In this one, we are going to explore the effect of interest rate shifts in portfolios. Consider two zero coupon bonds. Bond A has a maturity of 5 years with a ytm of 5% and bond B has a maturity of 15 years with a ytm of 7%. Both have $100 face value.

a. Create a portfolio that consists of one of bond B and enough of bond A such that the dollar duration of the portfolio is zero. How many of bond A do you need to buy or sell? How much does the portfolio cost you on net?

b. What is the value of this portfolio if there is a parallel shift in the yield curve up 2 percentage points (ie yields for all maturities increase by 2 percentage points)?

c. What is the value of this portfolio if there is a parallel shift in the yield curve down 2 percentage points (ie yields for all maturities decrease by 2 percentage points)?

d. What is the value of this portfolio if only the yield for 15 years increases by 4 percentage points?

e. If you believe short term interest rates will rise relative to long term interest rates, what trade should you make to take advantage, but still protect yourself in the event of a parallel shift in the yield curve?