$4.$ You are a fund manager. A client sold her company for $$50,000,000$ and you expect the funds on August $18$th$.$ Today is May $5$th$.$ During this time, you expect the market to decrease. Your client desires a portfolio consisting of $70\%$ stock and $30\%$ risk free T$-$Bonds. The risk$-$free rate equals zero. The beta on the stock portfolio will equal one $(1).$ How can you use the futures market to hedge the portfolio?

Information: S&P on May $5$th closed at $4,000,$ AUG Future Price is $3,900.$

How much of the portfolio will be in stock and how much in risk$-$free bonds?

Describe the initial trade to hedge the portfolio using the S&P $500$ Index.

How many S&P $500$ contracts do you need $($Note: each contract $=$ $$250)?$

Information: On August $15$th S&P $500$ is $4,100.$

Describe the trade to close the position.

Did you earn a profit or loss? How much?

What is the value of the portfolio?

What are the benefits of having a portion of the portfolio is risk$-$free bonds?