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UNIVERSITY OF TORONTO AT SCARBOROUGH
DEPARTMENT OF MANAGEMENT
MGTC71: Introduction to Derivatives Markets
Problem Set – 2 (Supplemental Questions)
_______________________________________________________________________________
Interest Rate & Interest Rate Futures:
Problem1
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 $6 million for a 6month
period starting in two months. The current two month and eightmonth USD LIBOR rates are 2% p.a.
and 2.5% p.a., respectively. What is the value of this forward rate agreement to the firm?
Problem2
a) You manage a portfolio of 10,000 5 years zero bonds with a face value of 1,000 and YTM of 5%
continuously compounded. You think his portfolio is too risky and intend to bring its duration down to 0
by selling the original portfolio and reinvesting the proceeds into 3 months treasury bills. What is his new
portfolio allocation (how much long (or short) in 5 years bond, how much in treasury bills).
b) As a bond portfolio manager you have just sold 10,000 unit of 10 year zero coupon bonds with a face
value of 1,000 and YTM of 8%. This manager wants to hedge his position and thinks one of three T
bonds will be cheapest to deliver; some data for these three bonds are as follows:
Bond
Quoted Price ($)
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 9308 which bond is cheapest to deliver? Explain why by
showing calculations.
b
2
) How should the portfolio manager use March Tbond futures to produce a new portfolio having an
overall duration of zero? How many contracts? Long or short?
Problem3
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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b) The futures price for March Tbonds is 9627. The manager of a $100M bond portfolio, the duration of
which will be 6.7 years in March, wishes to use these futures for hedging this portfolio. This manager
thinks one of two Tbonds will be cheapest to deliver; some data for these two bonds are as follows:
Bond
Quoted Price ($)
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 Spring '11
 mazaheri
 Management

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