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Systematic Risk in Publicly Listed Private Equity: An Empirical Study Using Score-Driven Beta Models

  • August Jörding and Szabolcs Blazsek EMAIL logo
Published/Copyright: September 26, 2025
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Abstract

We investigate systematic risk dynamics using the LPX Group’s 10 indices, which represent publicly listed private equity (PLPE) market indices as well as different PLPE investment styles and PLPE performance at alternative geographic regions. PLPE is a hybrid asset class that combines private capital exposure with public market liquidity. Using daily data from 2002 to 2025 and a recent score-driven modeling framework, i.e. the autoregressive conditional beta (ACB) model for the t-distribution (t-ACB), we demonstrate that the betas and volatility are highly time-varying and LPX-specific, particularly during periods of macroeconomic or financial crisis. Contrary to classical theory, LPX betas do not converge in crises, revealing persistent heterogeneity across PLPE firms. These findings challenge the assumptions underlying static asset pricing models and conventional methods for estimating the cost of equity. By capturing how systematic risk evolves across indices and regimes, this paper extends the literature by offering a more accurate framework for valuing hybrid assets and managing risk in an increasingly institutionalized segment of the private equity market.

JEL Classification: C22; C51; C52; G12

Corresponding author: Szabolcs Blazsek, Stetson–Hatcher School of Business, Mercer University, 1511-1565 College Street, Macon, GA, 31207, USA, E-mail: 

Acknowledgments

We greatly appreciate the LPX Group’s help in providing the LPX index data. Computer codes are available from the authors upon request.

  1. Author contributions: All the authors have accepted responsibility for the entire content of this submitted manuscript and approved submission.

  2. Conflict of interest: The authors declare no conflicts of interest regarding this article.

  3. Research funding: This research did not receive funding.

References

Adrian, T., E. Etula, and T. Muir. 2014. “Financial Intermediaries and the Cross-Section of Asset Returns.” Journal of Finance 69 (6): 2557–96. https://doi.org/10.1111/jofi.12189.Search in Google Scholar

Aigner, P., G. Beyschlag, T. Friederich, M. Kalepky, and R. Zagst. 2012. “Modeling and Managing Portfolios Including Listed Private Equity.” Computers and Operations Research 39 (4): 753–64. https://doi.org/10.1016/j.cor.2010.12.015.Search in Google Scholar

AnalystPrep. 2024. “Beta and the Cost of Equity – CFA Level I and II Study Guide.” https://analystprep.com/cfa-level-1-exam/corporate-finance/beta-cost-capital-project/.Search in Google Scholar

Ang, A., and J. Chen. 2007. “CAPM over the Long Run: 1926–2001.” Journal of Empirical Finance 14 (1): 1–40. https://doi.org/10.1016/j.jempfin.2006.05.001.Search in Google Scholar

Angelidis, T., and S. Degiannakis. 2007. “On the Comparative Performance of Conditional Covariance Models.” Journal of Financial Econometrics 5 (2): 293–327. https://doi.org/10.1093/jjfinec/nbm004.Search in Google Scholar

Anson, M. 2024. “Amortizing Volatility across Private Capital Investments.” Journal of Portfolio Management 50 (1): 115–23. https://doi.org/10.3905/jpm.2024.1.608.Search in Google Scholar

Bilo, S., H. Christophers, M. Degosciu, and H. Zimmermann. 2005. “Risk, Returns and Biases of Listed Private Equity Portfolios.” Working paper No. 1/05, University of Basel, WWZ/Department of Finance. https://hdl.handle.net/10419/123348.Search in Google Scholar

Blasques, F., S. J. Koopman, and A. Lucas. 2015. “Information-theoretic Optimality of Observation-Driven Time Series Models for Continuous Responses.” Biometrika 102 (2): 325–43. https://doi.org/10.1093/biomet/asu076.Search in Google Scholar

Blasques, F., C. Francq, and S. Laurent. 2023. “Autoregressive Conditional Betas.” Journal of Econometrics 234 (2): 412–37. https://doi.org/10.1016/j.jeconom.2023.105630.Search in Google Scholar

Blazsek, S., A. Jörding, and N. Rai. 2024. “Generalized Autoregressive Conditional Betas: A New Multivariate Score-Driven Filter.” Studies in Nonlinear Dynamics and Econometrics 29 (1): 95–128. https://doi.org/10.1515/snde-2023-0019.Search in Google Scholar

Brown, G. W., O. R. Gredil, and S. N. Kaplan. 2020. “Do Private Equity Funds Manipulate Reported Returns?” Journal of Financial Economics 135 (2): 255–77. https://doi.org/10.1016/j.jfineco.2019.06.003.Search in Google Scholar

Carhart, M. M. 1997. “On Persistence in Mutual Fund Performance.” Journal of Finance 52 (1): 57–82. https://doi.org/10.1111/j.1540-6261.1997.tb03808.x.Search in Google Scholar

CFA Institute. 2021. “Revisiting Beta: How Well Has Beta Predicted Returns?” CFA Institute Blog. https://blogs.cfainstitute.org/investor/2021/09/01/revisiting-beta-how-well-has-beta-predicted-returns/.Search in Google Scholar

Chakrabarti, G., and R. Das. 2021. “Time-varying Beta, Market Volatility and Stress: A Comparison between the United States and India.” IIMB Management Review 33 (1): 9–23. https://doi.org/10.1016/j.iimb.2021.03.003.Search in Google Scholar

Chen, N., R. Roll, and S. A. Ross. 1986. “Economic Forces and the Stock Market.” Journal of Business 59 (3): 383–403. https://doi.org/10.1086/296344.Search in Google Scholar

Choudhry, T., L. Lu, and K. Peng. 2010. “Time-varying Beta and the Asian Financial Crisis: Evidence from the Asian Industrial Sectors.” Japan and the World Economy 22 (2): 88–104. https://doi.org/10.1016/j.japwor.2010.06.003.Search in Google Scholar

Creal, D., S. J. Koopman, and A. Lucas. 2008. “A General Framework for Observation Driven Time-Varying Parameter Models.” Tinbergen Institute Discussion Paper 08-108/4. https://papers.tinbergen.nl/08108.pdf.10.2139/ssrn.1297183Search in Google Scholar

Creal, D., S. J. Koopman, and A. Lucas. 2013. “Generalized Autoregressive Score Models with Applications.” Journal of Applied Econometrics 28 (5): 777–95. https://doi.org/10.1002/jae.1279.Search in Google Scholar

Cumming, D., L. H. Haß, and D. Schweizer. 2013. “Private Equity Benchmarks and Portfolio Optimization.” Journal of Banking and Finance 37 (9): 3515–28. https://doi.org/10.1016/j.jbankfin.2013.04.010.Search in Google Scholar

Darolles, S., C. Francq, and S. Laurent. 2018. “Asymptotics of Cholesky GARCH Models and Time-Varying Conditional Betas.” Journal of Econometrics 204 (2): 223–47. https://doi.org/10.1016/j.jeconom.2018.02.003.Search in Google Scholar

Díaz, A., C. Esparcia, and L. Tegtmeier. 2025. “Private Equity Market Dynamics: Beyond the Surface.” International Review of Economics and Finance 100: 104087. https://doi.org/10.1016/j.iref.2025.104087.Search in Google Scholar

Döpke, J., and L. Tegtmeier. 2018. “Global Risk Factors in the Returns of Listed Private Equity.” Studies in Economics and Finance 35 (2): 340–60. https://doi.org/10.1108/SEF-03-2017-0069.Search in Google Scholar

Engle, R. F. 2016. “Dynamic Conditional Beta.” Journal of Financial Econometrics 14 (4): 643–66. https://doi.org/10.1093/jjfinec/nbw006.Search in Google Scholar

Fama, E. F., and K. R. French. 1992. “The Cross-Section of Expected Stock Returns.” Journal of Finance 47 (2): 427–65. https://doi.org/10.1111/j.1540-6261.1992.tb04398.x.Search in Google Scholar

Fama, E. F., and K. R. French. 1993. “Common Risk Factors in the Returns on Stocks and Bonds.” Journal of Financial Economics 33 (1): 3–56. https://doi.org/10.1016/0304-405X(93)90023-5.Search in Google Scholar

Fama, E. F., and K. R. French. 1996. “Multifactor Explanations of Asset Pricing Anomalies.” Journal of Finance 51 (1): 55–84. https://doi.org/10.1111/j.1540-6261.1996.tb05202.x.Search in Google Scholar

Fama, E. F., and K. R. French. 2015. “A Five-Factor Asset Pricing Model.” Journal of Financial Economics 116 (1): 1–22. https://doi.org/10.1016/j.jfineco.2014.10.010.Search in Google Scholar

Gagliardini, P., E. Ossola, and O. Scaillet. 2016. “Time-varying Risk Premium in Large Cross-Sectional Equity Data Sets.” Econometrica 84 (3): 985–1046. https://doi.org/10.3982/ECTA11243.Search in Google Scholar

Gorgi, P., C. S. A. Lauria, and A. Luati. 2024. “On the Optimality of Score-Driven Models.” Biometrika 111 (3): 865–80. https://doi.org/10.1093/biomet/asad067.Search in Google Scholar

Grassi, S., and F. Violante. 2021. “Asset Pricing Using Block-Cholesky GARCH and Time-Varying Betas.” CEIS Working Paper No. 510. https://doi.org/10.2139/ssrn.3802874.Search in Google Scholar

Grassi, S., and F. Violante. 2025. “Generalized Autoregressive Conditional Betas: Longitudinal Feedback in Multifactor Asset Pricing.” Journal of Business and Economic Statistics: 1–13. https://doi.org/10.1080/07350015.2025.2478984.Search in Google Scholar

Harvey, A. C. 2013. Dynamic Models of Volatility and Heavy Tails. Cambridge: Cambridge University Press.10.1017/CBO9781139540933Search in Google Scholar

Harvey, A. C., and T. Chakravarty. 2008. “Beta-t-(E)GARCH.” Cambridge Working Papers in Economics, 0840. https://doi.org/10.17863/CAM.5286.Search in Google Scholar

Hasnaoui, H., and I. Fatnassi. 2014. “Time-varying Beta and the Subprime Financial Crisis: Evidence from U.S. Industrial Sectors.” Journal of Applied Business Research 30 (6): 1819–32. https://doi.org/10.19030/jabr.v30i5.8799.Search in Google Scholar

Huss, M., and H. Zimmermann. 2018. “The Pricing of Liquidity Risk in Buyout Funds–A Public Market Perspective.” Schmalenbach Business Review 70 (3): 285–312. https://doi.org/10.1007/s41464-018-0050-6.Search in Google Scholar

Jegadeesh, N., R. Kräussl, and J. M. Pollet. 2015. “Risk and Expected Returns of Private Equity Investments: Evidence Based on Market Prices.” Review of Financial Studies 28 (12): 3261–303. https://doi.org/10.1093/rfs/hhv046.Search in Google Scholar

Kallenos, T. L., and G. P. Nishiotis. 2023. “Market-based Private Equity Returns.” Journal of Banking & Finance 157: 107045. https://doi.org/10.1016/j.jbankfin.2023.107045.Search in Google Scholar

Kurtovic, H., and G. Markarian. 2024. “Tail Risks and Private Equity Performance.” Journal of Empirical Finance 75: 101457. https://doi.org/10.1016/j.jempfin.2023.101457.Search in Google Scholar

Lahr, H., and F. T. Herschke. 2009. “Organizational Forms and Risk of Listed Private Equity.” The Journal of Private Equity 13 (1): 89–99. https://doi.org/10.3905/JPE.2009.13.1.089.Search in Google Scholar

Leung, T. N. 2013. “A Systematic Risk Analysis of Listed Private Equity.” Journal of Private Equity 16 (2): 8–21. https://doi.org/10.3905/jpe.2013.16.2.093.Search in Google Scholar

Lintner, J. 1965. “The Valuation of Risky Assets and the Selection of Risky Investments in Stock Portfolios and Capital Budgets.” Review of Economics and Statistics 47 (1): 13–37. https://doi.org/10.2307/1924119.Search in Google Scholar

McCourt, M. 2022. “Permanent Private Equity: Market Performance and Transactions.” Journal of Financial Research 45 (2): 339–83. https://doi.org/10.1111/jfir.12277.Search in Google Scholar

McKinsey and Company. 2023. “Global Private Markets Review 2023.” https://www.mckinsey.com/industries/private-capital/our-insights/mckinseys-private-markets-annual-review-2023.Search in Google Scholar

Metrick, A., and A. Yasuda. 2010. “The Economics of Private Equity Funds.” Review of Financial Studies 23 (6): 2303–41. https://doi.org/10.1093/rfs/hhq020.Search in Google Scholar

Newey, W. K., and K. D. West. 1987. “A Simple, Positive Semi-definite, Heteroscedasticity and Autocorrelation Consistent Covariance Matrix.” Econometrica 55 (3): 703–8. https://doi.org/10.2307/1913610.Search in Google Scholar

Patton, A. J., and M. Verardo. 2012. “Does Beta Move with News? Firm-specific Information Flows and Learning about Profitability.” Review of Financial Studies 25 (9): 2789–839. https://doi.org/10.1093/rfs/hhs073.Search in Google Scholar

Phalippou, L., and O. Gottschalg. 2009. “The Performance of Private Equity Funds.” Review of Financial Studies 22 (4): 1747–76. https://doi.org/10.1093/rfs/hhn014.Search in Google Scholar

Ross, S. A. 1976. “The Arbitrage Theory of Capital Asset Pricing.” Journal of Economic Theory 13 (3): 341–60. https://doi.org/10.1016/0022-0531(76)90046-6.Search in Google Scholar

Sharpe, W. F. 1964. “Capital Asset Prices: A Theory of Market Equilibrium under Conditions of Risk.” Journal of Finance 19 (3): 425–42. https://doi.org/10.1111/j.1540-6261.1964.tb02865.x.Search in Google Scholar

Sveriges Riksbank. 2025. “Private Equity: A Growing Market in Transition.” Financial Stability Report 2025: 1. https://www.riksbank.se/en-gb/research/financial-stability/financial-stability-reports/.Search in Google Scholar

Tegtmeier, L. 2023. “Modeling the Volatilities of Globally Listed Private Equity Markets.” Studies in Economics and Finance 40 (1): 29–51. https://doi.org/10.1108/SEF-04-2021-0129.Search in Google Scholar

Zhou, J. 2013. “Conditional Market Beta for REITs: A Comparison of Modeling Techniques.” Economic Modelling 30: 271–7. https://doi.org/10.1016/j.econmod.2012.09.030.Search in Google Scholar


Supplementary Material

This article contains supplementary material (https://doi.org/10.1515/snde-2025-0085).


Received: 2025-06-29
Accepted: 2025-09-17
Published Online: 2025-09-26

© 2025 Walter de Gruyter GmbH, Berlin/Boston

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