Calculating Value-Weighted Monthly Market Excess Returns

Summary

The document describes a researcher’s method for constructing monthly market excess returns while replicating Fama–French factors for German equities. The proposed calculation weights each company’s monthly simple return by its market value at the prior month-end, sums the weighted contributions to obtain the market return, and subtracts that month’s risk-free rate. The question arises because the resulting average excess return is below the figure reported in a cited study.

The material is a methodological question, not a resolved explanation: it does not identify an error or confirm that the proposed procedure matches the study’s conventions. It highlights the need to validate the sample and return construction against the reference. Details that could affect comparability—such as universe membership, treatment of delistings, market capitalization definitions, timing conventions, and the risk-free series—are not examined. No independent calculations or evidence are provided to reconcile the reported averages.

Key ideas

• The proposed market return weights each constituent’s monthly simple return by its previous-month market value.
• Summing weighted constituent returns produces the value-weighted market return for the month.
• The stated excess return subtracts that month’s risk-free rate from the market return.
• A difference from published averages does not by itself establish which construction step is incorrect.
• Sample definitions and data conventions may affect whether results match the cited study.

Tags

# How to calculate Market Return based on an own sample?


# How to calculate Market Return based on an own sample?












I have read several papers and am more confused than clearer about my problem after the reading. I am trying to validate my sample. I use the Schmidt et al. paper (2015) as a guidance to construct Fama-French factors for the german market. The mean of my monthly excess returns is lower than their mean (their's 0.39% vs my 0.31%) and for the love of god, I can't fathom where I went wrong. I am thinking now that I maybe did something wrong from the very beginning and ask a basic question:

How do you calculate the monthly excess return of a market (value weighted)?

My approach to calculate the excess market return for month $t$:

- Calculate the simple return of each company for this month.

- Multiply this return with the market value from $t-1$ and divide by the sum of all market values from $t-1$ (basically the market volume of $t-1$) to get the value weighted return of each company for month $t$.

- Sum over all value weighted returns of month $t$ to get get the market return for month $t$.

- Substract the risk free rate of month $t$ from this market return $t$ to get the market excess return of month $t$.

What am I doing wrong?

Reference:

Schmidt et al. (2015), On the Construction of Common Size, Value and Momentum Factors in International Stock Markets: A Guide with Applications, CER-ETH Economics working paper series, CER-ETH - Center of Economic Research (CER-ETH) at ETH Zurich.

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.