amortizing note is priced exactly at par with no accrued interest on the initial settlement date.

E) Suppose your boss told you to construct a hedge using Bond 2 and Bond 4 from the list provided in part C rather than using a single bond as you did above. She wants the hedge to be insensitive to both parallel shifts in the yield curve, as well as changes in the slope of the yield curve. What positions would you take in the named bonds? State the par value amount you would use of each bond and the direction (i.e. long or short) of the position taken.

F) Suppose you set up the hedge as you worked out in part E. Thus, you now own the amortizing note and have positions in Bond 2 and Bond 4. Suppose there is a large parallel shift in the yield curve. Given your position, will you make money, lose money, or have no change? Does your answer differ if you learn it is a large upward shift in the yield curve rather than a large downward shift? No calculations are required here.

G) Now suppose you chose to hedge the interest rate risk of the amortizing note by selling an appropriate amount of a zero-coupon bond that matures in exactly 20 years that yields 5.50% (APR payable semi-annually). After appropriately constructing a hedge with this security, what type of risk do you have in addition to the exposure to the credit spread? Provide a brief explanation.

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2) Frequently we observe two Government of Canada bonds that have the same payment dates. An example of such a pair is CAN 1.0 1-June-2027 (first issued July 2016) and CAN 8 1-June-2027 (first issued Apr 1996). The quoted yields on these two bonds, assuming a trade settlement date of 29 Sep 2017, are 2.125% and 2.115%, respectively, where yields are quoted under standard Canadian convention. As with any government bonds, these bonds can be “stripped.” That is, these bonds can be decomposed into their constituent cash flows (known as “coupons” and the “residual” and, collectively, “strips”) and the pieces sold off separately as zero-coupon bonds. There is a reasonably liquid market for stripped coupons and residuals in this country (and others). A property of such component pieces is that they are fungible. That is, zero-coupon bonds that are sourced from coupon payments of the original bonds are interchangeable regardless of what bond they originally came from. The residuals are also fungible. This fungibility allows for reconstitution of the original bonds: if you can find enough coupons and a residual to reconstitute an entire bond, you may do so and trade the package as a whole bond again.

A) Think like a trader. Given the noted yields and the 29 Sep 2017 settlement date, what should the price and yield of a “residual” maturing on 1-June-2027 be in a well-functioning market? You can ignore transaction costs and bid-offer spreads in your analysis.

B) Suppose you observe that you can transact in the residual maturing 1-June-2027 at a yield of 2.25%. Is there an arbitrage opportunity? If so, how would you execute a trade to exploit it?

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