# 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

• Any chance you could use TeX to cleanup the tables? – barrycarter Apr 2 '16 at 1:07
• Return Numbers for Security A mean: R_{t}x 10^{2} =-0.0083% standard deviation R_{t} : 0.1166 % mean:\left |R_{t} \right | =0.0737% standard deviation:\left | R_{t} \right |=0.0903% mean: R_{t}^{2}=0.0001% standard deviation: R_{t}^{2}=0.0007% – Tom Kistak Apr 2 '16 at 10:07
• Security B Average Volatility (%)= 0.0737582 Std Dev = 0.0312347 Minimum (%) =0.0290989 Maximum (%) = 0.2561527 – Tom Kistak Apr 2 '16 at 10:08
• I hope it is more legible now – Tom Kistak Apr 2 '16 at 10:09
• Actually, I meant could you 'edit' your question, not put the corrections in comments. – barrycarter Apr 2 '16 at 14:27