5a) An investor holds 1,000 2-year maturity zero coupon bonds with a face value of 1,000....

 

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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 4-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 4-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.< 2 2 t Factor sensitivities< Level factor Slope factor 1-year maturity 0.7< -0.2¹ 2-year maturity 0.74 0.1 4-year maturity 0.74 0.4 5b) Suppose that there is a change in both the level and slope factors by the amount of 0.01 (do₁=0.01 and do₂=0.01). Using the factor sensitivities given in the table in question5a, what will be the new values of the interest rates at 1-year, 2-years and 4-years? Usingcontinuous compounding, what will be the new prices of the 1-year, 2-year and 4-year zero-coupon bonds? Using your estimates of the holdings or shorting of the 1-year and 4- year bonds calculate the value of the portfolio before and after the change in the level andslope factors.< 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 4-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 4-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.< 2 2 t Factor sensitivities< Level factor Slope factor 1-year maturity 0.7< -0.2¹ 2-year maturity 0.74 0.1 4-year maturity 0.74 0.4 5b) Suppose that there is a change in both the level and slope factors by the amount of 0.01 (do₁=0.01 and do₂=0.01). Using the factor sensitivities given in the table in question5a, what will be the new values of the interest rates at 1-year, 2-years and 4-years? Usingcontinuous compounding, what will be the new prices of the 1-year, 2-year and 4-year zero-coupon bonds? Using your estimates of the holdings or shorting of the 1-year and 4- year bonds calculate the value of the portfolio before and after the change in the level andslope factors.<