Calendar-Time Versus Trading-Time Returns for Daily Analysis

Summary

The document asks whether daily return statistics should account for weekends and other gaps when markets are closed. Its proposed adjustment starts with the change in the natural logarithm of adjusted prices between consecutive trading sessions, scales that return by the square root of the elapsed calendar days, and weights the resulting observation by the same square-root factor. The aim is to express moments such as mean and variance on a calendar-time basis rather than treating every trading interval as equal in length.

The text frames this as a question about standard practice; it includes no answer, empirical comparison, or evidence that the proposed scaling is appropriate. Its procedure therefore remains a suggestion rather than a validated method. Whether this treatment is suitable depends on the return process and the statistic being estimated, and the document does not discuss those assumptions or alternatives for modeling closed-market intervals.

Key ideas

• Trading-day returns span different amounts of calendar time, especially across weekends.
• The proposed method uses log-price changes between consecutive trading sessions.
• It scales observations by the square root of elapsed calendar days and applies matching weights.
• The goal is to estimate moments on a calendar-time basis.
• The document asks whether this is standard but provides no answer or empirical validation.

Tags

# Is it more accurate to analyze returns on a calendar day basis than a trading day basis?


# Is it more accurate to analyze returns on a calendar day basis than a trading day basis?












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