Homework 3

due Feb 24 Wednesday

K Foster, Options & Futures, Eco 275, CCNY, Spring 2010

 

 

You are encouraged to form study groups to work on these problems.  However each student must hand in a separate assignment: the group can work together to discuss the papers and comment on drafts, but each study group member must write it up herself/himself.  When emailing assignments, please include your name and the assignment number as part of the filename.

Please write the names of your study group members at the beginning of your homework to acknowledge their contributions.

  1. Suppose a financial institution is creating synthetic Treasury "strips".  You set up a Special Purpose Vehicle that buys 100 Treasury bonds paying for 5 year s.  Each bond has $1m face value and pays $30,000 every 6 months.  This allows you to create 10 synthetic bonds paying $(3,000,000
     p) at some date in the next five years (and a zero-rate principal payment)
     each synthetic makes only one payment, making calculation of the zero rate simple.  The amount "p" is the price that you charge for these transactions.  If you charge 1bp what is the present discounted value of your fees for the transaction?      (Extra to think about: suppose one of those bonds defaults, 3 years into the deal
     what is the fairest way to spread the losses among the remaining synthetic payments?  Your lawyers will want to write up all of the "what if" statements.)
  2. The NYTimes (Feb 14, 2010, "Wall St Helped to Mask Debt Fueling Europe's Crisis"
     on Blackboard)     reported that Greece was enabled to hide some of its deficits through 'creative' utilization of financial contracts.  Consider a very simple example of a FRA between a country (call it Zembla, "Z") and "Stib" (Sharp-Toothed Investment Bank).  Assume current LIBOR forward for the period from 5 to 6 years into the future is 5%.  Both sides expect that the actual LIBOR in that same period will be 5.5% (assume neither side is fooled).  Assume that the principal is $1m.  Assume that money flows from Zembla to Stib after 6 years but Stib pays Zembla now.  What range of values for "RK," the rate of interest agreed in the FRA, would pay Zembla money now?  How much?  Explain the way(s) in which this is like and/or unlike a loan.
  3. Please complete Assignment Question 5.27 in Hull.
  4. Please complete Assignment Question 6.23 in Hull.
  5. Please complete Assignment Question 7.20 in Hull.
  6. Two riskless bonds for the same company are valued in the market (assume they are now riskless because the US government guarantees them!).  The first, with face of 10,000, pays this principal in six months.  It is currently worth 9875.78.  The second bond is a strip of the coupons, paying 500 in three months and then another 500 in six months.  It is currently worth 990.06.
    1. What is the six-month zero rate?
    2. What is the three-month zero rate?
    3. What is the three-to-six month forward rate?
  7. A portfolio of bonds includes the following:

§             Bond ZZZ pays a $4000 coupon every six months, including 6 months from today, 12 months from today, and 18 months from today.  It also pays its principal of $200,000 in 18 months at the same time as its last coupon.  Its current market value is $201,359.31.

§             Bond YYY pays its $8500 coupon in 6 months and then that coupon again in 12 months along with its $500,000 principal.  Its current market value is $499,342.04.

§             Bond VVV pays its principal of $600,000 plus its $8000 semi-annual coupon in 6 months.  Its current market value is $595,960.79.

a.      Find the six month zero rate (continuously compounded).

b.      Find the six-to-twelve month forward rate and the twelve month zero rate (continuously compounded).

c.       Find the twelve-to-eighteen month forward rate and the eighteen month zero rate (continuously compounded).

d.      Find the par yield for each bond.

e.      Find the semiannually-compounded (discrete time every 6 months) zero rates.

f.        What is the duration of bond VVV?

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