A fund manager has a well-diversified portfolio that mirrors the performance of the S&P 500 and is worth $360 million (the beta of the portfolio with respect to the S&P 500 is 1). The S&P 500 quotes 3,400, the multiplier is $250, and the portfolio manager would like to buy insurance against a reduction of more than 5% in the value of the portfolio over the next 6 months (not taking into account the cost of insurance). The continuous risk-free interest rate is 2% per annum. The continuous dividend yield on both the portfolio and the S&P 500 is 3%, and the volatility of the index is 16% per annum.

1. If the fund manager decides to provide insurance by using 6-month index futures, what should the initial position be?