One of the ways in which we can find constructive price patterns is by identifying those in which volume rises on rallies or falls or declines. This shows the proper type of action for a strong stock as volume dries up when the buyers leave the table. What this is in statistical terms is correlation. I hope these few notes will spur you on to perhaps create indicators, stock rankings, and base analysis statistics as an aid to identifying better stocks.
The theory is that when price and volume move together, the stock is "acting" correctly. Therefore, the higher the correlation, the better acting the stock is. If the correlation was strongly negative, we may see a constructive short forming. Based on this, let's look at the movement of volume and price for a baseline stock like Microsoft (MSFT).
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What we would like to see is that large increases in price correspond to large increases in volume, and vice versa. This would show us that price is being backed up by volume. A statistical way of saying that two series are moving together is correlation. Correlation is bound by 1 and -1, with 1 being a perfect positive correlation and -1 being a perfect negative correlation. An example of a high correlation series is the correlation between rainy days and days with clouds in the sky. An example of high negative correlation would be the correlation between rainy days and the days the pavement stays dry outside.
One thing must be noted though, correlation does not equal causation. Just because price and volume may be highly correlated does not mean that volume is the reason for the price moves. It may be earnings, news, etc. Correlation is calculated as the covariance of two series divided by the product of their standard deviation. By listing two series side by side (in this case, the percent change in price and the percent change in volume), we can calculate the mean, cross-product of the differences between actual percent change and the mean, and then the standard deviations, and arrive at the correlation. The correlation of price to volume for MSFT over the past 63 days is 0.12.
To calculate correlation, we used a 63 day history of 3 day returns and volume change for blocks of 3 days (immediate past 3 days total volume (t-0 - t-2) / sum of volume for t-1 - t-3). Here we see there is a low correlation between the two and this may not be helpful for MSFT. But what about a strong stock? Let's look at the table for Netflix (NFLX) to see if there a higher correlation. In this light, higher correlations would show us stronger stocks and could be used for ranking and screening of stocks more probable to move up than down.
We see that NFLX has a much higher correlation, and may have more constructive price action and supporting volume. However, is this reliable? One way to check is to use a scatterplot to find outliers. Values that are far away from the pack of observations (high variance from the sample) can skew the correlation and take away from its meaningfulness. Here is the scatterplot for NFLX:
Outliers exist in this graph to the upper right (some gap days to be sure, with high volume and high price moves). These outliers are stretching our correlation to a higher value and therefore are skewing our results. In this next plot, I have taken every observation outside of 2 standard deviations from the mean, and reduced it to a value of 1 standard deviation above the mean if it was positive, and 1 standard deviation below the mean if it was negative. In this way, we don't completely negate the occurrence of positive or negative price and volume, but rather restrict it so it won't skew our numbers as much. The reason for setting them to 1 and not my max, 2 standard deviations, was because I did not want to line the edge of my boundaries on my scatter plot with values. That would still skew my correlation. What we arrive at is a bounded scatterplot.
These numbers can now be better compared to other stocks for a determination if patterns, bases, or general price action is constructive or not. The new correlation after the adjustments is the one in parenthesis in the tables above. According to my research and observations, strong stocks have correlations greater than .25. One last thing to watch is how the correlations have acted recently. Are they unwinding or strengthening? For this we can look at historical trends for correlations. The uses for this are many, but for now I'll just post the graph.
Please expand on this idea and let me know what you come up with. Thanks.
Disclosure: I have no positions in any stocks mentioned, and no plans to initiate any positions within the next 72 hours.