XYZ Securities Economic Forecasting Department has predicted that the yield curve will steepen (long term rates will increase relative to short rates and/or short rates will decline relative to long rates). However, it is unable to say with any confidence at all what will happen to the overall level of interest rates (i.e. whether any parallel shift of the yield curve will be up or down.)
You have been asked to design a position that will profit if the prediction of the steepening yield curve is correct, but will not create a loss (or a profit) as a result of any one-time parallel shift of the yield curve. More specifically, the position is to be designed so that:
1. A (small) one-time equal change in the two yields will produce neither a profit nor loss.
2. A 1 basis point increase in the spread between the ten-year and two-year notes (for example, if the two year yield drops one basis point while the ten year is unchanged) will create a profit of $1,000.
As part of its ongoing trading and market-making function XYZ Securities maintains a portfolio that is particularly deep in ten-year and two-year treasury notes. Thus you have been asked to construct the position using these two securities. Current data shows the on-the-run two-year note carrying a 2% annual coupon (split into two equal payments made every six months) and yielding 1.555%. The on-the-run ten-year note has a 4% coupon and yields 3.697%. Write a memo describing how to implement the position. In particular address the following questions:
1. What are the durations of the two year and ten year notes? Note that because the yields and coupon rates differ, the prices will not equal the face value. [Answer: 1.97 years and 8.37 years. Verification left for practice.]
2. What is the basic structure of the position?
a. Do you buy (sell) the two-year note?
b. Do you buy (sell) the ten-year note?
3. What is the relative size of the positions in the two instruments? That is, for every dollar's worth of ten-year notes bought (or sold), how many dollars' worth of two-year notes are bought (or sold)? [Hint: Note that in order to satisfy objective (1) the two positions must effectively hedge each other.]
4. What is the absolute size of the position in the two instruments? [Hint: Consider for each instrument individually how large the position would need to be to satisfy objective (2). It might help to consider the case when the yield curve steepens because the ten-year rate increases by .01% while the two-year rate is unchanged. Or, conversely, if the ten-year rate is unchanged while the two-year rate falls by .01%.]
a. How many dollars' worth of two-year notes should be bought (or sold)?
b. How many dollars' worth of ten-year notes should be bought (or sold)?
5. Demonstrate that the position is hedged against an equal change in two-year and ten-year rates.