Suppose that JPMorgan Chase sells call options on $1.10 million worth of a stock

Question

Suppose that JPMorgan Chase sells call options on $1.10 million worth of a stock portfolio with beta = 1.45. The option delta is .52. It wishes to hedge out its resultant exposure to a market advance by buying a market-index portfolio. Suppose it uses market index puts to hedge its exposure. Each put option is on 100 units of the index, and 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 (Omit the "$" sign in your response.) Market index portfolio $

b. What is the delta a put option? (Round your answer to 2 decimal places. Negative amount should be indicated by a minus sign. Omit the "$" sign in your response.) The delta a put option is

c. Complete the following: (Negative amount should be indicated by a minus sign. Omit the "$" sign in your response.) Assuming the 1 percent market movement, JP Morgan should put contracts. Assume a market movement of 1 percent.

Explanation / Answer

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

=1.45*0.52* $1.10 million

= 0.754*1.10 million

= 0.8294 million

= 829,400

b)

delta of call on portfolio=d(c)/d(portfolio value)=0.52 (d=very small change )

=>delta of call on portfolio=d(c)/d(beta*index value)=0.52

=>d(c)/d(index value)=0.52*beta=0.52*1.45=0.754

delta of call on index=d(c)/d(index value)=0.754

delta of put option on index

=delta of call on index-1

=0.754-1

=-0.246

= - 0.25

The delta of a put option is - 0.25.

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/(0.25*100*1000)

=> Number of put contracts=829,400/25000

=> Number of put contracts=33.176=~33

So JP Morgan should buy 33 put contracts.

Related Questions

Navigate

• Browse (All)
• Browse S
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.