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High-Frequency Tail Risk Premium and Stock Return Predictability

Published online by Cambridge University Press:  31 October 2023

Caio Almeida Open the ORCID record for Caio Almeida [Opens in a new window] ,
Kym Ardison ,
Gustavo Freire ,
René Garcia  and
Piotr Orłowski
Caio Almeida*
Affiliation:
Princeton University Department of Economics and Bendheim Center for Finance
Kym Ardison
Affiliation:
SPX Capital kymmarcel@gmail.com
Gustavo Freire
Affiliation:
Erasmus University Rotterdam, Tinbergen Institute and ERIM freire@ese.eur.nl
René Garcia
Affiliation:
Université de Montréal and Toulouse School of Economics rene.garcia@umontreal.ca
Piotr Orłowski
Affiliation:
Department of Finance, HEC Montréal piotr.orlowski@hec.ca
*
calmeida@princeton.edu (corresponding author)
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Abstract

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We propose a novel measure of the market return tail risk premium based on minimum-distance state price densities recovered from high-frequency data. The tail risk premium extracted from intra-day S&P 500 returns predicts the market equity and variance risk premiums and expected excess returns on a cross section of characteristics-sorted portfolios. Additionally, we describe the differential role of the quantity of tail risk, and of the tail premium, in shaping the future distribution of index returns. Our results are robust to controlling for established measures of variance and tail risk, and of risk premiums, in the predictive models.

Type
Research Article
Information
Journal of Financial and Quantitative Analysis , Volume 59 , Issue 8 , December 2024 , pp. 3633 - 3670
Creative Commons
Creative Common License - CCCreative Common License - BY
This is an Open Access article, distributed under the terms of the Creative Commons Attribution licence (http://creativecommons.org/licenses/by/4.0), which permits unrestricted re-use, distribution and reproduction, provided the original article is properly cited.
Copyright
© The Author(s), 2023. Published by Cambridge University Press on behalf of the Michael G. Foster School of Business, University of Washington

Footnotes

We thank an anonymous referee, Thierry Foucault (the editor), Rodrigo Hizmeri, seminar participants at the Kellogg School of Management, and conference participants at the 2017 SoFiE Conference, the 2017 Vienna-Copenhagen Conference on Financial Econometrics, and the 2018 IAAE Meeting for useful comments and suggestions. Ardison acknowledges financial support from ANBIMA and FAPERJ. Garcia thanks the NSERC, the SSHRC, and the FQRSC research grant agencies for their financial support. He is a TSE associate faculty and a research Fellow of CIRANO and CIREQ.

References

Adrian, T., and Brunnermeier, M. K.. “CoVar.” American Economic Review, 106 (2016), 1705–1741.CrossRefGoogle Scholar
Ait-Sahalia, Y., and Lo, A. W.. “Nonparametric Estimation of State-Price Densities Implicit in Financial Asset Prices.” Journal of Finance, 53 (1998), 499–547.CrossRefGoogle Scholar
Ait-Sahalia, Y., and Lo, A. W.. “Nonparametric Risk Management and Implied Risk Aversion.” Journal of Econometrics, 94 (2000), 9–51.CrossRefGoogle Scholar
Allen, L.; Bali, T. G.; and Tang, Y.. “Does Systemic Risk in the Financial Sector Predict Future Economic Downturns?” Review of Financial Studies, 25 (2012), 3000–3036.CrossRefGoogle Scholar
Almeida, C.; Ardison, K.; Garcia, R.; and Vicente, J.. “Nonparametric Tail Risk, Stock Returns and the Macroeconomy.” Journal of Financial Econometrics, 15 (2017), 333–376.CrossRefGoogle Scholar
Almeida, C., and Freire, G.. “Pricing of Index Options in Incomplete Markets.” Journal of Financial Economics, 144 (2022), 174–205.CrossRefGoogle Scholar
Almeida, C., and Garcia, R.. “Economic Implications of Nonlinear Pricing Kernels.” Management Science, 63 (2017), 3361–3380.CrossRefGoogle Scholar
Andersen, T. G.; Bollerslev, T.; Diebold, F. X.; and Labys, P.. “Modeling and Forecasting Realized Volatility.” Econometrica, 71 (2003), 579–625.CrossRefGoogle Scholar
Andersen, T. G.; Fusari, N.; and Todorov, V.. “Short-Term Market Risks Implied by Weekly Options.” Journal of Finance, 72 (2017), 1335–1386.CrossRefGoogle Scholar
Andersen, T. G.; Fusari, N.; and Todorov, V.. “The Pricing of Tail Risk and the Equity Premium: Evidence from International Option Markets.” Journal of Business & Economic Statistics, 38 (2020), 662–678.CrossRefGoogle Scholar
Andrews, D. W. K. “Heteroskedasticity and Autocorrelation Consistent Covariance Matrix Estimation.” Econometrica, 59 (1991), 817.CrossRefGoogle Scholar
Ang, A.; Chen, J.; and Xing, Y.. “Downside Risk.” Review of Financial Studies, 19 (2006), 1191–1239.CrossRefGoogle Scholar
Artzner, P.; Delbaen, F.; Eber, J.; and Heath, D.. “Coherent Measures of Risk.” Mathematical Finance, 9 (1999), 223–228.CrossRefGoogle Scholar
Aït-Sahalia, Y.; Jacod, J.; and Xiu, D.. “Inference on Risk Premia in Continuous-Time Asset Pricing Models.” Working Paper No. 20–30, The University of Chicago (2020).CrossRefGoogle Scholar
Backus, D.; Chernov, M.; and Martin, I.. “Disasters Implied by Equity Index Options.” Journal of Finance, 66 (2011), 1969–2011.CrossRefGoogle Scholar
Bali, T. G.; Demirtas, K. O.; and Levy, H.. “Is There a Relation Between Downside Risk and Expected Stock Returns?” Journal of Financial and Quantitative Analysis, 44 (2009), 883–909.CrossRefGoogle Scholar
Bansal, R., and Yaron, A.. “Risks for the Long Run: A Potential Resolution of Asset Pricing Puzzles.” Journal of Finance, 59 (2004), 1481–1509.CrossRefGoogle Scholar
Bekaert, G., and Engstrom, E.. “Asset Return Dynamics Under Habits and Bad Environment–Good Environment Fundamentals.” Journal of Political Economy, 125 (2017), 713–760.CrossRefGoogle Scholar
Berkowitz, J., and O’Brien, J.. “How Accurate Are Value-at-Risk Models at Commercial Banks?” Journal of Finance, 57 (2002), 1093–1111.CrossRefGoogle Scholar
Bollerslev, T.; Li, S. Z.; and Todorov, V.. “Roughing Up Beta: Continuous vs. Discontinuous Betas, and the Cross-Section of Expected Stock Returns.” Journal of Financial Economics, 120 (2016), 464–490.CrossRefGoogle Scholar
Bollerslev, T.; Tauchen, G.; and Zhou, H.. “Expected Stock Returns and Variance Risk Premia.” Review of Financial Studies, 22 (2009), 4463–4492.CrossRefGoogle Scholar
Bollerslev, T.; Todorov, V.; and Li, S. Z.. “Jump Tails, Extreme Dependencies, and the Distribution of Stock Returns.” Journal of Econometrics, 172 (2013), 307–324.CrossRefGoogle Scholar
Bollerslev, T.; Todorov, V.; and Xu, L.. “Tail Risk Premia and Return Predictability.” Journal of Financial Economics, 118 (2015), 113–134.CrossRefGoogle Scholar
Bollerslev, T., and Todorov, V.. “Tails, Fears, and Risk Premia.” Journal of Finance, 66 (2011), 2165–2211.CrossRefGoogle Scholar
Bollerslev, T., and Todorov, V.. “Time-Varying Jump Tails.” Journal of Econometrics, 183 (2014), 168–180.CrossRefGoogle Scholar
Bonomo, M.; Garcia, R.; Meddahi, N.; and Tédongap, R.. “The Long and the Short of the Risk-Return Trade-Off.” Journal of Econometrics, 187 (2015), 580–592.CrossRefGoogle Scholar
Britten-Jones, M.; Neuberger, A.; and Nolte, I.. “Improved Inference in Regression with Overlapping Observations.” Journal of Business Finance & Accounting, 38 (2011), 657–683.CrossRefGoogle Scholar
Brownlees, C., and Engle, R.. “SRISK: A Conditional Capital Shortfall Measure of Systemic Risk.” Review of Financial Studies, 30 (2017), 48–79.CrossRefGoogle Scholar
Campbell, J. Y., and Thompson, S.. “Predicting Excess Stock Returns out of Sample: Does Anything Beat the Historical Average?” Review of Financial Studies, 21 (2008), 1509–1531.CrossRefGoogle Scholar
Campbell, J., and Cochrane, J.. “Force of Habit: A Consumption-Based Explanation of Aggregate Stock Market Behavior.” Journal of Political Economy, 107 (1999), 205–251.CrossRefGoogle Scholar
Castro, L. d., and Galvao, A. F.. “Dynamic Quantile Models of Rational Behavior.” Econometrica, 87 (2019), 1893–1939.CrossRefGoogle Scholar
Christoffersen, P. F. “Evaluating Interval Forecasts.” International Economic Review, 39 (1998), 841–862.CrossRefGoogle Scholar
Clark, T. E., and West, K. D.. “Approximately Normal Tests for Equal Predictive Accuracy in Nested Models.” Journal of Econometrics, 138 (2007), 291–311.CrossRefGoogle Scholar
Corsi, F. “A Simple Approximate Long-Memory Model of Realized Volatility.” Journal of Financial Econometrics, 7 (2009), 174–196.CrossRefGoogle Scholar
Drechsler, I., and Yaron, A.. “What’s Vol Got to Do with It.” Review of Financial Studies, 24 (2011), 1–45.CrossRefGoogle Scholar
Fama, E. F., and French, K. R.. “Common Risk Factors in the Returns on Stocks and Bonds.” Journal of Financial Economics, 33 (1993), 3–56.CrossRefGoogle Scholar
Fama, E. F., and French, K. R.. “Dissecting Anomalies with a Five-Factor Model.” Review of Financial Studies, 29 (2015), 69–103.CrossRefGoogle Scholar
Farago, A., and Tédongap, R.. “Downside Risks and the Cross-Section of Asset Returns.” Journal of Financial Economics, 129 (2018), 69–86.CrossRefGoogle Scholar
Ghysels, E., and Wang, F.. “Moment-Implied Densities: Properties and Applications.” Journal of Business & Economic Statistics, 32 (2014), 88–111.CrossRefGoogle Scholar
Gul, F. “A Theory of Disappointment Aversion.” Econometrica, 59 (1991), 667–686.CrossRefGoogle Scholar
Hansen, L., and Richard, S.. “The Role of Conditioning Information in Deducing Testable Restrictions Implied by Dynamic Asset Pricing Models.” Econometrica, 55 (1987), 587–613.CrossRefGoogle Scholar
Hou, K.; Xue, C.; and Zhang, L.. “Digesting Anomalies: An Investment Approach.” Review of Financial Studies, 28 (2014), 650–705.CrossRefGoogle Scholar
Huggenberger, M.; Zhang, C.; and Zhou, T.. “Forward-Looking Tail Risk Measures.” Working Paper, University of Mannheim (2018).CrossRefGoogle Scholar
Jorion, P. “Risk Management Lessons from the Credit Crisis.” European Financial Management, 15 (2019), 923–933.CrossRefGoogle Scholar
Kahneman, D., and Tversky, A.. “Prospect Theory: An Analysis of Decision Under Risk.” Econometrica, 47 (1979), 263–291.CrossRefGoogle Scholar
Kelly, B., and Jiang, H.. “Tail Risk and Asset Prices.” Review of Financial Studies, 27 (2014), 2841–2871.CrossRefGoogle Scholar
Kitamura, Y. “Empirical Likelihood Methods in Econometrics: Theory and Practice.” In Advances in Economics and Econometrics: Theory and Applications, Ninth World Congress, Vol. 3., Blundell, R., Newey, W., and Persson, T., eds. Cambridge, UK: Cambridge University Press (2007), 174–237.Google Scholar
Koenker, R. quantreg: Quantile Regression. R Package Version 5.83. Vienna: R Foundation for Statistical Computing. Available at: http://CRAN.R-project.org/package=quantreg (2013).Google Scholar
Koenker, R., and Gilbert Bassett, J.. “Regression Quantiles.” Econometrica, 46 (1978), 33–50.CrossRefGoogle Scholar
Koenker, R., and Machado, J. A.. “Goodness of Fit and Related Inference Processes for Quantile Regression.” Journal of the American Statistical Association, 94 (1999), 1296–1310.CrossRefGoogle Scholar
Kraus, A., and Litzenberger, R. H.. “Skewness Preference and the Valuation of Risk Assets.” Journal of Finance, 31 (1976), 1085–1100.Google Scholar
Mancini, C. “Non-Parametric Threshold Estimation for Models with Stochastic Diffusion Coefficient and Jumps.” Scandinavian Journal of Statistics, 36 (2009), 270–296.CrossRefGoogle Scholar
Mancini, C., and Gobbi, F.. “Identifying the Brownian Covariation from the Co-Jumps Given Discrete Observations.” Econometric Theory, 28 (2012), 249–273.CrossRefGoogle Scholar
Martin, I. “What Is the Expected Return on the Market?” Quarterly Journal of Economics, 132 (2017), 367–433.CrossRefGoogle Scholar
McNeil, A.; Rudiger, F.; and Paul, E.. Quantitative Risk Management. Princeton, NJ: Princeton University Press (2005).Google Scholar
Pettenuzzo, D.; Timmermann, A.; and Valkanov, R.. “Forecasting Stock Returns Under Economic Constraints.” Journal of Financial Economics, 114 (2014), 517–553.CrossRefGoogle Scholar
Routledge, B. R., and Zin, S. E.. “Generalized Disappointment Aversion and Asset Prices.” Journal of Finance, 65 (2010), 1303–1332.CrossRefGoogle Scholar
Siriwardane, E. “The Probability of Rare Disasters: Estimation and Implications.” Working Paper, New York University (2013).CrossRefGoogle Scholar
Vilkov, G., and Xiao, Y.. “Option-Implied Information and Predictability of Extreme Returns.” Working Paper, Goethe University (2013).CrossRefGoogle Scholar
Weller, B. “Measuring Tail Risks at High-Frequency.” Review of Financial Studies, 32 (2019), 3571–3616.CrossRefGoogle Scholar
Zeileis, A.; Köll, S.; and Graham, N.. “Various Versatile Variances: An Object-Oriented Implementation of Clustered Covariances in R.” Journal of Statistical Software, 95 (2020), 1–36.CrossRefGoogle Scholar