Оптимизация долгосрочного инвестирования на основе диверсификации Марковица
Аннотация
В работе рассмотрен алгоритм для долгосрочного инвестирования, позволяющий находить оптимальные решения в пространстве меньшей размерности. Снижение размерности достигается путем применения метода главных компонент или ядерного метода главных компонент. Подбор весов для портфеля осуществляется с помощью метода Марковица. В качестве гиперпараметров для модели рассмотрены размер окна, параметр сглаживания, период ребалансировки и доля объясненной дисперсии в методах уменьшения размерности. Представленный алгоритм содержит регуляризацию весов с учетом комиссии за перебалансировку портфеля. Подбор гиперпараметров осуществляется на основе коэффициента Мартина, что позволяет учитывать максимальную просадку для рассматриваемых алгоритмов. Показано, что предложенный алгоритм, оптимизированный на данных с 1990 по 2016 год, способен обеспечить более высокую доходность и значение коэффициента Шарпа, чем бенчмарк S&P 500 в период с 2017 по 2022 год. Это свидетельствует о том, что с помощью корректировки весов в портфеле можно улучшить производительность алгоритма.
Скачивания
Литература
The World Bank Group (2023) Market capitalization of listed domestic companies. World Federation of Exchanges database. Available at: https://data.worldbank.org/indicator/CM.MKT.LCAP.CD (accessed 20 November 2023).
Abramov A.E., Kosyrev A.G., Radygin A.D., Chernova M.I. (2021) Behavior of private investors in the stock markets of Russia and the US. Russian Economic Developments, vol. 18, pp. 11–16 (in Russian).
Markowitz H. (1952) Portfolio selection. The Journal of Finance, vol. 7, no. 1, pp. 77–91. https://doi.org/10.2307/2975974
Durall R. (2022) Asset allocation: From Markowitz to deep reinforcement learning. arXiv:2208.07158. https://doi.org/10.48550/arXiv.2208.07158
Best M.J., Grauer R.R. (1991) On the sensitivity of mean–variance-efficient portfolios to changes in asset means: Some analytical and computational results. The Review of Financial Studies, vol. 4, no. 2, pp. 315–342. https://doi.org/10.1093/rfs/4.2.315
Stefatos G., Hamza A.B. (2007) Cluster PCA for outliers detection in high-dimensional data. Proceedings of the 2007 IEEE International Conference on Systems, Man and Cybernetics, Montreal, QC, Canada, pp. 3961–3966. https://doi.org/10.1109/ICSMC.2007.4414244.
Saha B.N., Ray N., Zhang H. (2009) Snake validation: A PCA-based outlier detection method. IEEE Signal Processing Letters, vol. 16, no. 6, pp. 549–552. https://doi.org/10.1109/LSP.2009.2017477
Peng Y., Albuquerque P.H.M., do Nascimento I.F., Machado J.V.F. (2019) Between nonlinearities, complexity, and noises: An application on portfolio selection using kernel principal component analysis. Entropy, vol. 21, no. 4, 376. https://doi.org/10.3390/e21040376
Ma Y., Han R., Wang W. (2021) Portfolio optimization with return prediction using deep learning and machine learning. Expert Systems with Applications, vol. 165, 113973. https://doi.org/10.1016/j.eswa.2020.113973
Heaton J.B., Polson N., Witte J. (2016) Deep learning for finance: Deep portfolios. Applied Stochastic Models in Business and Industry, vol. 33, no. 1, pp. 3–12. https://doi.org/10.2139/ssrn.2838013
Chen K., Zhou Y., Dai F. (2015) A LSTM-based method for stock returns prediction: A case study of China stock market. Proceedings of the 2015 IEEE International Conference on Big Data (Big Data), Santa Clara, CA, USA, pp. 2823–2824. https://doi.org/10.1109/BigData.2015.7364089
Yun H., Lee M., Kang Y.S., Seok J. (2020) Portfolio management via two-stage deep learning with a joint cost. Expert Systems with Applications, vol. 143, 113041. https://doi.org/10.1016/j.eswa.2019.113041
Chong E., Han C., Park F. (2017) Deep learning networks for stock market analysis and prediction: Methodology, data representations, and case studies. Expert Systems with Applications, vol. 83, pp. 187–205. https://doi.org/10.1016/j.eswa.2017.04.030
Fischer T., Krauss C. (2018) Deep learning with long short-term memory networks for financial market predictions. European Journal of Operational Research, vol. 270, no. 2, pp. 654–669. https://doi.org/10.1016/j.ejor.2017.11.054
Hoseinzade E., Haratizadeh S. (2019) CNNpred: CNN-based stock market prediction using a diverse set of variables. Expert Systems with Applications, vol. 129, pp. 273–285. https://doi.org/10.1016/j.eswa.2019.03.029
Kim J., Lee M. (2023) Portfolio optimization using predictive auxiliary classifier generative adversarial networks. Engineering Applications of Artificial Intelligence, vol. 125, 106739. https://doi.org/10.1016/j.engappai.2023.106739
Siaw R., Ofosu-Hene E., Tee E. (2017) Investment portfolio optimization with GARCH models. Elk Asia Pacific Journal of Finance and Risk Management, vol. 8, no. 2. Available at: https://ssrn.com/abstract=2987932 (accessed 04 August 2024).
Bardenet R., Bengio Y., Bergstra J., Kégl B. (2011) Algorithms for hyper-parameter optimization. Proceedings of the Advances in Neural Information Processing Systems 24 (NIPS 2011).
Martin P.G., McCann B.B. (1989) The investor’s guide to fidelity funds. John Wiley & Sons.
S&P Global (2023) S&P 500. S&P Dow Jones Indices. Available at: https://www.spglobal.com/spdji/en/indices/equity/sp-500/#overview (accessed 20 November 2023).
Beneish M.D., Whaley R.E. (1997) A scorecard from the S&P game. Journal of Portfolio Management, vol. 16, no. 2, 23.
Latham S., Braun M. (2010) Does short-termism influence firm innovation? An examination of S&P 500 firms 1990–2003. Journal of Managerial Issues, vol. 22, no. 3, pp. 368–382.
Zhang Z. (2022) Study of portfolio performance under certain restraint comparison: Markowitz Model and Single Index Model on S&P 500. Proceedings of the 2022 7th International Conference on Social Sciences and Economic Development, pp. 1930–1938. https://doi.org/10.2991/aebmr.k.220405.323
Lien G. (2002) Non-parametric estimation of decision makers’ risk aversion. Agricultural Economics, vol. 27, no. 1, pp. 75–83. https://doi.org/10.1016/S0169-5150(01)00063-9
Fama E.F., MacBeth J. (1973) Risk, return, and equilibrium: Empirical tests. Journal of Political Economy, vol. 71, pp. 607–636.
Paolella M.S. (2017) The univariate collapsing method for portfolio optimization. Econometrics, vol. 5, no. 2, 18. https://doi.org/10.3390/econometrics5020018
The CVXPY authors (2023) CVXPY 1.4 Manual. Available at: https://www.cvxpy.org/index.html (accessed 20 November 2023).
Bakir G., Weston J., Schölkopf B. (2003) Learning to find pre-images. Proceedings of the Advances in Neural Information Processing Systems 16 (NIPS 2003).
The SciPy community (2023) SciPy v1.11.4 Manual. Available at: https://docs.scipy.org/doc/scipy/tutorial/optimize.html (accessed 20 November 2023).
Drenovak M., Rankovic V. (2014) Markowitz portfolio rebalancing with turnover monitoring. Economic Horizons, vol. 16, no. 3, pp. 207–217. https://doi.org/10.5937/ekonhor1403211D
scikit-learn. Machine Learning in Python (2023) API Reference. sklearn.model_selection. RandomizedSearchCV. Available at: https://scikit-learn.org/stable/modules/generated/sklearn.model_selection.RandomizedSearchCV.html (accessed 20 November 2023).
GitHub (2023) yfinance documentation. Available at: https://yfinance.readthedocs.io/en/documentation/ (accessed 20 November 2023).
scikit-learn. Machine Learning in Python (2023) API Reference. sklearn.model_selection. TimeSeriesSplit. Available at: https://scikit-learn.org/stable/modules/generated/sklearn.model_selection.TimeSeriesSplit.html (accessed 20 November 2023).
Interactive chart of research results. Available at: https://disk.yandex.ru/d/5nF7RiXKIWp1ig (accessed 20 November 2023).
.jpg)
