Question

A trader uses delta hedging strategy to hedge a portfolio of short positions in call option on Apple Computer stocks. The trader sells 50 call option contracts (1 contract controls 100 shares) on Apple stock. The option price is $5, the stock price is $230, and the option’s delta is 0.8.
a. Does the trade short or long the stock to create a delta-neutral position? (Sample answer: long; or short)
b. How many shares does the trader need to create a delta-neutral position?  (Sample answer: 3000 shares)
c. Suppose the next day, the stock price increases to $240 and the delta changes to 0.85. Do you long additional shares or short shares? (Sample answer: long additional 20 shares; or short additional 20 shares)

Answer 1

a) Since the trader is in a short position in call option, a delta-neutral position would be a Long stock strategy.

b) Since the delta/risk is 0.8, the trader needs to create equal number of shares to neutralize the risk/delta.

Therefore, shares = 4000 shares (100 shares *0.8 delta * 50 no.of contracts)

c) Long additional 250 shares

Explanation: Based on the volatility, the trader needs to shift his position accordingly.

Due to a change in the risk/delta, the number of shares/stocks to be purchased changes accordingly to form a delta-neutral position in the portfolio. Hence, additional 250 shares (delta variance*no.of shares*no.of contracts = 0.05*100*50 = 250) needs to be purchased by the trader.