For this part, use the Fama-Bliss tab in hw4data.xls. This file contains zero-coupon yields (reported in %).
1. It is August 29, 2003 and you hold a $1mm (market value) long position in the 1-yr zero-coupon bond. Using modified durations, determine how much of the 5-yr zero- coupon bond you need to short so that your portfolio remains approximately unchanged if the 1-yr and 5-yr zero rates move in parallel. This is known as a steepened trade – you profit if the yield curve becomes steeper.
2. What actually happens during the following month? Calculate the value of your portfolio. A 1-yr bond is now an 11-month bond and a 5-yr bond becomes a 4-year 11-month bond. Assume for pricing purposes that the 5-yr rate applies to the 4-yr 11-month bond and the 1-yr rate applies to an 11-month bond when calculating bond prices. Why did your portfolio value change from before?
3. What would the change in your portfolio value have been if the 1-yr rate had stayed the same and the 5-yr rate had gone up by 0.25 percentage points?