基于AdaBoost的投资组合优化

doi:10.12341/jssms21059

系统科学与数学 ›› 2022, Vol. 42 ›› Issue (2): 271-286.DOI: 10.12341/jssms21059

基于AdaBoost的投资组合优化

钱龙¹, 韦江², 赵慧敏³, 倪宣明⁴

1. 清华大学经济管理学院, 北京 100084;
2. 清华大学学生处, 北京 100084;
3. 中山大学管理学院, 广州 510275;
4. 北京大学软件与微电子学院, 北京 100871

收稿日期:2021-02-01 修回日期:2021-07-01 出版日期:2022-02-25 发布日期:2022-03-21
通讯作者: 倪宣明,Email:nixm@ss.pku.edu.cn.
基金资助:
国家自然科学基金（71991474）资助课题.

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钱龙, 韦江, 赵慧敏, 倪宣明. 基于AdaBoost的投资组合优化[J]. 系统科学与数学, 2022, 42(2): 271-286.

QIAN Long, WEI Jiang, ZHAO Huimin, NI Xuanming. Portfolio Optimization Based on AdaBoost[J]. Journal of Systems Science and Mathematical Sciences, 2022, 42(2): 271-286.

Portfolio Optimization Based on AdaBoost

QIAN Long¹, WEI Jiang², ZHAO Huimin³, NI Xuanming⁴

1. School of Economics & Management, Tsinghua University, Beijing 100084;
2. Students' Affairs Office, Tsinghua University, Beijing 100084;
3. School of Business, Sun Yat-Sen University, Guangzhou 510275;
4. School of Software & Microelectronics, Peking University, Beijing 100871

Received:2021-02-01 Revised:2021-07-01 Online:2022-02-25 Published:2022-03-21

文章利用AdaBoost集成学习技术提升均值-方差（MV）策略的表现.首先，文章对二次期望效用损失函数进行了分歧分解，从理论上表明集成学习技术有助于提升投资组合策略的表现.其次，文章将收益率均值和协方差压缩估计量中的压缩强度设定为样本外绩效驱动，并利用迭代有效集法和梯度下降法最大化效用的值函数，从而构建了参数化的MV策略作为文章策略AdaBoost.PT的弱学习器.在实证方面，文章利用A股近25年和美股近40年的全股票样本数据，考察了集成投资组合策略在夏普率、标准差、换手率和最大回撤方面的样本外表现，并利用假设检验对夏普率差异的显著性进行验证.基于因子组合数据集的实证结果显示，基于收益率均值压缩估计量的集成策略在4个评估指标下和差异性统计检验中能够取得优于基准策略的结果，此外，使用行业组合数据集的稳健性检验同样显示出一致的结果.

关键词： 投资组合优化, 集成学习, 分歧分解

This paper adopts the AdaBoost ensemble learning technique to boost the performance of mean-variance (MV) strategy. Firstly, this paper conducts an ambiguity decomposition on the quadratic cost function of expected utility, which proves that ensemble learning can boost the performance of portfolio strategies. Secondly, we parameterize the shrinkage intensity of the mean and covariance shrinkage estimator of return to be out-of-sample driven, and use iterative active set and gradient descent algorithms to maximize the value function, constructing parameterized MV strategy as the weak learner of proposed AdaBoost.PT. In terms of empirical study, we utilize the full panel stock data of A shares in near 25 years and American shares in near 40 years, and examine the performance of ensemble portfolio strategies in terms of Sharpe ratio, standard deviation, turnover and maximum drawdown, and then conduct a hypothesis test to check the significance of Sharpe ratio's difference. The empirical results show that the ensemble strategies based on return shrinkage estimator are superior to the baseline strategies under all four indices and statistical tests, and the robust tests based on industrial portfolios also show the same results.

Key words: Portfolio optimization, ensemble learning, ambiguity decomposition

MR(2010)主题分类:

68Q32
91G10

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[1] Markowitz H. Portfolio selection. The Journal of Finance, 1952, 7(1):77-91.
[2] Merton R C. On estimating the expected return on the market:An exploratory investigation. Journal of Financial Economics, 1980, 8(4):323-361.
[3] Michaud R O. The Markowitz optimization enigma:Is 'optimized' optimal? Financial Analysts Journal, 1989, 45(1):31-42.
[4] Best M J, Grauer R R. On the sensitivity of mean-variance-efficient portfolios to changes in asset means:Some analytical and computational results. The Review of Financial Studies, 1991, 4(2):315-342.
[5] Chopra V K, Ziemba W T. The effect of errors in means, variances, and covariances on optimal portfolio choice. The Journal of Portfolio Management, 1993, 19(2):6-11.
[6] Frost P A, Savarino J E. For better performance:Constrain portfolio weights. The Journal of Portfolio Management, 1988, 15(1):29-34.
[7] Jagannathan R, Ma T. Risk reduction in large portfolios:Why imposing the wrong constraints helps. The Journal of Finance, 2003, 58(4):1651-1683.
[8] DeMiguel V, Garlappi L, Nogales F J, et al. A generalized approach to portfolio optimization:Improving performance by constraining portfolio norms. Management Science, 2009, 55(5):798-812.
[9] Chan L K C, Karceski J, Lakonishok J. On portfolio optimization:Forecasting covariances and choosing the risk model. The Review of Financial Studies, 1999, 12(5):937-974.
[10] Bekaert G, Hodrick R J, Zhang X. International stock return comovements. The Journal of Finance, 2009, 64(6):2591-2626.
[11] Ledoit O, Wolf M. Honey, I shrunk the sample covariance matrix. Journal of Portfolio Management, 2004, 30(4):110-119.
[12] Jobson J D, Korkie R M. Putting Markowitz theory to work. Journal of Portfolio Management, 1981, 7(4):70-74.
[13] Jorion P. Bayesian and CAPM estimators of the means:Implications for portfolio selection. Journal of Banking & Finance, 1991, 15(3):717-727.
[14] Pastor L', Stambaugh R F. Comparing asset pricing models:An investment perspective. Journal of Financial Economics, 2000, 56(3):335-381.
[15] Black F, Litterman R. Global portfolio optimization. Financial Analysts Journal, 1992, 48(5):28-43.
[16] Ben-Tal A, Nemirovski A. Robust convex optimization. Mathematics of Operations Research, 1998, 23(4):769-805.
[17] Tutuncu R H, Koenig M. Robust asset allocation. Annals of Operations Research, 2004, 132(1):157-187.
[18] Garlappi L, Uppal R, Wang T. Portfolio selection with parameter and model uncertainty:A multi-prior approach. The Review of Financial Studies, 2007, 20(1):41-81.
[19] Kan R, Zhou G. Optimal portfolio choice with parameter uncertainty. Journal of Financial and Quantitative Analysis, 2007, 42(3):621-656.
[20] Tu J, Zhou G. Markowitz meets Talmud:A combination of sophisticated and naive diversification strategies. Journal of Financial Economics, 2011, 99(3):204-215.
[21] Jiang C, Du J, An Y. Combining the minimum-variance and equally-weighted portfolios:Can portfolio performance be improved? Economic Modelling, 2019, 80:260-274.
[22] 倪宣明, 沈鑫圆, 赵慧敏, 等. 基于多任务相关学习的投资组合优化. 系统工程理论与实践, 2021, 41(6):1428-1438. (Ni X M, Shen X Y, Zhao H M, et al. Portfolio optimization based on multi-task relationship learning. Systems Engineering-Theory & Practice, 2021, 41(6):1428-1438.)
[23] Ren Y, Zhang L, Suganthan P N. Ensemble classification and regression-recent developments, applications and future directions. IEEE Computational Intelligence Magazine, 2016, 11(1):41-53.
[24] Freund Y, Schapire R E. Experiments with a new boosting algorithm. Proceedings of the 13th International Conference on Machine Learning, ICML, 1996, 148-156.
[25] Freund Y, Schapire R E. A decision-theoretic generalization of on-Line learning and an application to boosting. Journal of Computer and System Sciences, 1997, 55(1):119-139.
[26] Drucker H. Improving regressors using boosting techniques. Proceedings of the 14th International Conference on Machine Learning, ICML, 1997, 107-115.
[27] Shrestha D L, Solomatine D P. Experiments with AdaBoost.RT, an improved boosting scheme for regression. Neural Computation, 2006, 18(7):1678-1710.
[28] 钱龙, 彭方平, 沈鑫圆, 等. 基于已实现半协方差的投资组合优化. 系统工程理论与实践, 2021, 41(1):34-44. (Qian L, Peng F P, Shen X Y, et al. Portfolio optimization based on realized semi-covariance. Systems Engineering-Theory & Practice, 2021, 41(1):34-44.)
[29] 孙会霞, 倪宣明, 钱龙, 等. 基于长期CVaR约束的高频投资组合优化. 系统科学与数学, 2021, 41(2):344-360. (Sun H X, Ni X M, Qian L, et al. High-frequency portfolio optimization with long-term CVaR constraints. Journal of Systems Science & Mathematical Sciences, 2021, 41(2):344-360.)
[30] Best M J. An algorithm for the solution of the parametric quadratic programming problem. Applied Mathematics and Parallel Computing, Physica-Verlag HD, New York, 1996, 57-76.
[31] DeMiguel V, Garlappi L, Uppal R. Optimal versus naive diversification:How inefficient is the 1/N portfolio strategy? The Review of Financial Studies, 2007, 22(5):1915-1953.
[32] DeMiguel V, Martin-Utrera A, Nogales F J. Size matters:Optimal calibration of shrinkage estimators for portfolio selection. Journal of Banking & Finance, 2013, 37(8):3018-3034.
[33] Krogh A, Vedelsby J. Neural network ensembles, cross validation, and active learning. Advances in Neural Information Processing Systems, Cambridge, MA:MIT Press, 1995.
[34] Ban G Y, El Karoui N, Lim A E. Machine learning and portfolio optimization. Management Science, 2016, 64(3):1136-1154.
[35] Jobson J D, Korkie B M. Performance hypothesis testing with the Sharpe and Treynor measures. The Journal of Finance, 1981, 36(4):889-908.
[36] 黄嵩, 倪宣明, 钱龙, 等. 基于集成学习的在线高维投资组合策略. 系统科学与数学, 2020, 40(1):1-13. (Huang S, Ni X M, Qian L, et al. Large-dimensional online portfolio strategy based on ensemble learning. Journal of Systems Science & Mathematical Sciences, 2020, 40(1):1-13.)
[37] Cochrane J H. Presidential address:Discount rates. The Journal of Finance, 2011, 66(4):1047-1108.
[38] Black F, Litterman R. Asset allocation:Combining investor views with market equilibrium. Goldman Sachs Fixed Income Research, 1990, 1(2):7-18.

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