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This is all of the information that was given in my book. Therefore no more information...

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)

Solutions

Expert Solution

Zack is holding a portfolio of BlackRock S&P500 Supreme fund which is a passive fund tracking S&P500 index. His total investment in the portfolio is $ 120 million

Current index value of S & P is 2300 and portfolio values is 120 million

So he is holding = 120,000,000/ 2300 = 52,174 Units

He expects that S&P500 index will decline to 2100 and at that level his portfolio value will become

= 109,565,400 $ and so unless he hedges he is going to incur a loss of 120,000,000 - 109,565,400 = 10,434,600 $

So in order to hedge his portfolio from this downside risk he plans to buy put option with the strike price of 2280 and a premium of 10

In case the S&P500 index will decline to 2100 he can exercise his put option at 2280 and make a gain of

2280 - 2100 = 180 per contract

The options are priced at $ 250 times the quoted premium of 10 and hence it is valued at  250 * 10 = 2500 $

He needs buy the number of option contracts which will cover him for his possible entire loss of 10,434,600 $ plus option price 2500 $ i.e  10,434,600 + 2500 = 10,437,100 $

So the number of contracts he needs = 10,437,100/180 = 57,984

So Zach needs to purchase 57,984 contracts to fully hedge his portfolio.

jeff jeffy answered 1 year ago
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