Why Volume Changes Can Appear More Variable Than Price Changes
Summary
The discussion asks why percentage changes in trading volume often show larger swings than percentage price changes, even after attempts to adjust for seasonal patterns. One reply stresses that variance depends on scale: raw volume and price changes have different units and typical magnitudes, so comparing their variances directly can be misleading. It also notes that volume is nonnegative while price changes can be positive or negative, which affects how directional moves can offset in statistical summaries.
Other replies suggest that bursts of trading activity may precede or accompany price moves, and emphasize that volume is a flow while price is a level. These are possible intuitions rather than a demonstrated general law. The exchange offers no data analysis or formal test, and its explanations should not be read as proving that volume changes always lead price changes. Comparisons require careful normalization and attention to measurement units.
Key ideas
- Volume and price have different units and scales, so their variances are not directly comparable without normalization.
- Trading volume is nonnegative, whereas price changes can have either sign.
- Volume is a flow and price is a level, which makes raw variance comparisons conceptually difficult.
- The suggestion that volume changes precede price changes is presented without empirical support in the discussion.
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Full text
# Why in general is the variance of volume changes higher than variance of price changes? # Why in general is the variance of volume changes higher than variance of price changes? Why, in general, is the variance of volume changes higher than variance of price changes? I understand that these two quantities are functions of some very different factors, but I don't understand fully why the variance of volume is changing so much. I've heard that even if one accounts for seasonal changes in volatility (by standardizing daily stock volume by daily volume of basket of stocks/volume of index), the variance of the volume changes is much higher. Edition : I meant quantities measured in percentage. High jumps in volume are very common, whereas high price changes aren't. ## Answer by Vic Colborn (score 1) https://quant.stackexchange.com/a/3346 Not to over simplify, but there is the different scaling to consider here as well. - Volumes and volume changes are observed in 1000s and 100s, while prices and price changes are observed in 100s and 1s. For most medium and smaller stocks prices and price changes are observed in 1s and 0.01s. - Clarify this through the identity Var(aX) = a²Var(X). - Since the numerical values you are comparing are an order of magnitude in difference, naturally their variance, and thus changes in local variance, will also be quite different. Additionally, price changes are directional and volume changes are not. - Quite possibly you are observing that many consecutive minutes are 'confused', being reported with high volume and comparatively little change in price. - Clarify this through the inequality |E[X]| <= E[|X|], and its relation to variance as Var(X) = E[X²] - E[X]². - This means that even if the volume was somehow scaled down to the same magnitude of price, that the expectation of volume (being non-negative) would always be higher than the expectation of price. ## Answer by Tom Au (score 0) https://quant.stackexchange.com/a/3350 Volume changes LEAD to price changes. That is to say that prices go up or down because larger (or smaller) volumes of people want to buy or sell. So volumes change FIRST, and in larger amounts. It is as a result of those volume changes that prices change. ## Answer by Tal Fishman (score 0) https://quant.stackexchange.com/a/3351 Volume is a flow, whereas price is a stock. As wikipedia notes, > Stocks and flows have different units and are thus not commensurable – they cannot be meaningfully compared, equated, added, or subtracted. It makes no sense to compare the variance of price to the variance of volume. They are simply two fundamentally different things.
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