ONLY 5B

5a) An investor holds 1,000 2-year maturity zero coupon bonds with a face value of 1,000. They want to invest in a 1-year zero coupon bond (face value 100) and a 5-year zero coupon bond (face value 100) with the aim of using factor duration to immunize the portfolio against changes in the level and the slope of the term structure. Using the information below, calculate the number of 1-year and 5-year bonds that are held or shorted. The term structure is currently flat and the 2-year bond trades at 941.765 using continuous compounding. Factor sensitivities Level factor Slope factor 1-year maturity 0.7 2-year maturity 5-year maturity 0.7 0.7 -0.2 0.1 0.4 (30 marks) 5b) Suppose that there is a change in both the level and slope factors by the amount of -0.01 (di=-0.01 and d2=-0.01). Using the factor sensitivities given in the table in question 5a, what will be the new values of the interest rates at 1-year, 2-years and 5- years? Using continuous compounding, what will be the new prices of the 1-year, 2-year and 5-year zero-coupon bonds? Using your estimates of the holdings or shorting of the 1- year and 5-year bonds calculate the value of the portfolio before and after the change in the level and slope factors