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Portfolio Optimization Via Online Gradient Descent and Risk Control

Author

Listed:
  • J. D. M. Yamim

    (Federal University of Juiz de Fora)

  • C. C. H. Borges

    (Federal University of Juiz de Fora
    Federal University of Juiz de Fora)

  • R. F. Neto

    (Federal University of Juiz de Fora
    Federal University of Juiz de Fora)

Abstract

Since Markowitz’s initial contribution in 1952, portfolio selection has undoubtedly been one of the most challenging topics in finance. The development of online optimization techniques indicates that dynamic learning algorithms are an effective approach to portfolio construction, although they do not evaluate the risk associated with each investment decision. In this work, the performance of the well-known Online Gradient Descent (OGD) algorithm is evaluated in comparison with a proposed approach that incorporates portfolio risk using $$\beta $$ β control of portfolio assets modeled with the CAPM strategy and considering a time-varying $$\beta $$ β that follows a random walk. Thus, the traditional OGD algorithm and the OGD with $$\beta $$ β constraints are compared with the Uniform Constant Rebalanced Portfolio (UCRP) and two specific indexes for the Brazilian market, consisting of small caps and the assets belonging to the Bovespa index. The experiments have shown that $$\beta $$ β control, combined with an appropriate definition of the $$\beta $$ β interval by the investor, is an efficient strategy, regardless of market periods with gains or losses. Moreover, time-varying $$\beta $$ β has been shown to be an efficient measure to force the desired correlation with the market and also to reduce the volatility of the portfolio, especially during hazardous bear markets.

Suggested Citation

  • J. D. M. Yamim & C. C. H. Borges & R. F. Neto, 2023. "Portfolio Optimization Via Online Gradient Descent and Risk Control," Computational Economics, Springer;Society for Computational Economics, vol. 62(1), pages 361-381, June.
    • Handle: RePEc:kap:compec:v:62:y:2023:i:1:d:10.1007_s10614-022-10284-0
    DOI: 10.1007/s10614-022-10284-0
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    References listed on IDEAS

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    1. Robert M. Bell & Thomas M. Cover, 1980. "Competitive Optimality of Logarithmic Investment," Mathematics of Operations Research, INFORMS, vol. 5(2), pages 161-166, May.
    2. Michalski, Grzegorz, 2007. "Portofolio Managament Approach in Trade Credit Decision Making," Journal for Economic Forecasting, Institute for Economic Forecasting, vol. 4(3), pages 42-53, September.
    3. Robert Bell & Thomas M. Cover, 1988. "Game-Theoretic Optimal Portfolios," Management Science, INFORMS, vol. 34(6), pages 724-733, June.
    4. Aleksandras Rutkauskas & Jelena Stankeviciene, 2006. "Integrated asset and liability portfolio as instrument of liquidity management in the commercial bank," Journal of Business Economics and Management, Taylor & Francis Journals, vol. 7(2), pages 45-57.
    5. Alexei Gaivoronski & Fabio Stella, 2000. "Stochastic Nonstationary Optimization for Finding Universal Portfolios," Annals of Operations Research, Springer, vol. 100(1), pages 165-188, December.
    6. Carlo Acerbi & Dirk Tasche, 2002. "Expected Shortfall: A Natural Coherent Alternative to Value at Risk," Economic Notes, Banca Monte dei Paschi di Siena SpA, vol. 31(2), pages 379-388, July.
    7. Durbin, James & Koopman, Siem Jan, 2012. "Time Series Analysis by State Space Methods," OUP Catalogue, Oxford University Press, edition 2, number 9780199641178.
    8. Bin Li & Jialei Wang & Dingjiang Huang & Steven C. H. Hoi, 2018. "Transaction cost optimization for online portfolio selection," Quantitative Finance, Taylor & Francis Journals, vol. 18(8), pages 1411-1424, August.
    9. Zhao, Yonggan, 2007. "A dynamic model of active portfolio management with benchmark orientation," Journal of Banking & Finance, Elsevier, vol. 31(11), pages 3336-3356, November.
    10. 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.
    11. Philippe Artzner & Freddy Delbaen & Jean‐Marc Eber & David Heath, 1999. "Coherent Measures of Risk," Mathematical Finance, Wiley Blackwell, vol. 9(3), pages 203-228, July.
    12. Thomas M. Cover, 1991. "Universal Portfolios," Mathematical Finance, Wiley Blackwell, vol. 1(1), pages 1-29, January.
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