It is currently June 1st. The price of a Dec. 1 future for $100 FV of a 10-year government coupon bond is $80. The contract size for this future is $100,000.

Suppose you go short 2 contracts of this future, and the price of the future then moves from $80 to $82. What is your profit on this position?

Suppose that this price movement from $80 to $82 happened due to the interest rate factor decreasing by 1%. If the $-Duration of a banks assets liabilities is currently 8M, can the bank hedge by shorting, or longing this future (write short, or long).

To get as close to perfect hedge as possible, how many contracts of this future should the bank trade?