# 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.

• Do you have bars that include volatility? How exactly is your volatility defined? And shouldn’t the volatility of all bars be included in the estimate of the 5h normalised return? Apr 19, 2023 at 5:52
• Thank you. the bars are OHLC of 1hr. Atm I am just measuring realised vol as stdev. Not sure if i understanding you correctly, of course, one would need the vol of 5hr to normalise the 5hr return. However, I am aware by scaling 1hr vol (measured over a period) by sqrt(5) is not entirely accurate because intraday vol is not constant. Apr 19, 2023 at 22:03

To calculate monthly volatility based on hourly return data, you can use the following steps:

1. Calculate the hourly returns for the month.
2. Calculate the daily returns by taking the average of the hourly returns for each day.
3. Calculate the monthly returns by taking the average of the daily returns for each month.
4. 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.

• This doesn’t really answer the question. Apr 19, 2023 at 5:53