A fixed$-$income money manager has a bond portfolio of BB$+$ corporate bond with market value $$100$ million and a duration of $4\mathrm{.}48$ years.

The manager wishes to cross$-$hedge the bond portfolio against interest rate risk.

There is a futures contract on a portfolio of AAA bonds available which the manager decides is the best hedge. The portfolio of AAA bonds has a value of $$27,483$ and a maturity of $5\mathrm{.}89$ years.

How many short futures contract should the manager enter into for a hedge against the market moves for the BB$+$ corporate bond portfolio?