Stock Trading – Volume and Volatility

What about the relationship between the volume of trades and stock prices? And while we are on the topic, how about linkages between volume, volatility, and stock prices?

These questions have absorbed researchers for decades, recently drawing forth very sophisticated analysis based on intraday data.

I highlight big picture and key findings, and, of course, cannot resolve everything. My concern is not to be blindsided by obvious facts.

Relation Between Stock Transactions and Volatility

One thing is clear.

From a “macrofinancial” perspective, stock volumes, as measured by transactions, and volatility, as measured by the VIX volatility index, are essentially the same thing.

This is highlighted in the following chart, based on NYSE transactions data obtained from the Facts and Figures resource maintained by the Exchange Group.


Now eyeballing this chart, it is possible, given this is daily data, that there could be slight lags or leads between these variables. However, the greatest correlation between these series is contemporaneous. Daily transactions and the closing value of the VIX move together trading day by trading day.

And just to bookmark what the VIX is, it is maintained by the Chicago Board Options Exchange (CBOE) and

The CBOE Volatility Index® (VIX®) is a key measure of market expectations of near-term volatility conveyed by S&P 500 stock index option prices. Since its introduction in 1993, VIX has been considered by many to be the world’s premier barometer of investor sentiment and market volatility. Several investors expressed interest in trading instruments related to the market’s expectation of future volatility, and so VIX futures were introduced in 2004, and VIX options were introduced in 2006.

Although the CBOE develops the VIX via options information, volatility in conventional terms is a price-based measure, being variously calculated with absolute or squared returns on closing prices.

Relation Between Stock Prices and Volume of Transactions

As you might expect, the relation between stock prices and the volume of stock transactions is controversial

It seems reasonable there should be a positive relationship between changes in transactions and price changes. However, shifts to the downside can trigger or be associated with surges in selling and higher volume. So, at the minimum, the relationship probably is asymmetric and conditional on other factors.

The NYSE data in the graph above – and discussed more extensively in the previous post – is valuable, when it comes to testing generalizations.

Here is a chart showing the rate of change in the volume of daily transactions sorted or ranked by the rate of change in the average prices of stocks sold each day on the New York Stock Exchange (click to enlarge).


So, in other words, array the daily transactions and the daily average price of stocks sold side-by-side. Then, calculate the day-over-day growth (which can be negative of course) or rate of change in these variables. Finally, sort the two columns of data, based on the size and sign of the rate of change of prices – indicated by the blue line in the above chart.

This chart indicates the largest negative rates of daily change in NYSE average prices are associated with the largest positive changes in daily transactions, although the data is noisy. The trendline for the rate of transactions data is indicated by the trend line in red dots.

The relationship, furthermore, is slightly nonlinear,and weak.

There may be more frequent or intense surges to unusual levels in transactions associated with the positive side of the price change chart. But, if you remove “outliers” by some criteria, you colud find that the average level of transactions tends to be higher for price drops, that for price increases, except perhaps for the highest price increases.

As you might expect from the similarity of the stock transactions volume and VIX series, a similar graph can be cooked up showing the rates of change for the VIX, ranked by rates of change in daily average prices of stock on the NYSE.


Here the trendline more clearly delineates a negative relationship between rates of change in the VIX and rates of change of prices – as, indeed, the CBOE site suggests, at one point.

Its interesting a high profile feature of the NYSE and, presumably, other exchanges – volume of stock transactions – has, by some measures, only a tentative relationship with price change.

I’d recommend several articles on this topic:

The relation between price changes and trading volume: a survey (from the 1980’s, no less)

Causality between Returns and Traded Volumes (from the late 1990’)

The bivariate GARCH approach to investigating the relation between stock returns, trading volume, and return volatility (from 2011)

The plan is to move on to predictability issues for stock prices and other relevant market variables in coming posts.

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