Class Notes (809,637)
Finance (26)
MGFC30H3 (3)
Ata (3)
Lecture

Problem Set 2

10 Pages
179 Views

School
University of Toronto Scarborough
Department
Finance
Course
MGFC30H3
Professor
Ata
Semester
Fall

Description
UNIVERSITY OF TORONTO SCARBOROUGH DEPARTMENT OF MANAGEMENT MGTC71: Introduction to Derivatives Markets Problem Set – 2 (Supplemental Questions) _______________________________________________________________________________ Interest Rate & Interest Rate Futures: (Required for Test-1) 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 inMarch 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. b2) 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). 1 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 Duration inMarch A 111-22 1.1462 9.3 years B 106-26 1.0987 10.2 years b1) Which bond is cheapest to deliver? Explain why by showing calculations. b ) How should the portfolio manager use March T-bond futures to produce a new portfolio having an 2 overall duration of zero? How many contracts? Long or short? Verify your solution i.e. show that your new combined portfolio is perfectly hedged. Swap: (Required for Test-2) Problem-1 Suppose company A and B encounter the following borrowing terms: Fixed % Floating % Company A 3.6 LIBOR + 1 Company B 4.0 LIBOR + 2 A wants a fixed rate loan while B wants a floating rate loan. a) If the swap rate is 2.5%, show that both A and B would benefit from the swap. What is the gain? b) What is he maximum gain from swap? Find a swap rate that splits this gain evenly between A and B. Problem-2 Companies A and B face the following borrowing costs: Fixed rate Floating rate A 7% 6-m LIBOR B 9% 6-m LIBOR + 1% a) Explain any comparative advantage A and/or B mayhave in fixed rate and/or floating borrowing. If the two sides decide to engage in a swap what would be is maximum gain possible? b) Suppose B wants a fixed rate loan while A wants a floating rate loan. If the swap rate is 7.5%, show that both A and B would gain from the swap. What is the gain? Ignore Parts (a) and (b): Suppose the one-year zero rate is 4% and the 2-year zero rate is 6% both continuously compounded. Consider a 2-year, annual pay, fixed-for-floating interest rate swap between risk-free borrowers. a) Find the equilibrium swap rate as of today? 2 b) If after three months the zero curve flatten to 5%, what would be the value of the swap contract. Who gained and who lost? Problem 3: A Corp. wishes to be a floating-rate dollar borrower, which it can be at LIBOR + 1%. B Corp. strongly prefers fixed-rate debt, but it must pay 1.5% more than the 6.25% coupon that A’s notes would carry. a) If B Corp, can borrow LIBOR +1.5%. What is the maximum possible cost savings to A. from engaging in a currency swap with B.? What should be Swap rate for A. to enjoy this maximum gain? a) If B Corp, can borrow LIBOR +.5%. What is maximum gain from the swap trade? Suppose a bank charges 0.8% to arrange the swap and A and B split the resulting cost savings. How much A will pay for its floating-rate money and B will pay for its fixed-rate money Ignore Parts (a) and (b): Suppose the LIBOR spot rate are given by the table below. Consider a 3-year plan vanilla interest swap whose float payments are the LIBOR rate. Maturity LIBOR 1.0 1.0 2.0 1.5 3.0 2.0 a) Find the par swap rate? b) If after 6 months the yield curve flattens to 2%, what would be the value of the Swap contract. Who will lose and who will gain by how much? 3 Solutions Interest Rate & Interest Rate Futures Problem-1: We need the six-month forward rate but since we only learned the continuously compound version of the forward rate formula I first convert the 2 months and 8 months discrete zero rates to CC version, find the forward rate then convert the forward rate back to discrete version. 0.02 r2c= 6 ln(1 + ) 1.997% 6 0.025 r8c= 1.5 ln(1 + ) = 2.479% 1.5 f = 0.6667×2.479% −0.1667×1.997% = 2.64 c
More Less

Related notes for MGFC30H3

OR

Don't have an account?

Join OneClass

Access over 10 million pages of study
documents for 1.3 million courses.

Join to view

OR

By registering, I agree to the Terms and Privacy Policies
Just a few more details

So we can recommend you notes for your school.