How Volume and Dollar Bars Change Return Distributions

Summary

The document compares sampling financial prices at fixed time intervals with constructing volume or dollar bars, where each observation is triggered by traded activity. It notes that returns from volume or dollar bars can appear closer to normally distributed than returns from ordinary time bars. This approach is presented as a partial improvement in normality, not a guarantee that returns become normal.

The proposed explanation is that activity-based sampling changes the clock used to observe prices, and the cited volume-clock research argues this can improve statistical properties. The text also contrasts this with volatility-normalizing each security and demeaning the resulting series, concluding that the methods differ. However, it provides no direct comparison, dataset, quantitative result, or details of a normalization procedure. The claim is therefore a high-level distinction rather than evidence establishing which approach is preferable or how large the difference is.

Key ideas

• Volume bars and dollar bars sample prices according to trading activity rather than fixed time intervals.
• Returns sampled with activity bars are described as closer to normally distributed than time-bar returns.
• Activity-based sampling may partially improve normality, but it does not establish that returns are truly normal.
• The document distinguishes activity-based sampling from per-security volatility normalization and demeaning.
• It gives no empirical comparison that quantifies the difference between the two approaches.

Tags

# Volume or Dollar bars vs. volatility normalized and demeaned financial time series


# Volume or Dollar bars vs. volatility normalized and demeaned financial time series












In his book - Advances in Financial Machine Learning, Marcos Lopez de Prado familiarises the reader with a number of ways of normalizing our financial time series data. Below I provide a couple of examples (source: here) for the purpose of this question:









When transforming time bars of prices to volume bars or dollar bars, the returns of the resulting time series are much closer to normally distributed.

Another very standard way of normalizing time serie would be to:

- Volatility normalize per security

- Demean the time series

My question is: Is there a significant difference between the normalization of Volume or Dollar bars vs. Vol normalize and Demean?

## Answer by Jacques Joubert (score 11, accepted)

https://quant.stackexchange.com/a/44872

The dollar bars certainly allow for a partial recovery of normality through a price sampling process subordinated to a volume, tick, dollar clock.

It is well known that returns are assumed to be normally distributed but in reality they have a high kurtosis and fat tails, they are leptokurtic.

Dr de Prado posits in several papers but mainly in a well known paper titled The Volume Clock, that if we sample prices based on a volume clock rather than fixed time interval sampling, then we get better statistical properties.

The following is a jupyter notebook that shows the results on real data: Notebook.

In response to your question: Yes there is a significant difference between the techniques.

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This summary was written by Stratmill's research agent from the original; it is not a copy of the source.