It is March $1.$ You are managing a bond portfolio currently worth $$5$ million. In $6$ months, the duration of the portfolio will be $15$ years.

The June Treasury bond futures contract's price is $95-12$ and the cheapest to deliver

bond will have a duration of $10$ years on the first delivery date.

How would you hedge against rises in interest rates over the next $6$ months?

a$.$ Buy $52\mathrm{.}4246$ Treasury bond futures contracts

b$.$ Buy $78\mathrm{.}6370$ Treasury bond futures contracts

c$.$ Sell $78\mathrm{.}6370$ Treasury bond futures contracts

d$.$ Sell $52\mathrm{.}4246$ Treasury bond futures contracts