Interpreting Weekly Returns and Daily Returns Scaled to Weekly

Summary

The document raises a distinction between calculating returns from weekly prices and converting daily returns into a weekly measure. For log returns, summing the daily returns across a week gives the same result as the log return computed from the week’s starting and ending prices, assuming consistent endpoints and no missing observations. The post also considers overlapping weekly returns calculated at daily intervals, which form a different series because each observation spans a week but starts on a different day.

The assignment’s comparison of histograms implies that “daily returns scaled to weekly” may mean a rescaled daily-return distribution rather than simply aggregating daily returns. The document does not resolve that terminology or provide an authoritative method. The appropriate comparison depends on the assignment’s definition: aggregation estimates realized weekly returns, while rescaling daily returns requires assumptions about how returns and volatility evolve over time.

Key ideas

• Summing daily log returns over a week equals the log return between the week’s endpoints when the periods align.
• Overlapping weekly returns use a one-week horizon but begin on successive days, creating a different sample.
• The phrase “daily returns scaled to weekly” is ambiguous without the assignment’s definition.
• A histogram comparison depends on whether the daily series is aggregated or statistically rescaled.

Tags

# weekly returns and the daily returns scaled to weekly


# weekly returns and the daily returns scaled to weekly












I am new in this blog and first of all I want to apologise for my english. I have to calculate, for a university project, the weekly returns and daily scaled returns to weekly for few stocks

For weekly returns, no problem i calculated them by: ln(Pt+1/Pt).

I have difficulties to understand what daily returns scaled to weekly mean.

My possbile solutions are:

- to calculate daily return with daily data ln(Pt+1/Pt) and then adding them up in order to obtain weekly returns, but this way is the same thing of calculating weekly return as shown above.

- other solution is to calculate weekly return for every day, I mean to calculate weekly overlap return.

In my opinion the first solution is the most logic and i think that this is a trick question.

But the full question in the assignment is: "the histogram plot of the weekly returns and the daily returns scaled to weekly. Which is the difference? What do you think is more suitable to estimate the weekly return?"

Thus, by this answer I imply that there'll be a difference and hence my first solution is wrong.

Could you help me?

Thanksss!!

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