Suppose that JPMorgan Chase sells call options on $1.65 million worth of a stock
ID: 2799158 • Letter: S
Question
Suppose that JPMorgan Chase sells call options on $1.65 million worth of a stock portfolio with beta = 2.00. The option delta is .78. 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
Since the stock portfolio has a beta of 2, when the market-index rises by 1%, stock portfolio will increase by 1% * 2 = 2%
Worth of stock portfolio rises by 2% of $1650000 = $33000
Since delta = 0.78, option portfolio will increase by = $33000 * 0.78 = $25740
As 1% change in market-index results in $25740 change in options, to hedge 100% portfolio worth 2574000 must be bought
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Delta of put option = -0.01
Each put option represents 100 units of the market index and delta of puts are negative because as market index rises, value of put declines.
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Value of portfolio to be hedged = $1650000
Number of Put contracts = Value of portfolio to be hedged/ Notional value of put contract = $1650000/100 *$1000 = 16.5
Adjusting for beta, we get number of put contracts = 16.5 * 2 = 33