Only question 1 needs to be answered. Show your work/process to getting the answ
ID: 2802181 • Letter: O
Question
Only question 1 needs to be answered. Show your work/process to getting the answer.
MM=million
It is April 13, 2017. Consider the following Treasury yield curve YTM 3/31/19 2.00% 100.00 3/15/22 3.50% 100-00 2/28/27 4.75% 100-00 Maturity Price 2-year 5-year 10-year There are 2 portfolios, each with $100MM market value. Portfolio l: 5-year bullet. Portfolio Il: 2-year/10-year barbell. 1.) Today, you invest the $100MM in each portfolio, so that the portfolios have the same duration. The trades settle tomorrow. How much is invested in the 2-year and in the 10-year? Suppose on October 14, 2017 the 2-year ytm increases 50bp and the 10-year ytm increases 25 bp. 2.) What are the price and yield for the 5-year that produce the same realized total rate of return for the bullet and the barbell for this 6-month investment period? 3.) Discuss the issues/complexities involved with solving these questions.Explanation / Answer
Soln: A bullet portfolio is where all the principal is paid at maturity
For 5 year bullet portfolio the duration = maturity= 5 years as no coupon in between.
Barbell is startegy where one invest in risky short term bond along with investment in long term and safe bonds
As coupon rates are not given, we are considering that 2 year and 10 year also dont have nay coupon in between.
In that case their individual duration will be 2 and 5 years respectively.
Let x be the value invested in 2 year bond and 1-x in 10 year bond.
Duration of both the portfolio should be same.
Hence, we can say 2*x +(1-x) *10 = 5 or 8x = 5, x = 0.625
That is $62.5 million invested in 2 year bond and remaining 100-62.5 = 37.5 million invested in 10 year bond.
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