In dealing with option trading, one often tries to find clever ways to beat the system. One which admittedly looks very promising, is the following: Let’s say we are interested in writing a call option at a strike price of 100 for some stock. In order to hedge our risk, we decide to buy 1 unit of a stock if the price of the stock passes 100, and sell 1 unit if the stock goes below 100. For the beginner, this looks like a great strategy, as we hedged our risk and no matter what happens, we are covered.
To see this, let’s suppose the stock finished at 102. We are obliged to sell the stock for 100. Since we bought it at 100, we haven’t lost a dime and we are able to sell it without a loss. On the other hand, if the stock finished at 98, the stock expires worthless and we had sold it when it went below 100. You might argue that we won’t be able to buy and sell at 100 each time so for the sake of the argument, we can also assume we buy at 100.1 and sell at 99.9. We would lose $0.2 each time but the question that remains to be asked is if the cost would outweigh the profit of writing the option.
The quick answer is NO. The longer answer is that mathematically, these small costs accumulate to at least the price of the option which leaves us with no revenue at all or even loss. If you do that for long enough time, on average you’d always have a loss.
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