# local price return and volume relationship

I wanted to see how the stock price and volume relationship is locally.

So I tried ranking both the daily return (at day t) and volume (at day t) base on a 30 day rolling window with historical daily stock data and plotted the distribution as shown in the below figure (top). The ranking is based on sorting values in ascending order, and as you can see, when volume is locally high the price return is either locally low or high.

I have also plotted the distribution of ranking of the next day return (at day t+1) and volume (at day t) to see if this "shape" remains, as shown in the figure (bottom), and it does.

Can anyone explain why this shape still remains for day t+1? This kind of price volume relationship must have been researched extensively... is there some classic papers that you quant experts would recommend?

Thanks. A screen shot of the code is provided here.

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For now, I think these plots demonstrate that when volume is high, the distribution of the price return has a fatter tail, and this fat tail persists for the following day. –  teng Feb 26 '12 at 16:38
I just found myself some reading materials, Tauchen and Pitts 1983 and articles (1,2) based on Karpoff, 1987. –  teng Feb 27 '12 at 12:04

## 2 Answers

When volatility is high, daily volume is high. And when volatility is high, daily returns are high. That's why when volume is high, the price returns are high.

Volatility (like volumes) is autocorrelated. This is the phenomenon of volatility clustering (large changes tend to be followed by large changes, of either sign) and volume clustering (large volumes tend to be followed by large volumes). It explains why when return is high (in absolute value) at day t it's likely to remain high (in absolute value) for day t+1. But of course it doesn't give you the sign of the return...

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Thank you for the answer. I am assuming when you say daily returns are high, you actually mean daily returns are volatile. If so, I agree with the first part of your statement. But can you elaborate on the second part? How is high/volatile returns explained by volume autocorrelation? I'm a bit lost. –  teng Feb 27 '12 at 0:19

The technical analysis point of view: an increase in volume (assuming the price has been in a downtrend) means the crowd are throwing in the towel, i.e. everyone is dumping the stock and assuming that hoped-for rise is now never going to happen. The same on the way up: everyone jumps on the bandwagon.

In other words, high volume typically means crowd psychology dominated. And that takes time to work its way out. Out of a given crowd population, people who missed it at t, will try and get in/out at t+1, and those still left will get in/out at t+2, etc. until the crowd is exhausted.

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