Suppose that JPMorgan Chase sells call options on $1.20 million worth of a stock portfolio with beta = 1.60. The option delta is 0.60. 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? b. What is the delta of a put option? (Round your answer to 2 decimal places. Negative amount should be indicated by a minus sign.) c. Complete the following: (Negative amount should be indicated by a minus sign.)

Explanation:

a) dollars’ worth of the market-index portfolio should it purchase to hedge its position

=1.60*0.6* $1.2 million

= $115200

b)

delta of call on portfolio=d(c)/d(portfolio value)=0.6 (d=very small change )

=>delta of call on portfolio=d(c)/d(beta*index value)=0.6

=>d(c)/d(index value)=0.6*beta=0.6*1.60=0.96

delta of call on index=d(c)/d(index value)=0.96

delta of put option on index

=delta of call on index-1

=0.96-1

=-0.04

= - 0.04

The delta of a put option is - 0.04

c)

Number of put contracts*delta of put*100*1000*%chg in value of index=%chg in value of index*829,400

=> Number of put contracts=829,400/(delta of put*100*1000)

=> Number of put contracts=829,400/(0.04*100*1000)

=> Number of put contracts=829,400/40000

=> Number of put contracts=20.735=~21

So JP Morgan should buy 21 put contracts.