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This is a level 5 question.
Suppose a stock that is currently trading at 50 is expected either to rise or fall in price by 50 percent over the next period. The interest rate over this time frame is 10 percent. There is a one-period call option available with a strike price of 65. How many of these call options would an investor need to buy/sell in order to hedge against these price changes in the stock?
The number of 65 call options needed to hedge in your example depends heavily on 2 factors not given in the example - time to expiration and implied volatility. For example, if "period" were equal to 1 month and these calls were trading with an implied volatility of 20%, then the option would have a bid price of zero and no amount of calls could be sold!
With 6 months to expiration and an implied volatility of 100%, the call would sell for about 10. Coincidentally, this is equal to the intrinsic amount of the option if the stock were to rise in price by 50% to $75. Thus, 2.5 options contracts would be required for each 100 shares of stock. If the stock drops by 50% to 25, then the premium of 25 collected for selling 2.5 contracts would exactly cover the 25 points lost on the stock. The options in this case finish out of the money. If the stock rose to 75, then the 25 premium collected for selling the calls is offset by the 25-point outlay from the in-they-money amount (10 points in the money x 2.5 contracts). The remaining $25 stock gain is pocketed.
Of course, if the time to expiration and volatility conditions lie somewhere in between these 2 extremes, then the effects and contracts have to be adjusted accordingly. The key would be to avoid selling so many contracts in the event the option is trading at $2, for example, that the loss when the stock hits $75 becomes too excessive.
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Question Level Key
Level One--Basic Jargon, Definitions, Basic Mechanics of Trading.
Level Two--Introductory Points, Practical Points and Simple Strategies
Level Three--More Advanced Strategies and Repairs
Level Four--Risk Management, Psychology, and How Best to Evaluate Things.
Level Five--High end questions concerning Portfolio Analysis, Managing a Portfolio
of Options, Option Pricing Models, and Nuances of Trading. Included could be a variety of
other topics.
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