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Option Basics: Random Price Distribution

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Often when discussing the markets with other traders and investors, it comes as a surprise to them to hear that the percent price movement of an asset (stock, future, ETF, etc.) on a daily basis is random (it follows a geometric Brownian motion, an assumption incorporated in the Black-Scholes option pricing model).

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It is also a revelation to hear that the further out in time (for example, 6 months or longer), the less random the percent price action. This is one reason we prefer using Weekly options that expire within 7-days.

Why should this be of interest to traders? Most traders enter trades with a directional expectation (that the price of the asset will be moving up or down) without any quantitative measure of POP (probability of profit). In general, directional trades have a POP of 50% or less (you are either right about direction, or not; and if you are using stops, you are likely to lower the POP). However, with options (a derivative of an underlying asset) you can set the POP to much higher levels; even in excess of 90%.

So, if an underlying asset's price action is truly random, then we can use the current IV (implied volatility) to determine the expected move for one-standard deviation (1 SD). For example, if XYZ has a current price of $100, and a 1 SD expected move of $10 (for a given period of time), then we can expect the price of the underlying will stay within $90 and $110 with a confidence level of 68%. If we chose to use 2 SDs, then the price should remain within $80 and $120 (for that same time period) and our confidence level (or POP) rises to 95%.

This use of random price action to determine the POP, is referred to as the Probability Model. This model can be used as one criteria for selecting assets to trade (you can compare POPs relative to expected returns). Incidentally, most option based trading platforms can easily determine the POP. A good example is TD Ameritrade's ThinkorSwim (TOS) platform (see chart above).

It is therefore important that our assumption of randomness is not just opinion, but fact. At Options Annex we conducted a 5-year test for skew (a measure of randomness) on the SPX (S&P500 index) and the results support the assumption that the daily percent price action of the SPX is random. Others, including Tasty Trade (with their permission), have done more extensive research and it's this research that we will present as proof that the daily percent price action of an asset is truly random.

The Tasty Trade study first looked at the S&P500 over a 63-year period. During that period (22,995 days; 15,876 trading days), there were only 21 outliers (moves of 6% or greater; like the 1987 crash) of which 13 were down moves, and 8 were up. Removing these outliers, the graph (see graphs above) was clearly bell-shaped, indicative of random price action.

Next, Tasty Trade looked at the daily price action of two stocks: IBM (51-years), and AAPL (29-years). The results were similar (see graphs above), again indicating that the daily percent price action is random. Note: the AAPL chart shows the affects of higher IV vs. IBM and S&P500.

In conclusion, the daily percent price action of assets (whether stocks or indices) is, in fact, random and the reason it is used in the Black-Scholes option pricing model. As a result, we can confidently apply the Probability Model to determine the POP for a given IV and period of time. Keep in mind, the shorter the time period (Weekly vs. Monthly), the more accurate the Probability Model.

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