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Suppose that JPMorgan Chase sells call options on $1.35 million worth of a stock portfolio with beta = 1.70. The option delta is 0.70. It wishes to hedge its resultant exposure to a market advance by buying a market-index portfolio. Suppose it use market index puts to hedge its exposure. The index at current prices represents $1,000 worth of stock. a. How many dollars’ worth of the market-index portfolio should it purchase to hedge its position?

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Answer:

Particulars                         Amount                                      Explanation

Call options                        1350000  

Beta of stock                            1.7  

Delta                                      0.7  

Market change                       1%                    Implied stock change is 1.7

Stock changes by 1.7                1.19                     Implied exposure on call

                                                                                options on stock  ( ie 1.7*0.7)

Amount of exposure          1606500               Derived by multiplying

                                                                                      1.19*1,350,000

Hence market index portfolio worth $1,606,500 should be bought , however the market index portfolio trade in multiples of 1000 hence $1,607,000 worth should be obtained to hedge the exposure

Explanation:

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