Assume that you are an equity portfolio manager with a well-diversified portfolio valued at $2.5 million with a beta of 1.1, but you have a positive outlook on the short-term prospects of the stock market and want to increase your market risk using index futures by increasing your beta to 1.6. Assume that the S&P500 is trading at a price of 2655, the futures multiplier is $250, and the futures price is currently 2670.

How many contracts would you need to go long or short to adjust the portfolio to the desired beta?

Assume that the risk-free interest rate is 2% and the continuous market dividend yield is 2%. Furthermore, assume that 6-months later the index is trading at 2785 and the futures price is 2795. What is the value of the total position (equity portfolio plus gains or losses from the futures contract)?

What are some reasons that a futures contract cannot provide a perfect hedge to an equity portfolio in a situation like this?