You currently hold a 7-year fixed rate bond 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.

Maturity              β₁                                   β₂                          Z(t, 1)

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