Joyce is a fund manager at Excel International Investment Limited. Today, beginning of $2023,$ Excel International holds a portfolio of $66,800$ stock funds including CoffeeBean. This portfolio had a value of $$1$ million in $2022,$ today the value has increased by $25\%.$ The recent political and economic uncertainty in Ukraine and Palestine is perceived to decline the value of the portfolio. Joyce suggests hedging the portfolio using an S&P $500$ stock index futures contract. The historical index in $2022$ was $1200$ points, today is $1,600$ points and one contract is for delivery of $$60$ times the index. The beta of the stock portfolio is $1\mathrm{.}3.$

a$)$ What strategy should the manager follow to hedge the portfolio against the index futures?

b$)$ What action should the manager take to reduce the beta of his portfolio to $0\mathrm{.}6?(5$