Hedge against changes in the level and the slope of yield

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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

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