Contrarian traders, by nature, tend to buck the prevailing market trend. According to some, when the options market gets too bearish one should get bullish. This is in line with the old theory that the market tends to punish the greatest amount of people possible.

When options traders get overly bearish, the relative price of an out-of-the-money (OTM) put is pumped up compared to a similar probability OTM call: the skew is increased.

Apple (AAPL) shares have slid more than 25% from their all-time high, and questions over the company's valuation are also getting heated. Moreover, Apple options volume typically surges before earnings; thus, Apple is a perfect candidate to test the idea of options skew.

Benzinga went back eight earnings reports and gathered data on weekly 34 delta Apple options.

The 34 delta options were chosen because prices between the two options represent a one standard deviation range -- a 68% chance Apple expires between the two strikes.

If 34 delta options were not listed, the closest options were chosen. Both have a similar probability of expiring in the money (ITM), but trade at two different prices.

The data is presented in the following excel sheet. The sheet includes the price of a 34 delta OTM put and call, the quotient of the prices, and implied volatilities.

Any number over one in the quotient column represents the skew. These prices should more or less be the same, for the probability of an up move versus a down move is the same in random walk and options pricing models.

Skew can be a function of sentiment, or what is called an "index phenomenon."

Apple can almost be considered an index because of its massive weighting in portfolios, another reason why it was chosen. Managers tend to sell OTM calls and buy OTM puts on indices in order to hedge their portfolio. The result is index skew.

Another reason why this exists is simply human nature. Investors tend to be more fearful of downside than upside. This is consistent with the given prices. One explanation could be that Apple is a massively held stock and thus it reflects the "index phenomenon" where calls are cheap because of overwriting (selling) and puts are expensive because of hedging (buying).

This is backed up by the data, for AAPL is held in large amounts by mutual and pension funds -- not to mention retail -- more than any other stock.

The correlation coefficient between the earnings move and skew was 0.04. This figure is negligible because of its weak nature. A coefficient over plus or minus 0.80 is considered rather strong.

Considering the relationship was near zero, there is not a correlation between Apple's earnings and skew. This is not to say that contrarian trading does not work. In this instance, it was just not supported by the data.

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