# 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 $t$:

1. Calculate the simple return of each company for this month.
2. 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 $t$.
3. Sum over all value weighted returns of month $t$ to get get the market return for month $t$.
4. 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.

• That doesn't appear to be a huge difference to me, TBH. But are you using the same universe of securities? Same data sources? Same risk-free rates? Same periods? Are stats reported in the same convention? Any of these (and other) data issues could be a culprit. – Helin Sep 13 '18 at 2:45
• I agree with @Helin that your results are fairly close to theirs and could be due to simple calculation method and dataset differences for the individual issues or risk free rates. However, what do you mean when you say "basically the market volume of t-1"? Do you mean you are dividing by the total market capitalization? – Jared Marks Sep 13 '18 at 10:53
• yes, by the total market capitalization of t-1, that's what I mean with market volume. sorry for the misunderstandings. what's weird too: the correlation of my monthly market excess returns is above 97.6% with another german data set, but they have an even higher mean than schmitd et al. @Helin yes, I am using the same data source(thomson reuters datastream) and tried to follow nearly all their steps and screenings. just a little different time period (their's goes til 2012, mine til 2018) and I am using, I believe, a different risk-free rate proxy. but can that have that much of an impact? – AahuM Sep 13 '18 at 11:26