**Finance 462
**

**Problem Set #6
**

1) Suppose that you take a 3 month long position in a cocoa future at a price of $1,803 per metric ton (the standard future size is 10 metric tons). Upon expiration of this future, cocoa is selling for $1,790 per metric ton. What is your profit/loss for this future?

2) Prove that the dollar duration of a 90 day T-Bill Future is $2,500 (recall that a 90 day T-Bill future calls for delivery/purchase of a 90 day T-Bill with $1M of face value). To do this,

a) Calculate the change in the discount yield for every 1 point change in the IMM index.

b) Calculate the change in price (per $100 face value) for the change in DY from (a)

c) Scale that up to the contract size of $1M

3) Suppose that we have the following yield curve:

Term |
Yield |

90 Days |
2% |

180 Days |
3% |

1 year |
4% |

A T-Bill future with an expiration date six months from now currently has a price of 93. IS there a profit opportunity here and, if so, what would you do?

4) Why do holders of Treasury bond/note futures have to worry about “conversion factors”?

5) Suppose that you are currently holding a 3 year corporate bond (non-callable) with a face value of $5M and an annual coupon of 8%.

a) Calculate the dollar duration of this bond assuming that is currently selling at par value.

b) How would you hedge your interest rate risk with T-Bill futures (i.e., what position and how many contracts).

c) Suppose that you learned that short term interest rates were less volatile that long term rates. How would this affect your answer to (b)?