SPY Range Expansion Behaviour

This is a study on the probability of SPY expanding its range as a multiple of the average range over 10 days period.

The study was originally done by our member smilingsynic. I am just reproducing the results here using data from 1993 up to last Friday Feb 25, 2011.

First, a comparison based on similar starting point in percentage basis with fixed increment up to 1 times average range away.

1DR / AR is the ratio of 1 day range and the average range over 10 days period from the trading day before.

2DR / AR is the ratio of 2 day range and the average range over 10 days period from 2 trading days before.

The reason for adjusting the average range reference point is to avoid leakage of the measured range into the reference average range.

So, according to the table below, for any 3-day period, SPY has 25.17% chance to reach 2.3 times or more of the average range.

Next is the data presented in a graph.

Second, a comparison based on fixed probability range to show the extend of the changes in average range multiples.

Note: The results I got is slightly different from smilingsynic’s results because the range expansion behaviour in last 2 years has skewed the results towards stronger range expansion bias in the tail end of the distribution.

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