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# chapter4/4 expected returns

Chapter 4

#### Expected Returns

The greatest probability of the future price of a stock is the current price.

The graph of the probability of future stock prices changes is a classic bell curve, with the peak of the curve at the current price. The probability of the stock actually being at the same price in the future is small, but that probability is still higher than the probability of the stock being at any other price.

 Probability of a Stock's Future Price

What is of interest is that the area under the curve is much greater near the center than the edges. Option strategies with a neutral bias have a greater probability of a profitable return, albeit that return is limited. Option strategies that are overly bullish or bearish are less likely to be profitable, but the amount returned from long or short strategies can be much higher than neutral strategies.

If it's cheap buy it, if it's expensive sell it.

Some people liken the stock market to gambling. In the casino, the odds are predetermined and the gambler is consistently at a disadvantage to the house. It would be nice to be able to hop on the other side of the Blackjack table and share the dealer's advantage. Unlike the casino, traders in the stock market can take either side of a bet. If you think the odds of profiting from a trade are against you, take the other side of the trade.

Mathematical pricing models compute the prices at which expected returns on any option strategy are equal whether the trader is long or short. It would not be favorable to buy a strategy if its synthetic equivalent were cheaper. If, for some reason, buying a strategy was theoretically more favorable than selling it, buyers would swarm to the cheap position driving up the price, making the sale of the strategy more attractive. This is the classic force of supply and demand, and it applies to the option market as well as the stock market. A large demand for options will impact the price of the stock, since professional traders will hedge positions by trading other options or the underlying stock.

Quite often options may appear overpriced. An option is not overpriced simply because it has a high price. An option is overpriced if its synthetic equivalent is cheaper. Expensive options at parity with their synthetic equivalent represent high volatility, which represents a high expectation that the underlying stock's price will change. If the option looks overpriced simply by virtue of having a high price, the inclination may be to sell it. There are two opposing views on this. The first is that the most likely probability is that the stock price will remain near where it is, therefore expensive options should be sold for the premium. The second view is that options are trading at a premium because the stock is likely to move, therefore one should only buy expensive options as those are the trades most likely to end in a profit. It is the existence of opposing viewpoints, and traders willing to act on them, that make a market.

Data Provided by HistoricalOptionData.com
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