A corporate takeover bid is often pursued in stages as the acquiring firm seeks a

controlling interest in the acquisition. A company, company A$,$ has identified company B as

an acquisition target. B$\text{'}$s stock is currently trading at $$73$ per share. If word leaks, then the

stock price will likely be driven up$,$ increasing the cost of the acquisition. The firm therefore

wants to hedge against this possibility.

a$.$ The company wants to buy $100,000$ shares on December $17.$ Company B$\text{'}$s stock

currently has a beta of $2.$ March contracts on the S&P $500$ are trading at $2807,$ with a

multiplier of $$250$ times the index price. Based on this, construct an optimal hedge

using the March S&P contract.

b$.$ On December $17,$ B$\text{'}$s stock is trading at $$76\mathrm{.}50$ and the March futures price is $2842.$

Calculate the additional cost of the shares as well as the gain$/$loss on the futures

position. Was the hedge successful? Explain.