On December $1,$ an investor holds $50,000$ shares of a certain stock. The market price is $$30$ per share. The investor is interested in hedging against movements in the market over the next month an decides to use an index futures contract. The index futures price is currently $1,500$ and one contract is for delivery of $$50$ times the index. The beta of the stock is $1\mathrm{.}3.$ What strategy should the investor follow? Under what circumstances will it be profitable?