2. A) Formulate mathematically factor duration, clearly defining the terms you use. B) Using the continuous time pricing formula and the chain rule of differentiation to derive mathematically the factor duration for a zero coupon bond. C) Hence, calculate the factor duration of a 6-month zero coupon bond with respect to the slope of the term structure using the table of factor sensitivities given below. Zero-coupon Maturity 6 months 1 year 2 years 4 years Factor Level Slope Curvature 1.1 1.0 1.0 1.0 -0.2 -0.1 0.1 0.2 -0.3 0.1 0.1 -0.4 D) An investor holds 100 one-year zero coupon bonds at a price of 97.50. The investor is concerned that the curvature of the term structure will become more pronounced affecting the value of her portfolio. If the price of a four year zero- coupon bond is 90, how many of these bonds does she have to buy or sell to immunize her portfolio to changes in the curvature of the term structure? [25%]