Comonotonicity and low volatility effect

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Discussions on low volatility effects often highlight the advantage of low volatility stocks outperforming high volatility stocks. Using comonotonicity tests, our study provides evidence of the downside of this effect: stock returns do not increase monotonically with low volatility, but volatility increases monotonically with specific risks. We find that, counterintuitively, the low volatility effect is mostly driven by high volatility stocks with high specific risks. Our empirical analysis addresses a cross section of stock returns across 23 developed countries and employs comonotonicity tests to show that expected stock returns do not increase monotonically with lower volatility. In addition, by decomposing volatility into its individual risk components, we show that volatility increases monotonically with its specific risk component. Finally, we also confirm that returns obtained from the low volatility effect in stocks are principally driven by the specific risk component rather than the systematic risk component.

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    See Novy-Marx (2014) for a detailed discussion of defensive equity strategies.

  2. 2.


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    Haugen and Heins (1975) Haugen and Baker (1996, 2010) and Baker et al. (2011).

  4. 4.

    The calibration period and portfolio formation methodology follows the work of Baker et al. (2011) and Baker and Wurgler (2015), except that their portfolios are based on U.S. CRSP data.

  5. 5.

    See results reported in Baker et al. (2011), Blitz and Van Vliet (2007), Bali and Cakici (2008), Chen et al. (2019) and Lin et al. (2018).


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Correspondence to Edward W. Sun.

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The authors would like to thank Philippe Bertrand, Kris Boudt, Felix Goltz, Bertrand Groslambert, Marie Lambert, Florencio Lopez de Silanes, Armin Schwienbacher and conference participants of the 33rd International Conference of the French Finance Association for their valuable comments and discussion.



Tables 9, 10 and 11 present the results of the time-series linear regressions of the volatility sorted quintile portfolios against different risk factors in their respective regions. The complete set of risk factors are consolidated from the standard single factor and four factor models with (low) risk-based factors, namely, a low beta factor and a low IV factor computed using the methodology described in Sect. 3.2. We then assess the factor exposures of the lowest and highest volatility portfolio returns, as well as the lowest minus highest volatility portfolio returns for the cross section of stocks listed in Europe, Asia Pacific and North America.

Table 9 Volatility sorted portfolios in Europe
Table 10 Volatility sorted portfolios in Asia Pacific
Table 11 Volatility sorted portfolios in North America

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Lai, W., Chen, Y. & Sun, E.W. Comonotonicity and low volatility effect. Ann Oper Res (2019).

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  • Asymmetric risk-return
  • Comonotonicity
  • Multi-factor model
  • Low volatility effect
  • Portfolio
  • Risk decomposition

JEL Classifications

  • C02
  • C10
  • C63