You are in charge of a 10 million portfolio. You suspect that the current market decline may continue for another 6 months. You would like to hedge the portfolio to a decline below 9.5 million and are considering options on the market index to hedge the portfolio. The portfolio has a beta of 1.5, the market index is standing at 500 and a 6 month put option on the index is available with a strike price of 492.5. The risk free rate is 5; 5% per year. (For now you may ignore any dividends on the index and portfolio).

How can you construct this hedge? If the annual index volatility is 20%, what would be the approximate cost of the option?