14 Jun Question only answer question part2, part3 and part4 is
Question
only answer question part2, part3 and part4 is okay
Part 3: Steepener Trade
For this part, use the Fama-Bliss tab in hw1data.xls. This file contains zero-coupon yields (reported in %). For simplicity, assume that the yields are annually compounded.
It is November 30, 2010 and you hold a $1mm (market value) long position in the 1-yr zero-coupon bond. Using modified durations, determine how much of the 5-yr zero- coupon bond you need to short so that your portfolio remains approximately unchanged if the 1-yr and 5-yr zero rates move in parallel. This is known as a steepener trade – you profit if the yield curve becomes steeper. What is the market value of your portfolio?
What actually happens during the following month? Calculate the value of your portfo- lio. A 1-yr bond is now an 11-month bond and a 5-yr bond becomes a 4-year 11-month bond. Assume for pricing purposes that the 5-yr rate applies to the 4-yr 11-month bond and the 1-yr rate applies to an 11-month bond when calculating bond prices. Why did your portfolio value change from before?
What would the change in your portfolio value have been if the 1-yr rate had stayed the same and the 5-yr rate had gone down by 0.5 percentage points?
Part 4: The Bootstrap Method
In practice, we can also derive a zero curve from market prices of Treasury securities, using the bootstrap method. Consider the data in the following table on a bond dealer’s quotes of five Treasury bills/notes. Note that the first two bills pay no coupons.
Bond principal ($) Time to maturity(years) Annual coupon ($) Bond price
100 0.50 0.0 98
100 1.00 0.0 95
100 1.50 6.2 101
100 2.00 8.0 104
Half the stated coupon is assumed to be paid every six months.
Calculate(semiannually-compounded)zeroratesformaturitiesof6months,12months,
18 months, and 24 months.
Estimate the price and yield of a 2-year bond providing a semiannual coupon of 7% per annum.
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