Advertisement

Comonotonicity and low volatility effect

  • 44 Accesses

Abstract

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.

This is a preview of subscription content, log in to check access.

Access options

Buy single article

Instant unlimited access to the full article PDF.

US$ 39.95

Price includes VAT for USA

Subscribe to journal

Immediate online access to all issues from 2019. Subscription will auto renew annually.

US$ 199

This is the net price. Taxes to be calculated in checkout.

Fig. 1
Fig. 2
Fig. 3

Notes

  1. 1.

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

  2. 2.

    Source: TrackInsight.com.

  3. 3.

    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).

References

  1. Ang, A., Hodrick, R. J., Xing, Y., & Zhang, X. (2006). The cross-section of volatility and expected returns. The Journal of Finance, 61(1), 259–299.

  2. Ang, A., Hodrick, R. J., Xing, Y., & Zhang, X. (2009). High idiosyncratic volatility and low returns: International and further us evidence. Journal of Financial Economics, 91(1), 1–23.

  3. Baker, M., Bradley, B., & Wurgler, J. (2011). Benchmarks as limits to arbitrage: Understanding the low-volatility anomaly. Financial Analysts Journal, 67(1), 40–54.

  4. Baker, M., & Wurgler, J. (2015). Do strict capital requirements raise the cost of capital? Banking regulation and the low risk anomaly. American Economic Review: Papers and Proceedings, 105(5), 315–320.

  5. Bali, T. G., Brown, S., Murray, S., & Tang, Y. (2016). A lottery demand-based explanation of the beta anomaly. Working paper (2408146).

  6. Bali, T. G., & Cakici, N. (2008). Idiosyncratic volatility and the cross section of expected returns. Journal of Financial and Quantitative Analysis, 43(01), 29–58.

  7. Black, F. (1972). Capital market equilibrium with restricted borrowing. Journal of Business, 45, 444–455.

  8. Blitz, D., & Van Vliet, P. (2007). The volatility effect: Lower risk without lower return. Journal of Portfolio Management, 34(1), 102–113.

  9. Carhart, M. M. (1997). On persistence in mutual fund performance. The Journal of Finance, 52(1), 57–82.

  10. Chen, C., & Zhou, Z.-G. (2001). Portfolio returns, market volatility, and seasonality. Review of Quantitative Finance and Accounting, 17(1), 27–43.

  11. Chen, Y.-T., Lai, W., & Sun, E. (2019). Jump detection and noise separation by a singular wavelet method for predictive analytics of high-frequency data. Computational Economics, 54(2), 809–844.

  12. Chen, Y.-T., Sun, E., & Yu, M.-T. (2015). Improving model performance with the integrated wavelet denoising method. Studies in Nonlinear Dynamics and Econometrics, 19(4), 445–467.

  13. Chen, Y.-T., Sun, E., & Yu, M.-T. (2018). Risk assessment with wavelet feature engineering for high-frequency portfolio trading. Computational Economics, 52, 653–684.

  14. Cheung, K. (2007). Characterization of conditional comonotonicity. Journal of Applied Probability, 44, 607–617.

  15. Cheung, K. (2008). Improved convex upper bound via conditional comonotonicity. Insurance: Mathematics and Economics, 42, 651–655.

  16. Cheung, K. (2009). Applications of conditional comonotonicity to some optimization problems. Insurance: Mathematics and Economics, 45, 89–93.

  17. Clarke, R. G., De Silva, H., & Thorley, S. (2010). Know your VMS exposure. The Journal of Portfolio Management, 36(2), 52–59.

  18. Dhaene, J., Denuit, M., Goovaerts, M. J., Kaas, R., & Vyncke, D. (2002a). The concept of comonotonicity in actuarial science and finance: Applications. Insurance: Mathematics and Economics, 31(2), 133–161.

  19. Dhaene, J., Denuit, M., Goovaerts, M. J., Kaas, R., & Vyncke, D. (2002b). The concept of comonotonicity in actuarial science and finance: Theory. Insurance: Mathematics and Economics, 31(1), 3–33.

  20. Dhaene, J., Vanduffel, S., Goovaerts, M. J., Kaas, R., Tang, Q., & Vyncke, D. (2006). Risk measures and comonotonicity: A review. Stochastic Models, 22, 573–606.

  21. Dutt, T., & Humphery-Jenner, M. (2013). Stock return volatility, operating performance and stock returns: International evidence on drivers of the ‘low volatility’ anomaly. Journal of Banking & Finance, 37(3), 999–1017.

  22. Fama, E. F., & French, K. R. (1993). Common risk factors in the returns on stocks and bonds. Journal of Financial Economics, 33(1), 3–56.

  23. Fama, E. F., & French, K. R. (2015). A five-factor asset pricing model. Journal of Financial Economics, 116(1), 1–22.

  24. Fama, E. F., & French, K. R. (2016). Dissecting anomalies with a five-factor model. Review of Financial Studies, 29(1), 69–103.

  25. Frazzini, A., & Pedersen, L. H. (2014). Betting against beta. Journal of Financial Economics, 111(1), 1–25.

  26. Fu, F. (2009). Idiosyncratic risk and the cross-section of expected stock returns. Journal of Financial Economics, 91(1), 24–37.

  27. Gangopadhyay, P., Yook, K. C., & Shin, Y. (2014). Insider trading and firm-specific return volatility. Review of Quantitative Finance and Accounting, 43(1), 1–19.

  28. Harvey, C. R., Liu, Y., & Zhu, M.-T. (2016). \(\ldots \) and the cross-section of expected returns. Review of Financial Studies, 29(1), 5–68.

  29. Haugen, R. A., & Baker, N. L. (1996). Commonality in the determinants of expected stock returns. Journal of Financial Economics, 41(3), 401–439.

  30. Haugen, R. A., & Baker, N. L. (2010). Case closed. In J. Guerard (Ed.), Handbook of portfolio construction (pp. 601–619). Boston, MA: Springer.

  31. Haugen, R. A., & Heins, A. J. (1975). Risk and the rate of return on financial assets: Some old wine in new bottles. Journal of Financial and Quantitative Analysis, 10, 775–784.

  32. Huang, W., Liu, Q., Rhee, S. G., & Zhang, L. (2009). Return reversals, idiosyncratic risk, and expected returns. The Review of Financial Studies, 23(1), 147–168.

  33. Jacod, J., & Shiryaev, A. (2013). Limit theorems for stochastic processes (Vol. 288). Berlin: Springer.

  34. Jegadeesh, N., & Titman, S. (1993). Returns to buying winners and selling losers: Implications for stock market efficiency. The Journal of Finance, 48(1), 65–91.

  35. Jordan, B. D., & Riley, T. B. (2015). Volatility and mutual fund manager skill. Journal of Financial Economics, 118(2), 289–298.

  36. Kaas, R., Dhaene, J., & Goovaerts, M. (2000). Upper and lower bounds for sums of random variables. Insurance: Mathematics and Economics, 27, 151–168.

  37. Kosowski, R., Timmermann, A., Wermers, R., & White, H. (2006). Can mutual fund “stars” really pick stocks? New evidence from a bootstrap analysis. The Journal of Finance, 61(6), 2551–2595.

  38. Lee, S., & Mykland, P. (2008). Jumps in financial markets: A new nonparametric test and jump dynamics. Review of Financial Studies, 21(6), 2535–2563.

  39. Leote de Carvalho, R., Lu, X., & Moulin, P. (2012). Demystifying equity risk-based strategies: A simple alpha plus beta description. The Journal of Portfolio Management, 38(3), 56–70.

  40. Lin, E., Sun, E., & Yu, M.-T. (2018). Systemic risk, financial markets, and performance of financial institutions. Annals of Operations Research, 262, 579–603.

  41. Nartea, G. V., & Wu, J. (2013). Is there a volatility effect in the hong kong stock market? Pacific-Basin Finance Journal, 25, 119–135.

  42. Novy-Marx, R. (2014). Understanding defensive equity. Working paper 20591, National Bureau of Economic Research.

  43. Patton, A. J., & Timmermann, A. (2010). Monotonicity in asset returns: New tests with applications to the term structure, the capm, and portfolio sorts. Journal of Financial Economics, 98(3), 605–625.

  44. Scherer, B. (2011). A note on the returns from minimum variance investing. Journal of Empirical Finance, 18(4), 652–660.

  45. Stambaugh, R. F., Yu, J., & Yuan, Y. (2015). Arbitrage asymmetry and the idiosyncratic volatility puzzle. The Journal of Finance, 70(5), 1903–1948.

  46. Sullivan, R., Timmermann, A., & White, H. (1999). Data-snooping, technical trading rule performance, and the bootstrap. Journal of Finance, 54, 1647–1691.

  47. Sun, E., & Meinl, T. (2012). A new wavelet-based denoising algorithm for high-frequency financial data mining. European Journal of Operational Research, 217, 589–599.

  48. Sun, W., Rachev, S., Fabozzi, F., & Kalev, P. (2009). A new approach to modeling co-movement of international equity markets: Evidence of unconditional copula-based simulation of tail dependence. Empirical Economics, 36, 201–229.

  49. White, H. (2000). A reality check for data snooping. Econometrica, 68(5), 1097–1126.

  50. Xu, Z. (2014). A new characterization of comonotonicity and its application in behavioral finance. Journal of Mathematical Analysis and Applications, 418(2), 612–625.

  51. Yin, S., Mazouz, K., Benamraoui, A., & Saadouni, B. (2018). Stock price reaction to profit warnings: The role of time-varying betas. Review of Quantitative Finance and Accounting, 50(1), 67–93.

Download references

Author information

Correspondence to Edward W. Sun.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

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.

Appendix

Appendix

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

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Lai, W., Chen, Y. & Sun, E.W. Comonotonicity and low volatility effect. Ann Oper Res (2019). https://doi.org/10.1007/s10479-019-03320-0

Download citation

Keywords

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

JEL Classifications

  • C02
  • C10
  • C63