In October, the portfolio manager for the SF Corporation has a stock portfolio of $ 5 million with a portfolio beta of 1.30. The portfolio manager plans on selling the stocks in the portfolio in December to be able to pay out funds to policyholders for annuities, and is worried about a fall in the stock market. In December, the CME Group E-Mini S&P 500 Futures contract index is 3039.00 for a December futures contract ($50 multiplier for the contract).

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?

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

What type of position to take and why long or short:

What is the beta portfolio here and how do you find that?

What is the # of Contracts?

If in December the stock market (S&P500 index) falls by 10% and the e-Mini S&P500 futures contract index falls by 10% too, how do you calculate the portfolio manager's spot gain or loss, the futures gain (loss) and the net hedging result?