结合领域知识的因子分析: 在金融风险模型上的应用

冯栩; 喻文健; 李凌

doi:10.16383/j.aas.c200342

结合领域知识的因子分析: 在金融风险模型上的应用

doi: 10.16383/j.aas.c200342

冯栩^1,,
喻文健^1,,
李凌^2,

1.
清华大学计算机科学与技术系北京信息科学与技术国家研究中心北京 100084
2.
善流投资管理有限公司上海 200000

基金项目: 国家自然科学基金(61872206)资助

详细信息

作者简介:
冯栩：清华大学计算机科学与技术系博士研究生. 2017年获得清华大学计算机科学与技术系学士学位. 主要研究方向为数值线性代数算法, 机器学习, 大数据分析. E-mail: fx17@mails.tsinghua.edu.cn

喻文健：清华大学计算机科学与技术系长聘教授. 2003年获得清华大学计算机科学与技术系博士学位, 随后留校任教. 主要研究方向为集成电路计算机辅助设计算法, 机器学习, 大数据分析算法、数值计算及其应用. 本文通信作者. E-mail: yu-wj@tsinghua.edu.cn

李凌：加州理工学院计算机科学博士(辅修电子工程). 主要研究方向为机器学习, 量化投资, 自动化交易. E-mail: liling@flowam.com

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出版历程
- 收稿日期: 2020-05-22
- 录用日期: 2020-12-31
- 网络出版日期: 2021-02-04
- 刊出日期: 2022-01-25

Combining Domain Knowledge with Statistical Factor Analysis: An Application to Financial Risk Modeling

FENG Xu^1
,,
YU Wen-Jian^1
,,
LI Ling^2
,

1.
Department of Computer Science and Technology, Beijing National Research Center for Information Science and Technology, Tsinghua University, Beijing 100084
2.
Flow Assets Management, Shanghai 200000

Funds: Supported by National Natural Science Foundation of China (61872206)

More Information

Author Bio:
FENG Xu　Ph. D. candidate in the Department of Computer Science and Technology, Tsinghua University. He received his bachelor degree from Tsinghua University in 2017. His research interest covers numerical linear algebra algorithms, machine learning, and big-data analytics

YU Wen-Jian　Professor in the Department of Computer Science and Technology, Tsinghua University. He received his Ph. D. degree in Computer Science from Tsinghua University in 2003. His research interest covers EDA algorithm and software, machine learning, big-data analytics, and numerical algorithms and applications. Corresponding author of this paper

LI Ling　Ph. D. in computer science (minor in electrical engineering) from California Institute of Technology. His research interest covers machine learning, quantitative investing, and automated trading

摘要

摘要: 因子分析是一种在工业领域广泛使用的统计学方法. 在金融资产管理中, 因子分析通过对历史价格波动的极大似然估计推导自适应的统计学因子来生成风险模型. 与通过使用预先设定具有经济学含义的因子来生成风险模型的基本面因子模型相比, 通过因子分析生成的模型不仅更灵活, 还能发现在基本面模型中缺失的因子. 然而, 由于因子分析所生成模型中的统计学因子缺少可解释性, 因此当金融数据中存在显著噪音时容易过拟合. 针对中国股市数据的风险模型生成问题, 本文提出快速因子分析算法以及将基本面因子结合到因子分析中的挑选基本面因子的混合因子分析方法, 使风险模型同时在因子探索及模型可解释性上达到最优. 实验结果显示快速因子分析方法能够达到31倍以上的加速比, 且新混合因子分析方法能够增大人造数据集以及真实数据集上预测的对数似然估计值. 在真实数据集上, 新方法能最好够达到平均对数似然估计值12.00, 比因子分析构建模型的7.56大4.44, 并且两个算法均值差值的标准差为1.58, 表现出新方法能构建更准确的风险模型.
- 因子分析 /
- 基本面因子 /
- 领域知识 /
- 风险模型 /
- 期望最大化过程
Abstract: Factor analysis is a statistical method widely used in many industrial domains. In financial portfolio management, a statistical risk model can be constructed via factor analysis, decomposing the risk into self-adapting factors and maximizing log-likelihood of the historical price movement. Compared to a fundamental model that uses well defined factors with economical meanings, it is more dynamic and may discover factors that are missed in the fundamental ones. On the other hand, statistical factors lack the intuitive interpretation, and thus are less stable and more prone to overfitting especially for the financial data with remarkable noises. In this work, we propose a fast factor analysis and a hybrid method that incorporates the fundamental factors into the statistical process, achieving an optimized combination of model interpretability and data exploitation. Our experiment results show that the acceleration of fast factor analysis is up to more than 31 times, and the new hybrid method yields improved out-of-sample log-likelihood on both synthetic and real-world data. The best mean of log-likelihood of proposed algorithm on real-world data is 12.00, which is larger than 7.56 of factor analysis with difference 4.44, and the standard deviation of the difference is 1.58. All the results shows the proposed algorithms estimate risk model more accurately.
- Factor analysis /
- fundamental factor /
- domain knowledge /
- risk model /
- expectation-maximization process

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图 1 算法1、算法3和算法6 $(r = 0.9)$前30天风险模型在真实数据集上预测的对数似然估计值的结果

Fig. 1 The predicted log-likelihood of the risk models estimated by Alg.1, Alg.3 and Alg.6 $(r = 0.9)$ on first 30 days

下载: 全尺寸图片幻灯片

表 1 算法1和算法2在第一个人造数据集上的实验结果

Table 1 Results on first synthetic dataset of Alg.1 and Alg.2

因子数	算法	$\delta=5$					$\delta=10$
因子数	算法	时间 (s)	${\rm E}\,(LL)$	$\sigma\,({\rm E})$	${\rm E}\,(iter)$	加速比	时间 (s)	$ {\rm E}\,(LL)$	$\sigma\,( {\rm E})$	$ {\rm E}\,(iter)$	加速比
$s=10$	算法1 (FA)	444.21	−1927.63	10.01	709.02	—	252.07	−2059.10	6.30	405.51	—
$s=10$	算法2 (FFA)	14.05	−1927.63	10.01	709.01	31.6	7.80	−2059.10	6.30	405.55	32.3
$s=13$	算法1 (FA)	653.60	−1861.02	11.48	1019.66	—	313.86	−2027.42	6.29	492.91	—
$s=13$	算法2 (FFA)	20.38	−1863.73	11.39	1020.77	32.1	9.58	−2027.08	6.24	492.79	32.8

下载: 导出CSV

表 2 算法1、算法2、算法3和算法4在第二个人造数据集上的实验结果

Table 2 Results on second synthetic dataset of Alg.1, Alg.2, Alg.3 and Alg.4

因子数	算法	$\delta=3$			$\delta=5$			$\delta=10$
因子数	算法	时间 (s)	${\rm E}\,(LL)$	$\sigma\,( {\rm E})$	时间 (s)	$ {\rm E}\,(LL)$	$\sigma\,( {\rm E})$	时间 (s)	$ {\rm E}\,(LL)$	$\sigma\,( {\rm E})$
$s=10,f=0$	算法1 (FA)	484.94	−3789.03	28.85	389.27	−3866.59	24.26	227.39	−4116.68	14.46
$s=10,f=0$	算法2 (FFA)	207.17	−3789.02	28.85	171.58	−3866.60	24.65	99.19	−4116.68	14.46
$s=0,f=10$	算法3 (OLS)	0.23	−3734.41	22.60	0.23	−3815.23	19.05	0.23	−4072.60	11.39
$s=13,f=0$	算法1 (FA)	779.07	−3617.34	33.82	562.08	−3732.61	25.96	279.78	−4046.25	13.46
$s=13,f=0$	算法2 (FFA)	331.09	−3616.64	33.72	247.17	−3731.49	26.16	121.48	−4045.92	13.46
$s=3,f=10$	算法4 (HFA)	123.49	−3564.72	25.94	92.44	−3678.27	20.23	48.63	−4002.81	10.52

下载: 导出CSV

表 3 算法1、算法2、算法3、算法4及算法6在第三个人造数据集上的实验结果

Table 3 Results on third synthetic dataset of Alg.1, Alg.2, Alg.3, Alg.4 and Alg.6

因子数	算法	$\delta=3$			$\delta=5$			$\delta=10$
因子数	算法	时间 (s)	$ {\rm E}\,(LL)$	$\sigma\,( {\rm E})$	时间 (s)	$ {\rm E}\,(LL)$	$\sigma\,( {\rm E})$	时间 (s)	$ {\rm E}\,(LL)$	$\sigma\,( {\rm E})$
$s=10,f=0$	算法1 (FA)	693.57	−3594.51	26.64	507.47	−3709.94	20.81	263.41	−4019.67	10.86
$s=10,f=0$	算法2 (FFA)	290.06	−3593.84	26.97	215.58	−3703.39	21.36	105.50	−4019.93	10.88
$s=0,f= 10$	算法3 (OLS)	0.24	−3712.75	22.24	0.25	−3796.19	18.78	0.24	−4059.71	11.19
$s+f=10$	算法6 (HFA⁺)	1726.79	−3561.04	25.26	1307.14	−3683.00	20.75	596.52	−4005.34	11.34
$s=13,f=0$	算法1 (FA)	845.15	−3389.00	30.54	721.67	−3550.65	21.55	312.41	−3955.47	10.07
$s=13,f=0$	算法2 (FFA)	351.61	−3389.82	30.89	304.29	−3549.53	21.45	123.93	−3955.47	10.07
$s=3,f=10$	算法4 (HFA)	111.30	−3536.52	28.39	81.30	−3661.63	22.11	48.15	−3993.70	11.43
$s+f=13$	算法6 (HFA⁺)	2314.11	−3378.86	32.36	1826.26	−3522.23	21.72	796.98	−3933.08	10.42

下载: 导出CSV

表 4 算法1、算法2、算法3和算法6在真实数据集上的实验结果比较

Table 4 Results on real-world dataset of Alg.1, Alg.2, Alg.3 and Alg.6

因子数	算法	$r$	时间 (s)	$ {\rm E}\,({LL})$	$\sigma\,( {\rm E})$	$ {\rm E}\,(LL_{Alg.6} - LL_{Alg.2})$	$\sigma( {\rm E}\,(LL_{Alg.6} - LL_{Alg.2}))$
$s=15, f=0$	算法1 (FA)	—	1.61	7.56	9.06	—	—
$s=15, f=0$	算法2 (FFA)	—	0.55	7.54	9.06	—	—
$s=0, f=22$	算法3 (OLS)	—	0.01	−108.0	15.50	—	—
$s+f=15$	算法6 (HFA⁺)	$0.6$	10.82	11.96	8.18	4.40	1.64
		$0.7$	10.90	11.86	8.20	4.29	1.61
		$0.8$	10.40	11.77	8.24	4.21	1.58
		$0.9$	10.51	12.00	8.25	4.44	1.58

下载: 导出CSV

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