Came across the following question from one of the FRM Level 1 tests…Kindly help me solve this
A trader in Mr. Raj’s bank has sold 200 call option contracts each on 100 shares of Mac Motors with time to maturity of 60 days at USD 2.10. The delta of the option on one share is 0.50. As a risk manager, what action must Mr. Raj take on the underlying stock in order to hedge the option exposure and keep it delta neutral
The trader has a short position in 200 call options of Mac Motors, which means he has the obligation to buy 20.000 (200x100) shares in the near future (within 60 days). The delta of the options is 0,5 which means that the option price moves with $0,5 by $1 increase/decrease of the value of the stock. This mean that if the trader want to have delta neutral position in his portfolio he has to buy 10.000 shares.
If the stock price increase with $1 the option price will be increase with $0,50. Which means that trader makes a loss on the option position because the premium will gain from 2,10 to 2,60. When the trader want to close the option position he has to pay 2,60, company loss $10.000 ($0,5*20.000). The loss will be compensated when trader bought 10.000 shares because he earns $10.000 ($10.000*$1).
A long position in calls gains when the underlying price increases, so a short position in calls loses when the underlying price increases. To hedge a short call postitioh, therefore, you need a position that gains when the underlying price increases: buy the underlying.
If you’re short 200 options on 100 shares each, that’s 20,000 shares. With a delta of 0.5, the price change is equivalent to being short 20,000 × 0.5 = 10,000 actual shares; buy 10,000 actual shares to offset that.
Note, by the way, that a delta of 0.5 means that the calls are at the money.
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