In February, Lucinda Leon, a portfolio manager for a prominent insurance company is managing a stock portfolio of $$800$ million with a portfolio beta of $1\mathrm{.}30.$ She plans on selling the stocks in the portfolio in June to be able to pay out funds to policyholders for annuities, and is worried about a fall in the stock market. In February, the CME Group E$-$Mini S&P $500$ Futures contract index is $5037\mathrm{.}25$ for a June futures contract $($$$50$ multiplier for the contract$).$

a$.$ What type of futures position should be taken to hedge against the stock market going down and how many future contracts are needed for this hedge?

$[$Hint: # contracts $=[$Amount Hedged $/$ Futures Index Price x Multiplier$]$ x Beta Portfolio

Type of Position $\_\_\_\_\_\_\_\_\_\_\_\_\_$

Explain why $\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_$

# of Contracts$\_\_\_\_\_\_\_\_\_\_\_\_\_$

b$.$ Suppose in June the stock market $($S&P$500$ index$)$ has fallen by $10\%$ and the S&P$500$ futures index has fallen by $10\%$ as well, what is the portfolio manager$$s opportunity loss $($gain$)$ on his portfolio, and his futures gain $($loss$)$ and the net hedging result?

Spot Gain or Loss $\_\_\_\_\_\_\_\_\_\_\_\_$ Futures Gain or Loss $\_\_\_\_\_\_\_\_\_\_\_$

Net Hedging Result $\_\_\_\_\_\_\_\_\_\_\_\_\_$