Checking Intraday Return Scales and Converting Volatility Horizons

Summary

The document asks whether reported five-minute returns and Parkinson volatility estimates are plausible in scale. It gives summary statistics for returns on one security across 29,500 intervals and daily Parkinson volatility calculations for another security, averaged over 365 days. The author is unsure whether the volatility values are too low and asks what references can guide checks against established intraday market behavior.

It also asks what time horizon a Parkinson estimate represents when calculated from five-minute data, and how to express five-minute volatility over longer intervals such as 30 minutes, a day, or a year. The text supplies no answers, formula details beyond naming the estimator, or evidence that the calculations are correctly scaled. The main learning value is in framing validation questions: distinguish the sampling interval from the horizon of an aggregated estimate, and specify the averaging and annualization convention before comparing volatility figures. Any conversion would depend on assumptions about return aggregation and dependence across intervals.

Key ideas

• The author reports five-minute return statistics for one security and Parkinson volatility estimates for another.
• Daily volatility estimates are averaged across a stated year-long sample.
• The document asks whether the reported scales are plausible but provides no validation or benchmark.
• A volatility figure's horizon depends on how interval data are aggregated and summarized.
• Converting volatility to longer horizons requires an explicit convention and assumptions about returns.

Tags

# Intraday return and volatility figures some sense check


# Intraday return and volatility figures some sense check












Some questions about intraday returns and volatility figures. It is with the objective of sense checking.

Firstly, for Security A, I am calculating the five minute interval return numbers over 29500 intervals. You can see below some of the results.

Secondly, for another security, I am calculating the Parkinson volatility numbers using five minute intervals. I use the following Parkinson volatility formula

I first calculate the parkinson numbers per each day and take the average of the days over 365 days.

Return Numbers for Security A at 5 minute intervals R_t(%) x 10^2 R_t(%) |R_t| (%) |R_t| (%) R_t^2(%) R_t^2(%) Mean Standard Deviation Mean Standard Deviation Mean Standard Deviation S -0.0083 0.1166 0.0737 0.0903 0.0001 0.0007

Volatility Numbers for Security B at 5 minute intervals

*calculated per day Average Vol (%) Std Dev Minimum (%) Maximum (%) 0.0737582 0.0312347 0.0290989 0.2561527

1) Do these return and volatility numbers make sense from a scale point of view? What source can guide us as to the stylized facts and expected scale of intraday return /volatility figures? Obviously, this will assure whether one's estimations are within reasonable ranges.The volatility numbers seem low to me.

2) The Parkinson volatility calculation as per the attached formula-what time horizon does it correspond to? daily? what is right frequency convention in the statement of intra-day volatility figures?

3) In terms of volatility conversion, how can one convert a 5 minute intraday volatility number into 30-min volatility numbers? Likewise into daily or annualized figures Your prompt response will be appreciated

Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)

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