Stock Hedging

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 and 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 $1\mathrm{.}3.$ Furthermore, suppose the risk$-$free rate is $3\%.$ Let's ignore

dividends entirely for this question.

What position in futures contracts would the investor take? $($positive for long,

negative for short$)$

$\frac{0}{1}$ point

Suppose the market drops by $5\%.$ Then, the investor will have outperformed the

market and locked in gains from the futures contract if the stock doesn't drop by

more than

$\%.$