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Deep Portfolio Optimization via Distributional Prediction of Residual Factors


  • Kentaro Imajo
  • Kentaro Minami
  • Katsuya Ito
  • Kei Nakagawa


Recent developments in deep learning techniques have motivated intensive research in machine learning-aided stock trading strategies. However, since the financial market has a highly non-stationary nature hindering the application of typical data-hungry machine learning methods, leveraging financial inductive biases is important to ensure better sample efficiency and robustness. In this study, we propose a novel method of constructing a portfolio based on predicting the distribution of a financial quantity called residual factors, which is known to be generally useful for hedging the risk exposure to common market factors. The key technical ingredients are twofold. First, we introduce a computationally efficient extraction method for the residual information, which can be easily combined with various prediction algorithms. Second, we propose a novel neural network architecture that allows us to incorporate widely acknowledged financial inductive biases such as amplitude invariance and time-scale invariance. We demonstrate the efficacy of our method on U.S. and Japanese stock market data. Through ablation experiments, we also verify that each individual technique contributes to improving the performance of trading strategies. We anticipate our techniques may have wide applications in various financial problems.

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  • Kentaro Imajo & Kentaro Minami & Katsuya Ito & Kei Nakagawa, 2020. "Deep Portfolio Optimization via Distributional Prediction of Residual Factors," Papers 2012.07245,
  • Handle: RePEc:arx:papers:2012.07245

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    References listed on IDEAS

    1. Krauss, Christopher & Do, Xuan Anh & Huck, Nicolas, 2017. "Deep neural networks, gradient-boosted trees, random forests: Statistical arbitrage on the S&P 500," European Journal of Operational Research, Elsevier, vol. 259(2), pages 689-702.
    2. Ladislav Kristoufek & Miloslav Vosvrda, 2014. "Measuring capital market efficiency: long-term memory, fractal dimension and approximate entropy," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 87(7), pages 1-9, July.
    3. Blitz, David & Huij, Joop & Martens, Martin, 2011. "Residual momentum," Journal of Empirical Finance, Elsevier, vol. 18(3), pages 506-521, June.
    4. Mensi, Walid & Hamdi, Atef & Shahzad, Syed Jawad Hussain & Shafiullah, Muhammad & Al-Yahyaee, Khamis Hamed, 2018. "Modeling cross-correlations and efficiency of Islamic and conventional banks from Saudi Arabia: Evidence from MF-DFA and MF-DXA approaches," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 502(C), pages 576-589.
    5. 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.
    6. Christopher Krauss & Anh Do & Nicolas Huck, 2017. "Deep neural networks, gradient-boosted trees, random forests: Statistical arbitrage on the S&P 500," Post-Print hal-01768895, HAL.
    7. 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.
    8. Fama, Eugene F. & French, Kenneth R., 2015. "A five-factor asset pricing model," Journal of Financial Economics, Elsevier, vol. 116(1), pages 1-22.
    9. Kei Nakagawa & Takumi Uchida & Tomohisa Aoshima, 2018. "Deep Factor Model," Papers 1810.01278,
    10. Fama, Eugene F, 1970. "Efficient Capital Markets: A Review of Theory and Empirical Work," Journal of Finance, American Finance Association, vol. 25(2), pages 383-417, May.
    11. Blitz, David & Huij, Joop & Lansdorp, Simon & Verbeek, Marno, 2013. "Short-term residual reversal," Journal of Financial Markets, Elsevier, vol. 16(3), pages 477-504.
    12. Amihud, Yakov & Mendelson, Haim, 1987. "Trading Mechanisms and Stock Returns: An Empirical Investigation," Journal of Finance, American Finance Association, vol. 42(3), pages 533-553, July.
    13. Poterba, James M. & Summers, Lawrence H., 1988. "Mean reversion in stock prices : Evidence and Implications," Journal of Financial Economics, Elsevier, vol. 22(1), pages 27-59, October.
    14. Jegadeesh, Narasimhan & Titman, Sheridan, 1993. "Returns to Buying Winners and Selling Losers: Implications for Stock Market Efficiency," Journal of Finance, American Finance Association, vol. 48(1), pages 65-91, March.
    15. Fama, Eugene F & French, Kenneth R, 1992. "The Cross-Section of Expected Stock Returns," Journal of Finance, American Finance Association, vol. 47(2), pages 427-465, June.
    16. Thomas Lux & Michele Marchesi, 2000. "Volatility Clustering In Financial Markets: A Microsimulation Of Interacting Agents," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 3(04), pages 675-702.
    17. Lee, Minhyuk & Song, Jae Wook & Kim, Sondo & Chang, Woojin, 2018. "Asymmetric market efficiency using the index-based asymmetric-MFDFA," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 512(C), pages 1278-1294.
    18. Cao, Guangxi & Cao, Jie & Xu, Longbing, 2013. "Asymmetric multifractal scaling behavior in the Chinese stock market: Based on asymmetric MF-DFA," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(4), pages 797-807.
    19. Fischer, Thomas & Krauss, Christopher, 2018. "Deep learning with long short-term memory networks for financial market predictions," European Journal of Operational Research, Elsevier, vol. 270(2), pages 654-669.
    20. Massoud Metghalchi & Juri Marcucci & Yung-Ho Chang, 2012. "Are moving average trading rules profitable? Evidence from the European stock markets," Applied Economics, Taylor & Francis Journals, vol. 44(12), pages 1539-1559, April.
    21. Fama, Eugene F. & French, Kenneth R., 1993. "Common risk factors in the returns on stocks and bonds," Journal of Financial Economics, Elsevier, vol. 33(1), pages 3-56, February.
    22. 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.
    23. repec:ebl:ecbull:v:7:y:2004:i:3:p:1-10 is not listed on IDEAS
    24. Sanford J. Grossman & Zhongquan Zhou, 1993. "Optimal Investment Strategies For Controlling Drawdowns," Mathematical Finance, Wiley Blackwell, vol. 3(3), pages 241-276, July.
    25. Charles W. Calomiris & Inessa Love & Maria Soledad Martinez Peria, 2010. "Crisis "Shock Factors" and the Cross-Section of Global Equity Returns," NBER Working Papers 16559, National Bureau of Economic Research, Inc.
    26. M. Hossein Partovi & Michael Caputo, 2004. "Principal Portfolios: Recasting the Efficient Frontier," Economics Bulletin, AccessEcon, vol. 7(3), pages 1-10.
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    Cited by:

    1. Vladislav N. Kovalnogov & Ruslan V. Fedorov & Dmitry A. Generalov & Andrey V. Chukalin & Vasilios N. Katsikis & Spyridon D. Mourtas & Theodore E. Simos, 2022. "Portfolio Insurance through Error-Correction Neural Networks," Mathematics, MDPI, vol. 10(18), pages 1-14, September.
    2. Shota Imaki & Kentaro Imajo & Katsuya Ito & Kentaro Minami & Kei Nakagawa, 2021. "No-Transaction Band Network: A Neural Network Architecture for Efficient Deep Hedging," Papers 2103.01775,
    3. Liu Ziyin & Kentaro Minami & Kentaro Imajo, 2021. "Theoretically Motivated Data Augmentation and Regularization for Portfolio Construction," Papers 2106.04114,, revised Dec 2022.

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