Estimating Daily Volatility from Intraday Returns

Summary

This document frames a comparison between estimating daily return volatility from daily closing prices and scaling minute-return standard deviation by the square root of the number of minutes in a day. It asks whether using daily observations discards information when minute-level stock prices are available, and what trade-offs follow from the two approaches. The scaling proposal relies on the familiar square-root-of-time relationship between volatility and horizon.

No answers or empirical results are included, so the document does not resolve which estimator is preferable. In practice, the scaling relationship depends on assumptions about return behavior, including serial dependence and stable variance; intraday price data can also contain market microstructure effects and time-of-day patterns. Daily close returns and aggregated intraday returns may therefore yield different estimates. The material is best read as an open methodological question, not as evidence that multiplying minute volatility by a fixed factor produces a reliable daily estimate in every setting.

Key ideas

• Daily close returns and scaled minute returns are two possible inputs to daily volatility estimates.
• Square-root-of-time scaling assumes a suitable relationship between return variance and sampling horizon.
• Intraday observations provide finer detail but may include microstructure noise and intraday seasonality.
• Serial dependence or changing volatility can make simple scaling inaccurate.
• The document poses the comparison without presenting an answer or empirical evidence.

Tags

# 71596


# What are the advantages and disadvantages of converting standard deviation of higher-frequency returns to a lower sampling frequency?












I have a minute-by-minute price series of a stock. I would like to calculate the daily volatility or standard deviation of the stock's returns.

One way to do so is to get the end-of-day prices (i.e. daily close prices), calculate daily returns, and then calculate the standard deviation of these daily returns.

The alternative method is to calculate the minute-by-minute returns, calculate the minutely standard deviation, and then convert this into a daily equivalent by multiplying by $\sqrt{1440}$ (i.e. the number of minutes in a day).

My questions are:

1- which method should I use, given that the minute-by-minute data is available to me?

2- Does using the daily returns result in loss of information?

3- Are there advantages/disadvantages of using one method over the other?

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