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Higher Order Effects in Asset Pricing Models with Long‐Run Risks




This paper shows that the latest generation of asset pricing models with long‐run risk exhibit economically significant nonlinearities, and thus the ubiquitous Campbell‐Shiller log‐linearization can generate large numerical errors. These errors translate in turn to considerable errors in the model predictions, for example, for the magnitude of the equity premium or return predictability. We demonstrate that these nonlinearities arise from the presence of multiple highly persistent processes, which cause the exogenous states to attain values far away from their long‐run means with nonnegligible probability. These extreme values have a significant impact on asset price dynamics.

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  • Walter Pohl & Karl Schmedders & Ole Wilms, 2018. "Higher Order Effects in Asset Pricing Models with Long‐Run Risks," Journal of Finance, American Finance Association, vol. 73(3), pages 1061-1111, June.
  • Handle: RePEc:bla:jfinan:v:73:y:2018:i:3:p:1061-1111
    DOI: 10.1111/jofi.12615

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    2. Nagel, Stefan & Xu, Zhengyang, 2019. "Asset Pricing with Fading Memory," CEPR Discussion Papers 13973, C.E.P.R. Discussion Papers.
    3. Jaroslav Borovička & John Stachurski, 2020. "Necessary and Sufficient Conditions for Existence and Uniqueness of Recursive Utilities," Journal of Finance, American Finance Association, vol. 75(3), pages 1457-1493, June.
    4. Wenzelburger, Jan, 2020. "Mean-variance analysis and the Modified Market Portfolio," Journal of Economic Dynamics and Control, Elsevier, vol. 111(C).
    5. Borovička, Jaroslav & Stachurski, John, 2021. "Stability of equilibrium asset pricing models: A necessary and sufficient condition," Journal of Economic Theory, Elsevier, vol. 193(C).
    6. Yun, Jaeho, 2020. "A re-examination of the predictability of stock returns and cash flows via the decomposition of VIX," Economics Letters, Elsevier, vol. 186(C).
    7. Andreasen, Martin M. & Jørgensen, Kasper, 2020. "The Importance of Timing Attitudes in Consumption-Based Asset Pricing Models," Journal of Monetary Economics, Elsevier, vol. 111(C), pages 95-117.
    8. Gao, Can & Martin, Ian, 2019. "Volatility, Valuation Ratios, and Bubbles: An Empirical Measure of Market Sentiment," CEPR Discussion Papers 13454, C.E.P.R. Discussion Papers.
    9. Flint O'Neil, 2020. "Existence and Uniqueness of Recursive Utility Models in $L_p$," Papers 2005.07067,
    10. Oliver de Groot & Alexander W. Richter & Nathaniel A. Throckmorton, 2018. "Valuation Risk Revalued," CDMA Working Paper Series 201803, Centre for Dynamic Macroeconomic Analysis.
    11. A Ronald Gallant & Mohammad R Jahan-Parvar & Hening Liu, 2019. "Does Smooth Ambiguity Matter for Asset Pricing?," Review of Financial Studies, Society for Financial Studies, vol. 32(9), pages 3617-3666.
    12. Andreou, Panayiotis C. & Kagkadis, Anastasios & Philip, Dennis & Taamouti, Abderrahim, 2019. "The information content of forward moments," Journal of Banking & Finance, Elsevier, vol. 106(C), pages 527-541.
    13. Alexis Akira Toda, 2018. "Data-based Automatic Discretization of Nonparametric Distributions," Papers 1805.00896,, revised May 2019.
    14. He, Yunhao & Leippold, Markus, 2020. "Short-run risk, business cycle, and the value premium," Journal of Economic Dynamics and Control, Elsevier, vol. 120(C).
    15. Kristof Lommers & Ouns El Harzli & Jack Kim, 2021. "Confronting Machine Learning With Financial Research," Papers 2103.00366,, revised Mar 2021.
    16. Ivan Sutoris, 2018. "Asset Prices in a Production Economy with Long Run and Idiosyncratic Risk," CERGE-EI Working Papers wp620, The Center for Economic Research and Graduate Education - Economics Institute, Prague.
    17. Andreas Tryphonides, 2018. "Equilibrium Restrictions and Approximate Models -- With an application to Pricing Macroeconomic Risk," Papers 1805.10869,, revised Dec 2020.
    18. Geert Bekaert & Eric Engstrom & Andrey Ermolov, 2020. "The Variance Risk Premium in Equilibrium Models," NBER Working Papers 27108, National Bureau of Economic Research, Inc.
    19. Gareth Lui-Evans & Shalini Mitra, 2019. "Informality and Bank Stability," Working Papers 201903, University of Liverpool, Department of Economics.
    20. Paolo Guasoni & Gu Wang, 2020. "Consumption in incomplete markets," Finance and Stochastics, Springer, vol. 24(2), pages 383-422, April.
    21. Gu, Shihao & Kelly, Bryan & Xiu, Dacheng, 2021. "Autoencoder asset pricing models," Journal of Econometrics, Elsevier, vol. 222(1), pages 429-450.
    22. Myroslav Pidkuyko & Raffaele Rossi & Klaus Reiner Schenk-Hoppé, 2019. "The Resolution of Long-Run Risk," The School of Economics Discussion Paper Series 1908, Economics, The University of Manchester.

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