IDEAS home Printed from https://ideas.repec.org/p/arx/papers/2107.13866.html
   My bibliography  Save this paper

Machine Learning and Factor-Based Portfolio Optimization

Author

Listed:
  • Thomas Conlon
  • John Cotter
  • Iason Kynigakis

Abstract

We examine machine learning and factor-based portfolio optimization. We find that factors based on autoencoder neural networks exhibit a weaker relationship with commonly used characteristic-sorted portfolios than popular dimensionality reduction techniques. Machine learning methods also lead to covariance and portfolio weight structures that diverge from simpler estimators. Minimum-variance portfolios using latent factors derived from autoencoders and sparse methods outperform simpler benchmarks in terms of risk minimization. These effects are amplified for investors with an increased sensitivity to risk-adjusted returns, during high volatility periods or when accounting for tail risk.

Suggested Citation

  • Thomas Conlon & John Cotter & Iason Kynigakis, 2021. "Machine Learning and Factor-Based Portfolio Optimization," Papers 2107.13866, arXiv.org.
  • Handle: RePEc:arx:papers:2107.13866
    as

    Download full text from publisher

    File URL: http://arxiv.org/pdf/2107.13866
    File Function: Latest version
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. Kelly, Bryan T. & Pruitt, Seth & Su, Yinan, 2019. "Characteristics are covariances: A unified model of risk and return," Journal of Financial Economics, Elsevier, vol. 134(3), pages 501-524.
    2. Zhenyu Wang, 2005. "A Shrinkage Approach to Model Uncertainty and Asset Allocation," Review of Financial Studies, Society for Financial Studies, vol. 18(2), pages 673-705.
    3. Jianqing Fan & Yuan Liao & Martina Mincheva, 2013. "Large covariance estimation by thresholding principal orthogonal complements," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 75(4), pages 603-680, September.
    4. Daniele Bianchi & Matthias Büchner & Tobias Hoogteijling & Andrea Tamoni, 2021. "Corrigendum: Bond Risk Premiums with Machine Learning [Bond risk premiums with machine learning]," Review of Financial Studies, Society for Financial Studies, vol. 34(2), pages 1090-1103.
    5. Andrew Ang & Geert Bekaert, 2002. "International Asset Allocation With Regime Shifts," Review of Financial Studies, Society for Financial Studies, vol. 15(4), pages 1137-1187.
    6. Jushan Bai & Serena Ng, 2002. "Determining the Number of Factors in Approximate Factor Models," Econometrica, Econometric Society, vol. 70(1), pages 191-221, January.
    7. Victor DeMiguel & Lorenzo Garlappi & Raman Uppal, 2009. "Optimal Versus Naive Diversification: How Inefficient is the 1-N Portfolio Strategy?," Review of Financial Studies, Society for Financial Studies, vol. 22(5), pages 1915-1953, May.
    8. Guanhao Feng & Stefano Giglio & Dacheng Xiu, 2020. "Taming the Factor Zoo: A Test of New Factors," Journal of Finance, American Finance Association, vol. 75(3), pages 1327-1370, June.
    9. Olivier Ledoit & Michael Wolf, 2017. "Nonlinear Shrinkage of the Covariance Matrix for Portfolio Selection: Markowitz Meets Goldilocks," Review of Financial Studies, Society for Financial Studies, vol. 30(12), pages 4349-4388.
    10. Michael W. McCracken & Serena Ng, 2016. "FRED-MD: A Monthly Database for Macroeconomic Research," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 34(4), pages 574-589, October.
    11. Louis K.C. Chan & Jason Karceski & Josef Lakonishok, 1999. "On Portfolio Optimization: Forecasting Covariances and Choosing the Risk Model," NBER Working Papers 7039, National Bureau of Economic Research, Inc.
    12. Ravi Jagannathan & Tongshu Ma, 2003. "Risk Reduction in Large Portfolios: Why Imposing the Wrong Constraints Helps," Journal of Finance, American Finance Association, vol. 58(4), pages 1651-1683, August.
    13. D’Hondt, Catherine & De Winne, Rudy & Ghysels, Eric & Raymond, Steve, 2020. "Artificial Intelligence Alter Egos: Who might benefit from robo-investing?," Journal of Empirical Finance, Elsevier, vol. 59(C), pages 278-299.
    14. Vijay K. Chopra & Chris R. Hensel & Andrew L. Turner, 1993. "Massaging Mean-Variance Inputs: Returns from Alternative Global Investment Strategies in the 1980s," Management Science, INFORMS, vol. 39(7), pages 845-855, July.
    15. Joachim Freyberger & Andreas Neuhierl & Michael Weber & Andrew KarolyiEditor, 2020. "Dissecting Characteristics Nonparametrically," Review of Financial Studies, Society for Financial Studies, vol. 33(5), pages 2326-2377.
    16. Kan, Raymond & Zhou, Guofu, 2007. "Optimal Portfolio Choice with Parameter Uncertainty," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 42(3), pages 621-656, September.
    17. Victor DeMiguel & Lorenzo Garlappi & Francisco J. Nogales & Raman Uppal, 2009. "A Generalized Approach to Portfolio Optimization: Improving Performance by Constraining Portfolio Norms," Management Science, INFORMS, vol. 55(5), pages 798-812, May.
    18. Daniele Bianchi & Matthias Büchner & Andrea Tamoni, 2021. "Bond Risk Premiums with Machine Learning [Quadratic term structure models: Theory and evidence]," Review of Financial Studies, Society for Financial Studies, vol. 34(2), pages 1046-1089.
    19. DeMiguel, Victor & Lassance, Nathan & Vrins, Frédéric, 2021. "Optimal Portfolio Diversification via Independent Component Analysis," LIDAM Reprints LFIN 2021012, Université catholique de Louvain, Louvain Finance (LFIN).
    20. Stephen A. Ross, 2013. "The Arbitrage Theory of Capital Asset Pricing," World Scientific Book Chapters, in: Leonard C MacLean & William T Ziemba (ed.), HANDBOOK OF THE FUNDAMENTALS OF FINANCIAL DECISION MAKING Part I, chapter 1, pages 11-30, World Scientific Publishing Co. Pte. Ltd..
    21. Gianluca De Nard & Olivier Ledoit & Michael Wolf, 2018. "Factor models for portfolio selection in large dimensions: the good, the better and the ugly," ECON - Working Papers 290, Department of Economics - University of Zurich, revised Dec 2018.
    22. Christopher J. Neely & David E. Rapach & Jun Tu & Guofu Zhou, 2014. "Forecasting the Equity Risk Premium: The Role of Technical Indicators," Management Science, INFORMS, vol. 60(7), pages 1772-1791, July.
    23. Stock, James H. & Watson, Mark, 2011. "Dynamic Factor Models," Scholarly Articles 28469541, Harvard University Department of Economics.
    24. MacKinlay, A Craig & Pastor, Lubos, 2000. "Asset Pricing Models: Implications for Expected Returns and Portfolio Selection," Review of Financial Studies, Society for Financial Studies, vol. 13(4), pages 883-916.
    25. Frahm, Gabriel & Memmel, Christoph, 2010. "Dominating estimators for minimum-variance portfolios," Journal of Econometrics, Elsevier, vol. 159(2), pages 289-302, December.
    26. Gabriel Frahm, 2010. "Linear statistical inference for global and local minimum variance portfolios," Statistical Papers, Springer, vol. 51(4), pages 789-812, December.
    27. Doron Avramov & Tarun Chordia, 2006. "Asset Pricing Models and Financial Market Anomalies," Review of Financial Studies, Society for Financial Studies, vol. 19(3), pages 1001-1040.
    28. Andrew Y. Chen & Tom Zimmermann, 2022. "Open Source Cross-Sectional Asset Pricing," Critical Finance Review, now publishers, vol. 11(2), pages 207-264, May.
    29. John Lintner, 1965. "Security Prices, Risk, And Maximal Gains From Diversification," Journal of Finance, American Finance Association, vol. 20(4), pages 587-615, December.
    30. Kozak, Serhiy & Nagel, Stefan & Santosh, Shrihari, 2020. "Shrinking the cross-section," Journal of Financial Economics, Elsevier, vol. 135(2), pages 271-292.
    31. Kewei Hou & Chen Xue & Lu Zhang, 2015. "Editor's Choice Digesting Anomalies: An Investment Approach," Review of Financial Studies, Society for Financial Studies, vol. 28(3), pages 650-705.
    32. Robert F. Engle, 2016. "Dynamic Conditional Beta," The Journal of Financial Econometrics, Society for Financial Econometrics, vol. 14(4), pages 643-667.
    33. Green, Richard C & Hollifield, Burton, 1992. "When Will Mean-Variance Efficient Portfolios Be Well Diversified?," Journal of Finance, American Finance Association, vol. 47(5), pages 1785-1809, December.
    34. Fama, Eugene F. & French, Kenneth R., 2015. "A five-factor asset pricing model," Journal of Financial Economics, Elsevier, vol. 116(1), pages 1-22.
    35. Chamberlain, Gary & Rothschild, Michael, 1983. "Arbitrage, Factor Structure, and Mean-Variance Analysis on Large Asset Markets," Econometrica, Econometric Society, vol. 51(5), pages 1281-1304, September.
    36. Nathaniel Light & Denys Maslov & Oleg Rytchkov, 2017. "Aggregation of Information About the Cross Section of Stock Returns: A Latent Variable Approach," Review of Financial Studies, Society for Financial Studies, vol. 30(4), pages 1339-1381.
    37. Hyonho Chun & Sündüz Keleş, 2010. "Sparse partial least squares regression for simultaneous dimension reduction and variable selection," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 72(1), pages 3-25, January.
    38. Ledoit, Oliver & Wolf, Michael, 2008. "Robust performance hypothesis testing with the Sharpe ratio," Journal of Empirical Finance, Elsevier, vol. 15(5), pages 850-859, December.
    39. Jianqing Fan & Alex Furger & Dacheng Xiu, 2016. "Incorporating Global Industrial Classification Standard Into Portfolio Allocation: A Simple Factor-Based Large Covariance Matrix Estimator With High-Frequency Data," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 34(4), pages 489-503, October.
    40. Forni, Mario & Hallin, Marc & Lippi, Marco & Reichlin, Lucrezia, 2005. "The Generalized Dynamic Factor Model: One-Sided Estimation and Forecasting," Journal of the American Statistical Association, American Statistical Association, vol. 100, pages 830-840, September.
    41. Alexander Kempf & Christoph Memmel, 2006. "Estimating the global Minimum Variance Portfolio," Schmalenbach Business Review (sbr), LMU Munich School of Management, vol. 58(4), pages 332-348, October.
    42. David E. Rapach & Jack K. Strauss & Guofu Zhou, 2013. "International Stock Return Predictability: What Is the Role of the United States?," Journal of Finance, American Finance Association, vol. 68(4), pages 1633-1662, August.
    43. Newey, Whitney & West, Kenneth, 2014. "A simple, positive semi-definite, heteroscedasticity and autocorrelation consistent covariance matrix," Applied Econometrics, Russian Presidential Academy of National Economy and Public Administration (RANEPA), vol. 33(1), pages 125-132.
    44. Engle, Robert F. & Ng, Victor K. & Rothschild, Michael, 1990. "Asset pricing with a factor-arch covariance structure : Empirical estimates for treasury bills," Journal of Econometrics, Elsevier, vol. 45(1-2), pages 213-237.
    45. Connor, Gregory & Korajczyk, Robert A., 1988. "Risk and return in an equilibrium APT : Application of a new test methodology," Journal of Financial Economics, Elsevier, vol. 21(2), pages 255-289, September.
    46. Yufeng Han, 2006. "Asset Allocation with a High Dimensional Latent Factor Stochastic Volatility Model," Review of Financial Studies, Society for Financial Studies, vol. 19(1), pages 237-271.
    47. Robert F. Engle & Olivier Ledoit & Michael Wolf, 2019. "Large Dynamic Covariance Matrices," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 37(2), pages 363-375, April.
    48. Turan G. Bali & Robert F. Engle & Yi Tang, 2017. "Dynamic Conditional Beta Is Alive and Well in the Cross Section of Daily Stock Returns," Management Science, INFORMS, vol. 63(11), pages 3760-3779, November.
    49. Ravi Jagannathan & Tongshu Ma, 2003. "Risk Reduction in Large Portfolios: Why Imposing the Wrong Constraints Helps," Journal of Finance, American Finance Association, vol. 58(4), pages 1651-1684, August.
    50. Merton, Robert C., 1980. "On estimating the expected return on the market : An exploratory investigation," Journal of Financial Economics, Elsevier, vol. 8(4), pages 323-361, December.
    51. Platanakis, Emmanouil & Sutcliffe, Charles & Ye, Xiaoxia, 2021. "Horses for courses: Mean-variance for asset allocation and 1/N for stock selection," European Journal of Operational Research, Elsevier, vol. 288(1), pages 302-317.
    52. Tobias J. Moskowitz, 2003. "An Analysis of Covariance Risk and Pricing Anomalies," Review of Financial Studies, Society for Financial Studies, vol. 16(2), pages 417-457.
    53. Kirby, Chris & Ostdiek, Barbara, 2012. "It’s All in the Timing: Simple Active Portfolio Strategies that Outperform Naïve Diversification," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 47(2), pages 437-467, April.
    54. repec:hal:journl:peer-00741629 is not listed on IDEAS
    55. Hjalmarsson, Erik & Manchev, Petar, 2012. "Characteristic-based mean-variance portfolio choice," Journal of Banking & Finance, Elsevier, vol. 36(5), pages 1392-1401.
    56. David Ardia & Guido Bolliger & Kris Boudt & Jean-Philippe Gagnon-Fleury, 2017. "The impact of covariance misspecification in risk-based portfolios," Annals of Operations Research, Springer, vol. 254(1), pages 1-16, July.
    57. Martin Lettau & Markus Pelger & Stijn Van Nieuwerburgh, 2020. "Factors That Fit the Time Series and Cross-Section of Stock Returns," Review of Financial Studies, Society for Financial Studies, vol. 33(5), pages 2274-2325.
    58. Pettenuzzo, Davide & Timmermann, Allan, 2011. "Predictability of stock returns and asset allocation under structural breaks," Journal of Econometrics, Elsevier, vol. 164(1), pages 60-78, September.
    59. Chen, Nai-Fu & Roll, Richard & Ross, Stephen A, 1986. "Economic Forces and the Stock Market," The Journal of Business, University of Chicago Press, vol. 59(3), pages 383-403, July.
    60. Engle, Robert & Colacito, Riccardo, 2006. "Testing and Valuing Dynamic Correlations for Asset Allocation," Journal of Business & Economic Statistics, American Statistical Association, vol. 24, pages 238-253, April.
    61. Massimo Guidolin & Allan Timmermann, 2008. "International asset allocation under regime switching, skew, and kurtosis preferences," Review of Financial Studies, Society for Financial Studies, vol. 21(2), pages 889-935, April.
    62. Jean Boivin & Serena Ng, 2005. "Understanding and Comparing Factor-Based Forecasts," International Journal of Central Banking, International Journal of Central Banking, vol. 1(3), December.
    63. Martin Lettau & Markus Pelger, 2020. "Factors That Fit the Time Series and Cross-Section of Stock Returns," Review of Finance, European Finance Association, vol. 33(5), pages 2274-2325.
    64. Engle, Robert, 2002. "Dynamic Conditional Correlation: A Simple Class of Multivariate Generalized Autoregressive Conditional Heteroskedasticity Models," Journal of Business & Economic Statistics, American Statistical Association, vol. 20(3), pages 339-350, July.
    65. Branger, Nicole & Lučivjanská, Katarína & Weissensteiner, Alex, 2019. "Optimal granularity for portfolio choice," Journal of Empirical Finance, Elsevier, vol. 50(C), pages 125-146.
    66. Moura, Guilherme V. & Santos, André A.P. & Ruiz, Esther, 2020. "Comparing high-dimensional conditional covariance matrices: Implications for portfolio selection," Journal of Banking & Finance, Elsevier, vol. 118(C).
    67. Becker, R. & Clements, A.E. & Doolan, M.B. & Hurn, A.S., 2015. "Selecting volatility forecasting models for portfolio allocation purposes," International Journal of Forecasting, Elsevier, vol. 31(3), pages 849-861.
    68. Best, Michael J & Grauer, Robert R, 1991. "On the Sensitivity of Mean-Variance-Efficient Portfolios to Changes in Asset Means: Some Analytical and Computational Results," Review of Financial Studies, Society for Financial Studies, vol. 4(2), pages 315-342.
    69. William F. Sharpe, 1964. "Capital Asset Prices: A Theory Of Market Equilibrium Under Conditions Of Risk," Journal of Finance, American Finance Association, vol. 19(3), pages 425-442, September.
    70. Carroll, Rachael & Conlon, Thomas & Cotter, John & Salvador, Enrique, 2017. "Asset allocation with correlation: A composite trade-off," European Journal of Operational Research, Elsevier, vol. 262(3), pages 1164-1180.
    71. Thomas J. Sargent & Christopher A. Sims, 1977. "Business cycle modeling without pretending to have too much a priori economic theory," Working Papers 55, Federal Reserve Bank of Minneapolis.
    72. Kewei Hou & Haitao Mo & Chen Xue & Lu Zhang, 2021. "An Augmented q-Factor Model with Expected Growth [Abnormal returns to a fundamental analysis strategy]," Review of Finance, European Finance Association, vol. 25(1), pages 1-41.
    73. Hui Zou & Trevor Hastie, 2005. "Addendum: Regularization and variable selection via the elastic net," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 67(5), pages 768-768, November.
    74. Chan, Louis K C & Karceski, Jason & Lakonishok, Josef, 1999. "On Portfolio Optimization: Forecasting Covariances and Choosing the Risk Model," Review of Financial Studies, Society for Financial Studies, vol. 12(5), pages 937-974.
    75. Stock J.H. & Watson M.W., 2002. "Forecasting Using Principal Components From a Large Number of Predictors," Journal of the American Statistical Association, American Statistical Association, vol. 97, pages 1167-1179, December.
    76. Hui Zou & Trevor Hastie, 2005. "Regularization and variable selection via the elastic net," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 67(2), pages 301-320, April.
    77. Fan, Jianqing & Fan, Yingying & Lv, Jinchi, 2008. "High dimensional covariance matrix estimation using a factor model," Journal of Econometrics, Elsevier, vol. 147(1), pages 186-197, November.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Gianluca De Nard & Olivier Ledoit & Michael Wolf, 2018. "Factor models for portfolio selection in large dimensions: the good, the better and the ugly," ECON - Working Papers 290, Department of Economics - University of Zurich, revised Dec 2018.
    2. Ruili Sun & Tiefeng Ma & Shuangzhe Liu & Milind Sathye, 2019. "Improved Covariance Matrix Estimation for Portfolio Risk Measurement: A Review," JRFM, MDPI, vol. 12(1), pages 1-34, March.
    3. Aït-Sahalia, Yacine & Xiu, Dacheng, 2017. "Using principal component analysis to estimate a high dimensional factor model with high-frequency data," Journal of Econometrics, Elsevier, vol. 201(2), pages 384-399.
    4. Carroll, Rachael & Conlon, Thomas & Cotter, John & Salvador, Enrique, 2017. "Asset allocation with correlation: A composite trade-off," European Journal of Operational Research, Elsevier, vol. 262(3), pages 1164-1180.
    5. Stadtmüller, Immo & Auer, Benjamin R. & Schuhmacher, Frank, 2022. "On the benefits of active stock selection strategies for diversified investors," The Quarterly Review of Economics and Finance, Elsevier, vol. 85(C), pages 342-354.
    6. Ding, Yi & Li, Yingying & Zheng, Xinghua, 2021. "High dimensional minimum variance portfolio estimation under statistical factor models," Journal of Econometrics, Elsevier, vol. 222(1), pages 502-515.
    7. Seyoung Park & Eun Ryung Lee & Sungchul Lee & Geonwoo Kim, 2019. "Dantzig Type Optimization Method with Applications to Portfolio Selection," Sustainability, MDPI, vol. 11(11), pages 1-32, June.
    8. Füss, Roland & Miebs, Felix & Trübenbach, Fabian, 2014. "A jackknife-type estimator for portfolio revision," Journal of Banking & Finance, Elsevier, vol. 43(C), pages 14-28.
    9. Clarke, Charles, 2022. "The level, slope, and curve factor model for stocks," Journal of Financial Economics, Elsevier, vol. 143(1), pages 159-187.
    10. Iason Kynigakis & Ekaterini Panopoulou, 2022. "Does model complexity add value to asset allocation? Evidence from machine learning forecasting models," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 37(3), pages 603-639, April.
    11. Yan, Cheng & Zhang, Huazhu, 2017. "Mean-variance versus naïve diversification: The role of mispricing," Journal of International Financial Markets, Institutions and Money, Elsevier, vol. 48(C), pages 61-81.
    12. Johannes Bock, 2018. "An updated review of (sub-)optimal diversification models," Papers 1811.08255, arXiv.org.
    13. Wang, Christina Dan & Chen, Zhao & Lian, Yimin & Chen, Min, 2022. "Asset selection based on high frequency Sharpe ratio," Journal of Econometrics, Elsevier, vol. 227(1), pages 168-188.
    14. Chen, Jia & Li, Degui & Linton, Oliver, 2019. "A new semiparametric estimation approach for large dynamic covariance matrices with multiple conditioning variables," Journal of Econometrics, Elsevier, vol. 212(1), pages 155-176.
    15. Cai, T. Tony & Hu, Jianchang & Li, Yingying & Zheng, Xinghua, 2020. "High-dimensional minimum variance portfolio estimation based on high-frequency data," Journal of Econometrics, Elsevier, vol. 214(2), pages 482-494.
    16. Caldeira, João F & Moura, Guilherme Valle & Santos, André Alves Portela, 2013. "Seleção de carteiras utilizando o modelo Fama-French-Carhart," Revista Brasileira de Economia - RBE, EPGE Brazilian School of Economics and Finance - FGV EPGE (Brazil), vol. 67(1), April.
    17. Hansen, Erwin, 2022. "Economic evaluation of asset pricing models under predictability," Journal of Empirical Finance, Elsevier, vol. 68(C), pages 50-66.
    18. Santos, André Alves Portela & Ferreira, Alexandre R., 2017. "On the choice of covariance specifications for portfolio selection problems," Brazilian Review of Econometrics, Sociedade Brasileira de Econometria - SBE, vol. 37(1), May.
    19. Hsu, Po-Hsuan & Han, Qiheng & Wu, Wensheng & Cao, Zhiguang, 2018. "Asset allocation strategies, data snooping, and the 1 / N rule," Journal of Banking & Finance, Elsevier, vol. 97(C), pages 257-269.
    20. Philipp J. Kremer & Andreea Talmaciu & Sandra Paterlini, 2018. "Risk minimization in multi-factor portfolios: What is the best strategy?," Annals of Operations Research, Springer, vol. 266(1), pages 255-291, July.

    More about this item

    JEL classification:

    • C38 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Classification Methdos; Cluster Analysis; Principal Components; Factor Analysis
    • C4 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics
    • C45 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - Neural Networks and Related Topics
    • C5 - Mathematical and Quantitative Methods - - Econometric Modeling
    • C58 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Financial Econometrics
    • G1 - Financial Economics - - General Financial Markets
    • G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:arx:papers:2107.13866. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: . General contact details of provider: http://arxiv.org/ .

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: arXiv administrators (email available below). General contact details of provider: http://arxiv.org/ .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.