Choosing Portfolio Weights When Testing the Value Premium
Summary
The document considers how to weight stocks after sorting an equity universe into portfolios by market-to-book ratio and then comparing excess-return regression alphas. Equal weighting gives each company the same portfolio influence, which can increase the impact of smaller firms. Value weighting scales influence by market capitalization and is recommended in the response as a more investable representation of the stock universe.
The rationale is that microcaps can account for a small share of aggregate market value while making up a much larger share of stock counts; equal-weighted returns can therefore give them substantial influence. Smaller stocks may also be less liquid and behave differently from larger firms. The question concerns S&P 500 constituents, so the cited microcap concern is less directly applicable there. The response suggests comparing both weighting schemes, since the resulting premium and alpha estimates can differ, and does not claim that one choice is universally correct.
Key ideas
- Equal weighting can give small firms more influence than their aggregate market value warrants.
- Value weighting makes each stock’s contribution proportional to its market capitalization.
- Microcaps may strongly affect equal-weighted return studies and can be less liquid.
- Comparing both weighting schemes can reveal how portfolio construction affects estimated value premiums and alphas.
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Full text
# Value premium analysis - Equal or Value-weighted Portfolios? # Value premium analysis - Equal or Value-weighted Portfolios? 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! ## Answer by Kevin (score 2, accepted) https://quant.stackexchange.com/a/49785 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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