Question

Suppose that JPMorgan Chase sells call options on $1.55 million worth of a stock portfolio with beta = 1.90. The option delta is .75. 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 (Click to select / buysell) -------put contracts. Assume a market movement of 1 percent.

rev: 11_03_2014_QC_57682

Answer 1

Hi,

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

Beta = 1.9, this means that 1% increase the portfolio will move by 1.9%

Increase in the portfolio = 1.9 * portfolio value = 0.019 * 1,550,000 = 29,450

Delta of call option = 0.75, this means if underlying moves up by 1$ then option will move by $ 0.75

Increase in Option = 0.75 * 29,450 = 22087.5

1% change in index will change 22,087.5 in the portfolio.

Therefore to hedge the entire portfolio we have to purchase = 22087.5 * 100 = 2,208,750 worth of market index portfolio.

Ans: 2,208,750 worth of market index portfolio

Additional info:

If this is only stock portfolio(without involding options) then the answer is pretty simple 1.9 * 1.55 million = 2.945 Million.

If this portfolio included options with delta of 1, then still it would result in the above answer. But luckily the delta is lower than 1 which is 0.75, hence in order to hedge the exposure we just need to invest approximately 2.2 million instead of 2.9 million.

b) What is the delta a put option?

Recollect Put-call parity of deltas, C - P = 1

Hence,  P = C-1

P = 0.75-1 = -0.25

Ans: delta of put is -0.25

Additional info:

Deltas of Put\call also depend on the direction of the trade.

• Delta of Put varies from 0 to -1(-ve) & Delta of call varies from 0 to 1 (+ve) ---> All this for Buy direction
• Delta of Call varies from 0 to -1(-ve) & Delta of Put varies from 0 to 1 (+ve) ---> All this for Sell direction

Just for arguement, the above mentioned delta in the question is practically not correct (should be -0.75 for sell call), but for simplicity purpose the author of the question has just mentioned it 0.75

c) Complete the following:

Assuming the 1 percent market movement, JP Morgan should (Click to select / buysell) ---Buy----put contracts.

Ans: Buy

Additional info:

The rules for this as well as hedging any portfolio is like below.

• If you want to hedge against down fall in market - Buy Put options or Sell call options (buy put is preferrable as they have limited loss & unlimited profits)
• If you want to hedge against up movement in market - Buy call options or Sell put opitons (buy Call is preferrable as they have limited loss & unlimited profits)

Here in this case JPM wants to protects its Index portfolio against a downfall in the market, so its optimal to buy puts.

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