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Microsoft Word - MGTC71-PS2A

# Microsoft Word - MGTC71-PS2A - UNIVERSITY OF TORONTO AT...

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1 UNIVERSITY OF TORONTO AT SCARBOROUGH DEPARTMENT OF MANAGEMENT MGTC71: Introduction to Derivatives Markets Problem Set – 2 (Supplemental Questions) _______________________________________________________________________________ Interest Rate & Interest Rate Futures: Problem-1 A firm entered into a forward rate agreement with a bank. The firm agreed to pay the bank a semi- annually compounded interest rate of 4% per annum on a notional deposit of \$6 million for a 6-month period starting in two months. The current two- month and eight-month USD LIBOR rates are 2% p.a. and 2.5% p.a., respectively. What is the value of this forward rate agreement to the firm? Problem-2 a) You manage a portfolio of 10,000 5 years zero bonds with a face value of 1,000 and YTM of 5% continuously compounded. You think his portfolio is too risky and intend to bring its duration down to 0 by selling the original portfolio and reinvesting the proceeds into 3 months treasury bills. What is his new portfolio allocation (how much long (or short) in 5 years bond, how much in treasury bills). b) As a bond portfolio manager you have just sold 10,000 unit of 10 year zero coupon bonds with a face value of 1,000 and YTM of 8%. This manager wants to hedge his position and thinks one of three T- bonds will be cheapest to deliver; some data for these three bonds are as follows: Bond Quoted Price (\$) Conversion Factor Duration in March A 99.5 1.0382 12.4 years B 143.5 1.5188 13.2 years C 119.75 1.2615 15.7 b1) If the March futures bond price is quoted at 93-08 which bond is cheapest to deliver? Explain why by showing calculations. b 2 ) How should the portfolio manager use March T-bond futures to produce a new portfolio having an overall duration of zero? How many contracts? Long or short? Problem-3 A portfolio manager manages a bond portfolio of 5,000 5 years zero bonds with a face value of 1,000 and YTM of 3% continuously compounded. The standard deviation of the change in the yield is assumed to be 2%. You think his portfolio is too risky and intend to bring its duration down to 0 by selling the original portfolio and reinvesting the proceeds into 6 months treasury bills. What is his new portfolio allocation (how much long (or short) in 5 years bond, how much in treasury bills).

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2 b) The futures price for March T-bonds is 96-27. The manager of a \$100M bond portfolio, the duration of which will be 6.7 years in March, wishes to use these futures for hedging this portfolio. This manager thinks one of two T-bonds will be cheapest to deliver; some data for these two bonds are as follows: Bond Quoted Price (\$) Conversion Factor
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