Jon Snow is managing a $5 million portfolio of corporate bonds. The duration of the portfolio today is 5.91 years and in six months it is expected to be 6.22 years. The 6-month Treasury bond futures contract is trading at USD 99.11.
The cheapest-to-deliver bond has a duration of 3.93 years today and an expected duration of 4.31 years at the maturity of the futures contract.
How many futures contracts should Jon short to hedge against changes in interest rates over the next six months?
Each futures contract is of USD 100,000 face value of bonds.