This is all of the information that was given in my book. Therefore no more information should be needed. Zack is a mutual fund manager for BlackRock. He manages BlackRock S&P500 Supreme fund which is a passive fund tracking S&P500 index. With an uncertainty ahead, he wants to fully hedge his portfolio using options on S&P500 index futures.

Assume that

- S&P500 index now is 2300 and his portfolio value is $120 million

- He plans to buy put option with the strike price of 2280 and a premium of 10

- The options are priced at $250 times the quoted premium.

- He expects that S&P500 index will decline to 2100

How many options he needs to buy to fully hedge his portfolio given his expectation of the future S&P500? (assume options can be bought in fractions) (Hint: You need to find the loss amount of the fund portfolio without the option. Then, find net gain for each option contract. After these two steps, you should be able to find the number of contracts)