Volatility Normalization for Returns at Multiple Time Horizons
Summary
The document asks how to scale returns calculated from hourly bars to create volatility-adjusted features at longer horizons, including several-hour and calendar-period returns. It specifically considers whether a multi-hour return should be divided by hourly volatility scaled by the square root of the number of hours. This highlights the usual time-scaling assumption behind volatility normalization and the need to align the return horizon with its volatility estimate.
The only proposed answer describes averaging hourly returns into daily and monthly figures, then computing a standard deviation, but it is attributed to a chatbot and offers no sound justification or validation. Averaging returns is not generally equivalent to compounding them, and the document does not address serial dependence, trading-hour calendars, or how to estimate volatility over matching horizons. It provides no reliable demonstrated normalization procedure, so its practical value is mainly in framing the feature-engineering question and its caveats.
Key ideas
- The question concerns volatility-scaled features derived from hourly returns at longer horizons.
- Square-root-of-time scaling assumes return variance grows proportionally with elapsed time.
- The included proposed procedure uses averages and standard deviation but gives no validation for the method.
- Return aggregation, serial dependence, and the choice of matching volatility horizon affect normalization.
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Full text
# Normalise 5hr, 10hr, weekly, monthly returns using 1hr time bar # Normalise 5hr, 10hr, weekly, monthly returns using 1hr time bar I have a question on normalisation of returns when working with high frequency bars, such as 10mins, 30mins or 1hr. Suppose I have a time series of 1hr bars. I'd like to compute 5hr, daily, weekly, quarterly, volatility normalised returns. would it still be correct to do the normalisation by computing return_5h / (vol_1hr / sqrt(5))? The purpose is to create vol adjusted return features for different time period. return_5h would be computed from 1hr bar using an offset of 5. This is my first time posting. Apologies if the terminology used is not tight. ## Answer by quantinho (score -1) https://quant.stackexchange.com/a/75270 I am testing Google Bard's capability for quantitative methods and saw your question. Asked your question and here's the answer: To calculate monthly volatility based on hourly return data, you can use the following steps: - Calculate the hourly returns for the month. - Calculate the daily returns by taking the average of the hourly returns for each day. - Calculate the monthly returns by taking the average of the daily returns for each month. - Calculate the standard deviation of the monthly returns. The standard deviation is the monthly volatility. For example, let's say you have hourly return data for the month of January. The following steps would show you how to calculate the monthly volatility: Calculate the hourly returns for January. | Hour | Return | | ---- | ------ | | 1 | 0.5% | | 2 | -0.3% | | 3 | 0.2% | | ... | ... | | 23 | 0.1% | | 24 | -0.4% | Calculate the daily returns by taking the average of the hourly returns for each day. |Day | Return| |--- | ------| |1 | 0.1% | |2 | -0.2% | |3 | 0.1% | |... | ... | |31 | -0.2% | Calculate the monthly returns by taking the average of the daily returns for each month. Month | Return ------- | -------- January | -0.1% Calculate the standard deviation of the monthly returns. Standard Deviation | 0.2% The standard deviation is the monthly volatility. In this example, the monthly volatility for January is 0.2%. This means that the price of the asset can be expected to fluctuate by up to 0.2% in either direction from the mean price in a given month. It is important to note that volatility is a measure of historical price changes. It does not predict future price changes.
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