Bias and misrepresentation revisited: Perspective on major equity indices

“Dow published the first U.S. stock market index in 1884, [...] Even practitioners who disdained Dow theory, however, found the Dow indices were tremendously useful for following the stock market as a whole.” Lo (2016, p.22)

How representative are leading equity indices to their total stock markets, given that they are only composed of a small fraction of the overall cross-section of publicly listed companies in a country? In this study, we analyze the common characteristics of leading stock market indices across 22 countries and aim to identify common misrepresentation biases relative to an approximation of their respective national equity markets as a whole.

Investors utilize leading stock market indices – such as the S&P 500 for the U.S. or the Nikkei 225 for Japan – as an important indicator for their respective stock markets. Moreover, these indices tend to be used regularly as a benchmark for fund managers to evaluate their performance (Cremers, Petajisto, Zitzewitz, 2012; Seifried and Zunft, 2012) and form the cornerstone of the stark growth of passive investment products. In contrast, the scientific community use market portfolios rather than lead indices to evaluate the performance of portfolios, thereby considereing a much larger cross-section. Widely considered examples of such market portfolios are the various country and region portfolios, which are provided by Kenneth French, amongst others, and constructed on the basis of data by the Center for Research in Security Prices (CRSP). Whilst these market portfolios are also only an approximation of the overall market, their cross-section spans far beyond the large-cap focus of most leading indices. Given the discrepancy in these two approaches, the question arises whether leading stock market indices are a legitimate representation of the whole market or if substantial biases have to be accepted in exchange for a simple and straight forward stock market barometer.

Seifried and Zunft (2012) argue, that leading stock market indices are indeed a questionable market-proxy as they are predominantly considering the largest (in terms of market-capitalization) and most liquid stocks. Besides a sample restriction, the underlying weighting scheme (equal,- price- or value-weighted) further adds to the subject of implicit size and style tilts. Daniel et al. (1997) and Cremers et al. (2012) report statistically significant nonzero alphas when testing index returns in various asset pricing models. These results indicate, that there are likely alternative drivers not captured by common multi-factor models and consequently resulting in non zero intercepts. Possible explanations are certain shortcomings in asset pricing models as discussed by Chan et al. (2009), who propose a different approach in constructing asset pricing factors to better account for different portfolio-styles or Asness et al. (2013) who argue in favour of a different methodology for the HML-factor. Moreover, index returns are potentially influenced by a reconstitution effect that occurs when stocks are added or removed from indices (Cremers et al., 2012). Given the mixed results and the criticism concerning the construction of leading stock market indices, the question whether leading stock market indices are a valid market proxy emerges as a natural consequence.