A large mutual fund holds $100,000$ shares of Alphabet $($Google$)$ common stock, which is

currently trading at $$1,\frac{202}{?}$ share with a beta of $1\mathrm{.}15.$ The CME Group E Mini Dow

futures contract trades at $$5$ times the index, which for the June contract is at $25,542.$

a$.$ The fund managers are worried about the volatility of the tech stocks in their

portfolio, so they want to hedge. Construct a hedge position $($short or long$)$ on the

basis of this fear.

b$.$ In June, their fears are realized. Alphabet has underperformed the market, closing at

$$1175$ while the index is at $26,056.$ Calculate the performance of the hedge by

computing the change in the portfolio position and the change in the futures position.

Was it successful? Explain.