Decomposing Global Equity Cross-Sectional Volatility

Jose Menchero and Andrei Morozov

Financial Analysts Journal, 2011, vol. 67, issue 5, 58-68

Abstract: The authors present an exact methodology for decomposing cross-sectional volatility into contributions from various factors. Treating country, industry, and style factors equally, they used their framework to investigate several relevant issues in the global equity markets, including the importance of country versus industry, emerging markets versus developed markets, and the strength of style factors vis-à-vis country and industry factors.Cross-sectional volatility (CSV) represents the degree of return dispersion within a universe of stocks and is computed as the standard deviation of returns over a single period. CSV is critical because it represents the opportunity to outperform a benchmark. On the one hand, if dispersion is small, all stocks behave similarly and security selection is of limited value. On the other hand, if dispersion is large, portfolio managers can add significant value by overweighting outperformers and underweighting underperformers.In this article, we present an exact methodology for decomposing cross-sectional volatility. We show that the contribution of an individual factor to CSV is given by the product of the factor return, the cross-sectional standard deviation of the factor exposures, and the cross-sectional correlation between the factor exposures and stock returns. Our approach treats country, industry, and style factors equally and enables one to identify the main drivers of global equity returns. We constructed a global factor model consisting of 48 country factors, 24 industry factors, and 8 style factors. We used our framework to investigate the relative importance of these factors over 1994–2010.We found that country factors dominated industry factors over 1994–1999, whereas industry factors surpassed country factors over 2000–2003. Since 2004, industry factors and country factors have been roughly equally important, with country factors perhaps retaining a slight edge. Surprisingly, style factors dominated both industry factors and country factors in the aftermath of the internet bubble (2000–2004), as well as during the financial crisis of 2008–2009.In addition, we used our methodology to investigate the relative importance of emerging markets vis-à-vis developed markets. We found that developed markets dominated emerging markets over most of the sample history, although the situation reversed over 2007–2009.We also drilled into each category of factors to identify the individual factors driving the CSV contributions. For industry factors, we found that the semiconductor industry was particularly strong during the internet bubble period whereas the energy industry was dominant over 2005–2010. For style factors, we found that the most important factor was usually volatility, which represents a good proxy for market beta. The contribution of the volatility factor to CSV was particularly strong in times of financial turmoil, such as in 2001 and 2009.Furthermore, we tested our results for robustness by considering different models with varying numbers of industry or style factors. In general, we found that our results are quite robust, with reasonable variations in factor structure leading to only small changes in CSV contributions.Finally, we generalized our methodology to investigate the main drivers of root mean squared (RMS) returns, which are more relevant for absolute return managers. We found that the world factor generally makes significant contributions to RMS returns. In fact, during the financial crisis of 2008–2009, the world factor was by far the main driver of RMS returns.

Date: 2011
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DOI: 10.2469/faj.v67.n5.1

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