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Choosing the Right Return Distribution and the Excess Volatility Puzzle

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  • Abootaleb Shirvani
  • Frank J. Fabozzi

Abstract

Proponents of behavioral finance have identified several "puzzles" in the market that are inconsistent with rational finance theory. One such puzzle is the "excess volatility puzzle". Changes in equity prices are too large given changes in the fundamentals that are expected to change equity prices. In this paper, we offer a resolution to the excess volatility puzzle within the context of rational finance. We empirically show that market inefficiency attributable to the volatility of excess return across time is caused by fitting an improper distribution to the historical returns. Our results indicate that the variation of gross excess returns is attributable to poorly fitting the tail of the return distribution and that the puzzle disappears by employing a more appropriate distribution for the return data. The new distribution that we introduce in this paper that better fits the historical return distribution of stocks explains the excess volatility in the market and thereby explains the volatility puzzle. Failing to estimate the historical returns using the proper distribution is only one possible explanation for the existence of the volatility puzzle. However, it offers statistical models within the rational finance framework which can be used without relying on behavioral finance assumptions when searching for an explanation for the volatility puzzle.

Suggested Citation

  • Abootaleb Shirvani & Frank J. Fabozzi, 2020. "Choosing the Right Return Distribution and the Excess Volatility Puzzle," Papers 2001.08865, arXiv.org.
    • Handle: RePEc:arx:papers:2001.08865
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    References listed on IDEAS

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    1. Andrew Ang & Robert J. Hodrick & Yuhang Xing & Xiaoyan Zhang, 2006. "The Cross‐Section of Volatility and Expected Returns," Journal of Finance, American Finance Association, vol. 61(1), pages 259-299, February.
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    7. Abootaleb Shirvani & Svetlozar T. Rachev & Frank J. Fabozzi, 2019. "Multiple Subordinated Modeling of Asset Returns," Papers 1907.12600, arXiv.org.
    8. LeRoy, Stephen F & Porter, Richard D, 1981. "The Present-Value Relation: Tests Based on Implied Variance Bounds," Econometrica, Econometric Society, vol. 49(3), pages 555-574, May.
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