Q4.16. You currently hold a 3-year fixed rate bond paying 5% annually. You would like to hedge against changes in the level and the slope of the yield curve and you plan to use a 1-year zero coupon bond and a 7-year zero coupon bond. Use the following table to compute the adequate positions in the hedging instruments [Hint: (1) calculate the factor durations (D₁ and D₂) of a 3-year coupon bond with factors 1 and 2 based on the equation on p.40 in Ch 4, (2) calculate the factor durations (D^S₁, D^S₂, D^L₁, D^L₂) of 1-year and 7-year zero coupon bonds, respectively (3) compute numbers (K_S and K_L) of required positions in 1-year and 7-year zero coupon bonds by using the equations on p.43 in Ch4.].

maturity	1	2	Z(t,T)
1.00	1.1150	-0.2540	0.9800
2.00	0.9940	-0.3010	0.9600
3.00	0.9640	-0.1470	0.9300
4.00	0.9330	0.0080	0.8900
5.00	0.9300	0.1620	0.8500
6.00	0.9260	0.3160	0.8100
7.00	0.9270	0.4230	0.7700
8.00	0.9270	0.5300	0.7300