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I'm rather new to the actual practice of this kind of analysis, but it just seems wrong to me to throw Mondays' returns in with the rest without accounting for the passage of time on the weekend when the market was closed, and yet I seem to come across analyses from time to time that do exactly that for daily returns, and simply assume so many trading days per month or per year.

To correct for this, I would take the difference in the natural logarithm of an adjusted security price from one trading day to the next, divide it by $\sqrt d$, and assign that data point a weight of $\sqrt d$, where $d$ is the number of calendar days elapsed. Then I could express the mean, variance, and all other moments (if they exist!) on a calendar day basis. Is this a standard practice?

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    $\begingroup$ Massaging returns for when the market is closed is definitely not standard practice. It will confuse a lot of people if you try to fight the 252-day year. $\endgroup$
    – chrisaycock
    Commented Jul 29, 2012 at 2:14
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    $\begingroup$ Agree with @chrisaycock and JL344. It is definetly not standard but assuming friday to monday returns come from the same distribution as thursday to friday is a bit insane. (most people might be) $\endgroup$
    – Zarbouzou
    Commented Jul 29, 2012 at 3:46
  • $\begingroup$ I should have asked more accurately: the real question is not "Is it more accurate?" but "Would it dominate in terms of being able to make inferences from the data?" $\endgroup$
    – JL344
    Commented Jul 29, 2012 at 4:18
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    $\begingroup$ Just a note: the time scaling I propose here is in accordance with what was discussed here quant.stackexchange.com/questions/3667/… and here quant.stackexchange.com/questions/3646/… -- according to bilkent.edu.tr/~berument/jef01.pdf Mondays' returns do have the highest variance, but it does not appear to be higher than that of the other days of the week by a factor of $\sqrt 3$ as one would expect from the natural scaling of i.i.d. returns by calendar time. $\endgroup$
    – JL344
    Commented Jul 29, 2012 at 4:50
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    $\begingroup$ check out [quant.stackexchange.com/questions/3205/… of treating time in the BS formula), where I mention 'elastic time'. That's useful for option risk management, in that it takes into account the fact that some days are more or less volatile than others (week-end day being an important example). $\endgroup$
    – joelhoro
    Commented Aug 20, 2012 at 14:24

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