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I got a question regarding the analysis of the value premium in the U.S. stock market.

The task is to use the market-to-book-value ratio to split the S&P500 in five portfolios (rank 1-100,101-200,..). Subsequently I have to do a regression for excess returns and analyze the alphas.

I'm just not sure wheter I should weight the companies within the portfolios equally or based on their market cap. I'd say that choosing equal weights would emphasize small companies. Because of the (small-)size effect I expect the observed value premium to be larger, with value-weights smaller.

But what is one method more appropriate/ better? I'm using Kenneth Frenchs market premium which is value-weighted, maybe because of that I should also use value-weighted portfolios?

Happy to hear your thougts!

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In principal, nothing stops you from doing both, constructing equally weighted and value weighted portfolios and see how the results differ :)

In principal, I'd advice to use value weighted portfolios though. As you say, size can have a significant influence on the cross section of stocks. Look at the RFS paper from Lu Zhang et al. (2018) which tests many known anomalies and disregards microstocks (stocks smaller than the 20th percentile of the market equity for NYSE stock). The results are unambiguous:

The key word is “microcaps.” Microcaps represent only 3.2% of the aggregate market capitalization but 60.7% of the number of stocks. Microcaps have the highest equal-weighted returns and the largest cross-sectional dispersions in returns and in anomaly variables. Many original studies overweight microcaps via equal-weighted returns and often with NYSE-Amex-NASDAQ breakpoints in portfolio sorts. Hundreds of studies perform cross-sectional regressions of returns on anomaly variables, mostly with ordinary least squares, which are highly sensitive to microcap outliers.

Obviously, you don't have microstocks in the S&P 500 but I would still tend to use value weighted portfolios. Smaller stocks are less liquid, it is much harder to invest a significant amount of money into them and they have a different behaviour than the rest of the cross section. Basically, you don't want to overestimate the influence of small stocks on the market.

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    $\begingroup$ Thanks, awesome answer which confirms me in my thoughts! $\endgroup$ – user43224 Nov 19 '19 at 9:44

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