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A Novel Black-Litterman Model with Time-Varying Covariance for Optimal Asset Allocation of Pension Funds

Author

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  • Yuqin Sun

    (Department of Mathematics and Computer Engineering, Ordos Institute of Technology, Ordos 017000, China)

  • Yungao Wu

    (Department of Mathematics and Computer Engineering, Ordos Institute of Technology, Ordos 017000, China)

  • Gejirifu De

    (State Grid Economic and Technological Research Institute Co., Ltd., Beijing 102209, China)

Abstract

The allocation of pension funds has important theoretical value and practical significance, which improves the level of pension investment income, achieves the maintenance and appreciation of pension funds, and resolves the pension payment risk caused by population aging. The asset allocation of pension funds is a long-term asset allocation problem. Thus, the long-term risk and return of the assets need to be estimated. The covariance matrix is usually adopted to measure the risk of the assets, while calculating the long-term covariance matrix is extremely difficult. Direct calculations suffer from the insufficiency of historical data, and indirect calculations accumulate short-term covariance, which suffers from the dynamic changes of the covariance matrix. Since the returns of main assets are highly autocorrelated, the covariance matrix of main asset returns is time-varying with dramatic dynamic changes, and the errors of indirect calculation cannot be ignored. In this paper, we propose a novel Black–Litterman model with time-varying covariance (TVC-BL) for the optimal asset allocation of pension funds to address the time-varying nature of asset returns and risks. Firstly, the return on assets (ROA) and the covariance of ROA are modeled by VARMA and GARCH, respectively. Secondly, the time-varying covariance estimation of ROA is obtained by introducing an effective transformation of the covariance matrix from short-term to long-term. Finally, the asset allocation decision of pension funds is achieved by the TVC-BL model. The results indicate that the proposed TVC-BL pension asset allocation model outperforms the traditional BL model. When the risk aversion coefficient is 1, 1.5, and 3, the Sharp ratio of pension asset allocation through the TVC-BL pension asset allocation model is 13.0%, 10.5%, and 12.8% higher than that of the traditional BL model. It helps to improve the long-term investment returns of pension funds, realize the preservation and appreciation of pension funds, and resolve the pension payment risks caused by the aging of the population.

Suggested Citation

  • Yuqin Sun & Yungao Wu & Gejirifu De, 2023. "A Novel Black-Litterman Model with Time-Varying Covariance for Optimal Asset Allocation of Pension Funds," Mathematics, MDPI, vol. 11(6), pages 1-21, March.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:6:p:1476-:d:1100395
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    as
    1. Klein, Roger W. & Bawa, Vijay S., 1976. "The effect of estimation risk on optimal portfolio choice," Journal of Financial Economics, Elsevier, vol. 3(3), pages 215-231, June.
    2. Laurens Defau & Lieven De Moor, 2021. "The investment behaviour of pension funds in alternative assets: Interest rates and portfolio diversification," International Journal of Finance & Economics, John Wiley & Sons, Ltd., vol. 26(1), pages 1424-1434, January.
    3. Barua, Ronil & Sharma, Anil K., 2022. "Dynamic Black Litterman portfolios with views derived via CNN-BiLSTM predictions," Finance Research Letters, Elsevier, vol. 49(C).
    4. Cong, F. & Oosterlee, C.W., 2016. "Multi-period mean–variance portfolio optimization based on Monte-Carlo simulation," Journal of Economic Dynamics and Control, Elsevier, vol. 64(C), pages 23-38.
    5. Brennan, Michael J. & Schwartz, Eduardo S. & Lagnado, Ronald, 1997. "Strategic asset allocation," Journal of Economic Dynamics and Control, Elsevier, vol. 21(8-9), pages 1377-1403, June.
    6. Oscar V. De la Torre-Torres & Francisco Venegas-Martínez & Mᵃ Isabel Martínez-Torre-Enciso, 2021. "Enhancing Portfolio Performance and VIX Futures Trading Timing with Markov-Switching GARCH Models," Mathematics, MDPI, vol. 9(2), pages 1-22, January.
    7. Campbell, John Y. & Viceira, Luis M., 2002. "Strategic Asset Allocation: Portfolio Choice for Long-Term Investors," OUP Catalogue, Oxford University Press, number 9780198296942.
    8. Wei-Hung Lin & Huei-Wen Teng & Chi-Chun Yang, 2020. "A Heteroskedastic Black–Litterman Portfolio Optimization Model with Views Derived from a Predictive Regression," World Scientific Book Chapters, in: Cheng Few Lee & John C Lee (ed.), HANDBOOK OF FINANCIAL ECONOMETRICS, MATHEMATICS, STATISTICS, AND MACHINE LEARNING, chapter 14, pages 563-581, World Scientific Publishing Co. Pte. Ltd..
    9. Dutta, Jayasri & Kapur, Sandeep & Orszag, J. Michael, 2000. "A portfolio approach to the optimal funding of pensions," Economics Letters, Elsevier, vol. 69(2), pages 201-206, November.
    10. Blake, David & Cairns, Andrew J. G. & Dowd, Kevin, 2001. "Pensionmetrics: stochastic pension plan design and value-at-risk during the accumulation phase," Insurance: Mathematics and Economics, Elsevier, vol. 29(2), pages 187-215, October.
    11. Wing Cheung, 2013. "The augmented Black--Litterman model: a ranking-free approach to factor-based portfolio construction and beyond," Quantitative Finance, Taylor & Francis Journals, vol. 13(2), pages 301-316, January.
    12. J. Tobin, 1958. "Liquidity Preference as Behavior Towards Risk," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 25(2), pages 65-86.
    13. Steven Haberman & Elena Vigna, 2002. "Optimal investment strategies and risk measures in defined contribution pension schemes," ICER Working Papers - Applied Mathematics Series 09-2002, ICER - International Centre for Economic Research.
    14. Haberman, Steven & Vigna, Elena, 2002. "Optimal investment strategies and risk measures in defined contribution pension schemes," Insurance: Mathematics and Economics, Elsevier, vol. 31(1), pages 35-69, August.
    15. Arenas Parra, M. & Bilbao Terol, A. & Rodriguez Uria, M. V., 2001. "A fuzzy goal programming approach to portfolio selection," European Journal of Operational Research, Elsevier, vol. 133(2), pages 287-297, January.
    16. Ding, Zhuanxin & Martin, R. Douglas, 2017. "The fundamental law of active management: Redux," Journal of Empirical Finance, Elsevier, vol. 43(C), pages 91-114.
    17. 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.
    18. Stoll, Hans R. & Whaley, Robert E., 1990. "The Dynamics of Stock Index and Stock Index Futures Returns," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 25(4), pages 441-468, December.
    19. Emmanouil Platanakis & Charles Sutcliffe, 2017. "Asset–liability modelling and pension schemes: the application of robust optimization to USS," The European Journal of Finance, Taylor & Francis Journals, vol. 23(4), pages 324-352, March.
    20. Philip Booth & Yakoub Yakoubov, 2000. "Investment Policy for Defined-Contribution Pension Scheme Members Close to Retirement," North American Actuarial Journal, Taylor & Francis Journals, vol. 4(2), pages 1-19.
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