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Using Statistical Measures to Determine Stretched Markets

Price is made up of 2 components:

1. Trend, whether it be up, down, or neutral

2. Volatility, which is the price action that deviates from the trend

When market participants look at technical analysis indicators, they are attempting to determine the trend and whether there is a good place to put risk on in the context of the volatility.

Sometimes, however, modelling the volatility is left to "fuzzy math" or esoteric indicators.

I'm looking for measurements that will provide a little more statistical robustness.

This is one area I'm developing.

Change Distributions

We know that stock price is a time series of data that can generally be modelled as a lognormal distribution.

Meaning, the price change will fall under a big bell curve.

Does this only apply to daily price changes?

Here's a time series of 10-day rolling returns in the $SPY, with a sample size of a few hundred trading days-- the most recent data on the left.

This is one useful measure of volatility as it gives us areas in which price can be "overbought" or "oversold."

But the problem is, eyeballing a time series of data won't really be helpful.

Below is a chart showing the distribution of those rolling returns, since 1993. Outliers are removed to improve chart readability.

As expected, price action is a lognormal distribution, whether we look at 1-day price performance or 10-day price performance.

Where it Gets Fun

We can curve fit this data to go under a bell curve, and so we will know the historical odds of the $SPY being above 5% on a 10-day basis.

If the options market is giving us higher odds than historical, then you can develop a statistical edge and create an option selling system that is statistically robust.

This is a Starting Point

Obviously I haven't shown you the "best" parameters to use, but you can take this methodology and start applying it to individual equities and indexes.

Parameters to potentially change are the sampling window from which you derive the distributions, and the length of the performance window.

What do you think about this line of reasoning? Have any improvements? Let me know in the comments section.

by Steven Place

Steven Place is the founder and head trader at