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The pricing of idiosyncratic risk: evidence from the implied volatility distribution

Abstract

A recent strand in the literature has investigated the relationship between idiosyncratic risk and future stock returns. Although several authors have found significant predictive power of idiosyncratic volatility, the magnitude and direction of the dependence is still being debated. Using a sample of all S&P 100 constituents, we identify positive risk premia for option-implied idiosyncratic risk. Depending on the model used to identify unsystematic risk, we observe a statistically and economically significant average annual premium of 1.72 percent. To investigate whether this impact is driven by the definition of idiosyncratic risk, we extend the pricing kernel by implied skewness. Using a double-sorting procedure, we show that the compensation of unsystematic risk is mainly driven by firms with high positive implied skewness.

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Notes

  1. 1.

    For more recent studies see, among others, Fu (2009), and Diavatopoulos et al. (2008).

  2. 2.

    See, e.g., Vanden (2006) and the references therein.

  3. 3.

    See, e.g., Bakshi and Madan (2006), Bollerslev et al. (2009), and the references therein on volatility and variance spreads. This collection is by no means exhaustive. Furthermore, see Driessen et al. (2009), Krishnan et al. (2009), and Buss and Vilkov (2011) for empirically observable correlation risk premia.

  4. 4.

    A great deal of literature compares the predictive power of implied and historical measures for volatility. Early research in this field found that estimators based on implied volatility typically outperform estimates based on historical volatility. See, e.g., Latané and Rendleman (1976), Schmalensee and Trippi (1978), and Beckers (1980). Contrary to these findings, Canina and Figlewski (1993), Day and Lewis (1992), and Lamoureux and Lastrapes (1993) deny predictive power of implied volatility. More recent work, for example, includes Blair et al. (2001), Lehar et al. (2001), Jiang and Tian (2005), and DeMiguel et al. (2011). Buss and Vilkov (2011), among others, find a high predictive power of intraday return data to estimate volatility. Others find a reasonable empirical fit for component models, such as Zhu (2009).

  5. 5.

    See Buss and Vilkov (2011).

  6. 6.

    Empirically, this was found by Krishnan et al. (2009).

  7. 7.

    Buss and Vilkov (2011) show that the correlation MIDAS matrix estimator is positive semi-definite if and only if the correlation matrix under the physical measure is positive semi-definite and ρ t ≤0.

  8. 8.

    For details, see Ledoit and Wolf (2003, 2004).

  9. 9.

    The outline of this section is based on Meucci (2009).

  10. 10.

    Examples of studies using Gaussian Random Matrix Theory for financial applications are Laloux et al. (2000), Drożdż et al. (2001), Plerou et al. (2002), and Malevergne and Sornette (2004). The robustness of the eigenvalue analysis is investigated by Rajkovic (2000), as well as by Sharifi et al. (2004).

  11. 11.

    See also Rajkovic (2000), as well as Sharifi et al. (2004).

  12. 12.

    For details on the estimation, see Meucci (2009).

  13. 13.

    This definition of implied skewness might seems a bit crude at first sight. However, more sophisticated measures, such as Bakshi et al. (2003), typically require liquid option quotes for far out-of-the-money strike prices. These are usually unavailable for equity options.

  14. 14.

    See also Pojarliev and Polasek (2003).

  15. 15.

    Our results are robust to forming value-weighted portfolios.

  16. 16.

    Among the most influential models are Kraus and Litzenberger (1976) and Harvey and Siddique (2000). However, there exists a vast literature on (co-)skewness models.

  17. 17.

    For the distributional properties of λ max, see Geman (1980), Baik et al. (2005), and the references therein.

  18. 18.

    See Burda et al. (2011).

  19. 19.

    See Kollo and Ruul (2003).

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Correspondence to Stephan Süss.

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Süss, S. The pricing of idiosyncratic risk: evidence from the implied volatility distribution. Financ Mark Portf Manag 26, 247–267 (2012). https://doi.org/10.1007/s11408-012-0183-4

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Keywords

  • Idiosyncratic risk
  • Implied volatility
  • Implied skewness
  • Principal portfolios
  • Random matrix theory

JEL Classification

  • G12