import numpy as np
import pandas as pd
import utils
import factor_analysis as fa
from get_data import get_data as gd
from factors_library import get_factors as gf
import seaborn as sns
import matplotlib.pyplot as plt
import matplotlib

returns = gd.get_stocks_monthly(from_month='2010-01',to_month='2021-11').set_index(['trade_month','stock_code'])
returns = returns[['Mretwd']].rename(columns={'Mretwd':'returns'})
returns

		returns
trade_month	stock_code
2010-01	000001	-0.109561
	000002	-0.135985
	000005	-0.104651
	000006	-0.120918
	000007	-0.017070
...	...	...
2021-11	900948	-0.085352
	900952	-0.000002
	900953	-0.055721
	900955	-0.079365
	900957	-0.040943

428134 rows × 1 columns

1. 数据准备与实证设定

1.1 股票池/剔除规则

• 流动性：考虑根据股票的流动性大小构造股票池来替代全样本股票池。参考中证指数的构造方式，构造的具体方式为：在每个换仓日计算每只股票的交易金额历史20日平均，排除排名后30%与过去20个交易日中交易天数不满10天的股票作为股票池。为尽可能保证排除流动性差的股票，另参考Amihud (2002) 的ILLIQ指标作为筛选条件，并排除排名前30%的股票。 $$ILLIQ^N_t = \frac{1}{N}\sum_{i=0}^{N-1}\frac{|R_{t-i}|}{Amount_{t-1}}$$
• 高风险：
  • 风险警示股：ST、PT股票，面临暂停上市与退市风险，基金合同明令禁投；
  • 次新股：上市不足一年的股票；
  • 其他自定义高风险标签：高负债股票、高商誉类股票等（暂未考虑）；
• 停牌股：换仓日当天停牌的股票。

all_a_pool = gd.get_stocks_daily(trade_date='2021-12-31',pool='all_a_market')
liquid_pool = gd.get_stocks_daily(trade_date='2021-12-31',pool='liquid_perc70')
mc_pool=pd.concat([pd.DataFrame({'市值对数':np.log(all_a_pool.Dsmvtll),'股票池':'全市场'}),pd.DataFrame({'市值对数':np.log(liquid_pool.Dsmvtll),'股票池':'高流动性'})])
fig, ax = plt.subplots(figsize=(10, 3),dpi=100)
matplotlib.rcParams['font.sans-serif']=['kaiti'] 

sns.kdeplot(data=mc_pool, x="市值对数", hue="股票池", fill=True, common_norm=False, alpha=0.4)
plt.ylabel("密度")
plt.title('20201年12月31日股票池成分股市值分布对比')
plt.show()

1.2 实证设定

• 回测设定：
  • 数据来源：CSMAR 和 Tushare；
  • 收益计算：CSMAR考虑现金红利再投资的日个股回报率；
  • 股票范围：全部A股，剔除低流通性股票；
  • 时间区间：2010年01月01日至2021年11月30日；
  • 调仓频率：月频，每月最后一个交易日收盘前换仓；
  • 黑名单：高风险股票（风险警示股、次新股等）；
  • 不可交易股：停牌股；
• 因子计算设定：
  • 最少交易日：
    • 月指标：考虑最近20个交易日，要求至少10个交易天数，否则标记为缺失值；
    • 年指标：考虑最近250个交易日，要求至少120个交易天数，否则标记为缺失值；
  • 异常值处理：Median Absolute Deviation（MAD）方法识别异常值 + 缩尾法替换异常值； $$ mad = med(|Yi – med(Yi)|)$$ $$ x \in (-\infty,med-3\times 1.4826\times mad)\cup (med+3\times 1.4826\times mad,\infty)$$
  • 缺失值处理：剔除法；
  • 标准化方法：Z-Score标准化；
  • 单变量排序：按变量大小从小到大将股票分为5组；
  • 投资组合内股票权重：按流通市值加权；

2. 因子测试

2.1 单因子测试流程

• 多空组合法：在每个截面上将股票按照因子暴露进行排序，并做多排名前N分位数股票，同时做空排名靠后的相同比例股票，构造出多空投资组合，计算该组合每一期的收益；排序分组方法包括：
  • 单变量排序（univariate sorting）
  • 因子正交化/中性化后排序：
    • 双重排序（Double Sorting）：暂未实现；
    • 回归法正交：在股票界面上以候选预测变量作为被解释变量，以其他风险因子变量作为解释变量进行回归，得到的残差代替原始变量作为预测变量（现平台实现行业中性化与市值中性化）；
• 时间序列回归：由异象变量构建的多空组合的收益率，能否被资产定价模型所解释（先支持CAPM模型，FF-3模型和FF-5模型）；
• 横截面回归：Fama-Macbeth回归中，异象变量与多因子模型中构造因子的变量同时作为解释变量，以个股超额收益作为被解释变量，在每个时刻t进行截面回归，检验异象的预期收益是否显著；

2.2 测试因子

• 交易摩擦类因子：
  • 市值类因子
  • 波动率类因子+高阶距类因子
  • 流动性类因子
  • Beta类因子
• 动量类因子

2.3 因子多空组合测试结果

summ_df.sort_values('夏普比率',ascending = False)

	t值	年化收益率(%)	累计收益率(%)	年化波动率(%)	夏普比率	最大回测(%)
换手率波动率（最近一月）	2.310941	16.615841	181.813800	22.790853	0.729057	26.770884
换手率（最近一月）	1.596955	11.960025	133.398811	24.198138	0.494254	29.917020
换手率波动率（最近一年）	1.568547	11.508702	128.607808	23.751577	0.484545	38.485839
下行Beta	1.540967	10.161958	114.204968	21.469125	0.473329	25.452989
市场Beta	1.515955	10.296559	115.651717	22.099795	0.465912	30.293591
非流动性(最近一月)	1.367809	9.358872	105.539207	22.351728	0.418709	31.780758
条件偏度	1.318597	9.053815	102.232151	22.459396	0.403119	22.119254
短期反转	1.195095	8.314845	94.185807	22.829977	0.364207	26.061225
总波动率（最近一年）	1.138422	8.936145	100.954246	25.688815	0.347861	24.994772
相对Beta	1.102729	6.912485	78.776576	20.694306	0.334028	40.689706
动量（最近一年）	1.102512	6.703755	76.467181	20.091596	0.333660	64.222693
特定动量	1.100871	7.043917	80.228610	21.111327	0.333656	35.749658
特定波动率（最近一年）	1.026657	8.307506	94.105642	26.552953	0.312866	33.988191
换手率（最近一年）	0.943649	7.326261	83.342374	25.584575	0.286355	38.560136
总市值对数	0.885551	6.742618	76.897478	25.154809	0.268045	41.691550
特定波动率（最近一月）	0.861525	5.512646	63.208899	21.253626	0.259374	30.370142
总波动率（最近一月）	0.820765	5.546495	63.587568	22.442749	0.247140	28.975416
非流动性（最近一年）	0.783385	5.486801	62.919695	23.266667	0.235822	38.745707
流通市值对数	0.689302	5.368181	61.591529	25.884174	0.207392	47.112967
异常换手率	0.620338	3.600087	41.629972	19.440172	0.185188	37.526980
特定偏度	0.616952	3.356662	38.857288	18.245002	0.183977	33.894420
动量（最近六月）	0.561019	3.235404	37.473884	19.349693	0.167207	91.670806
偏度	0.557971	2.470875	28.717054	14.909086	0.165729	29.771409
动量变化	0.462799	2.239504	26.055140	16.308854	0.137318	26.783360
非线性市值	0.395620	1.431782	16.718768	12.241886	0.116958	27.106548
上行Beta	0.247077	1.345683	15.719545	18.430242	0.073015	32.639894
流通市值占比	-0.241870	-0.553753	-6.525089	7.814972	-0.070858	40.363451

2.4 因子测试：换手率波动率（最近一月）

turn_std_1m_factor = liquidity_factor[['turn_std_1m']].rename(columns={'turn_std_1m':'factor'})
fa_turn_std_1m = fa.factor_analysis(factors=turn_std_1m_factor,returns=returns)

2.4.1 多空组合法

fa_turn_std_1m.quantile_returns_summ()

	t-stats	ann. return rate (%)	acc. return rate (%)	ann. volatility (%)	sharpe ratio	max drawdown (%)
quantiles
group 1	1.277648	7.374851	83.877475	19.017644	0.387790	32.581290
group 2	1.376906	10.775582	120.787332	25.412054	0.424034	42.028981
group 3	0.904695	7.546067	85.761254	27.460682	0.274795	52.976309
group 4	0.488848	4.355943	50.201458	29.748527	0.146426	66.640158
group 5	-0.903347	-8.021232	-97.936325	31.405951	-0.255405	120.961724
group longshort	2.310941	16.615841	181.813800	22.790853	0.729057	26.770884

fa_turn_std_1m.quantile_returns_plot()

2.4.2 时间序列回归法

• 定价模型选择：
  1. FF-3模型（构建因子方法：2$\times$3 double sorting)
  2. FF-5模型（构建因子方法：2$\times$3 double sorting）

fa_turn_std_1m.factor_ts_regr_cmpt(pricing_model='FF-3')

                            OLS Regression Results                            
==============================================================================
Dep. Variable:                returns   R-squared:                       0.674
Model:                            OLS   Adj. R-squared:                  0.667
Method:                 Least Squares   F-statistic:                     48.20
Date:                Fri, 14 Jan 2022   Prob (F-statistic):           2.04e-21
Time:                        04:09:44   Log-Likelihood:                 266.92
No. Observations:                 143   AIC:                            -525.8
Df Residuals:                     139   BIC:                            -514.0
Df Model:                           3                                         
Covariance Type:                  HAC                                         
===============================================================================
                  coef    std err          t      P>|t|      [0.025      0.975]
-------------------------------------------------------------------------------
const          -0.0203      0.003     -7.254      0.000      -0.026      -0.015
RiskPremium     0.2604      0.056      4.620      0.000       0.149       0.372
SMB             0.7911      0.113      7.009      0.000       0.568       1.014
HML            -0.2646      0.141     -1.871      0.063      -0.544       0.015
==============================================================================
Omnibus:                        7.260   Durbin-Watson:                   2.080
Prob(Omnibus):                  0.027   Jarque-Bera (JB):                7.466
Skew:                           0.410   Prob(JB):                       0.0239
Kurtosis:                       3.762   Cond. No.                         45.4
==============================================================================

Notes:
[1] Standard Errors are heteroscedasticity and autocorrelation robust (HAC) using 5 lags and without small sample correction

fa_turn_std_1m.factor_ts_regr_cmpt(pricing_model='FF-5')

                            OLS Regression Results                            
==============================================================================
Dep. Variable:                returns   R-squared:                       0.686
Model:                            OLS   Adj. R-squared:                  0.674
Method:                 Least Squares   F-statistic:                     47.44
Date:                Fri, 14 Jan 2022   Prob (F-statistic):           2.87e-28
Time:                        04:09:32   Log-Likelihood:                 269.46
No. Observations:                 143   AIC:                            -526.9
Df Residuals:                     137   BIC:                            -509.1
Df Model:                           5                                         
Covariance Type:                  HAC                                         
===============================================================================
                  coef    std err          t      P>|t|      [0.025      0.975]
-------------------------------------------------------------------------------
const          -0.0179      0.003     -5.818      0.000      -0.024      -0.012
RiskPremium     0.2294      0.067      3.446      0.001       0.098       0.361
SMB             0.5123      0.162      3.161      0.002       0.192       0.833
HML            -0.2333      0.180     -1.297      0.197      -0.589       0.122
RMW            -0.8605      0.323     -2.663      0.009      -1.499      -0.222
CMA            -0.5015      0.214     -2.342      0.021      -0.925      -0.078
==============================================================================
Omnibus:                        4.283   Durbin-Watson:                   2.104
Prob(Omnibus):                  0.118   Jarque-Bera (JB):                3.755
Skew:                           0.361   Prob(JB):                        0.153
Kurtosis:                       3.331   Cond. No.                         86.0
==============================================================================

Notes:
[1] Standard Errors are heteroscedasticity and autocorrelation robust (HAC) using 5 lags and without small sample correction

2.4.3 横截面/Fama-Macbeth回归法

定价模型选择：FF-3模型

fa_turn_std_1m.factor_fm_regr_cmpt()

                            FamaMacBeth Estimation Summary                           
=====================================================================================
Dep. Variable:                     returns   R-squared:                        0.0031
Estimator:                     FamaMacBeth   R-squared (Between):             -0.0558
No. Observations:                   215554   R-squared (Within):               0.0057
Date:                     Fri, Jan 14 2022   R-squared (Overall):              0.0031
Time:                             04:00:13   Log-likelihood                  1.29e+05
Cov. Estimator:    Fama-MacBeth Kernel Cov                                           
                                             F-statistic:                      166.72
Entities:                             4200   P-value                           0.0000
Avg Obs:                            51.322   Distribution:                F(4,215549)
Min Obs:                            1.0000                                           
Max Obs:                            143.00   F-statistic (robust):             23.893
                                             P-value                           0.0000
Time periods:                          143   Distribution:                F(4,215549)
Avg Obs:                            1507.4                                           
Min Obs:                            426.00                                           
Max Obs:                            2394.0                                           
                                                                                     
                              Parameter Estimates                              
===============================================================================
             Parameter  Std. Err.     T-stat    P-value    Lower CI    Upper CI
-------------------------------------------------------------------------------
const           0.0820     0.0270     3.0345     0.0024      0.0290      0.1350
factor         -0.0081     0.0009    -9.0512     0.0000     -0.0098     -0.0063
beta            0.0009     0.0032     0.2681     0.7886     -0.0055      0.0072
circ_mc_log    -0.0056     0.0018    -3.0357     0.0024     -0.0092     -0.0020
ep_ttm          0.0304     0.0330     0.9226     0.3562     -0.0342      0.0950
===============================================================================

2.4.3 信息系数（Information Coefficient，IC）法

fa_turn_std_1m.factor_ic_summ()

         Rank Information Correlation Summary         
======================================================
Start Date:   2010-01-01 Mean IC:              -0.0959
End Date:     2021-11-01 Std IC:                0.0814
Frequency:       Monthly Prob. Significant IC:  0.9161
No. Turnover:        143 Prob. IC > 0:          0.1189
                         Information Ratio:    -1.1782
------------------------------------------------------

附：因子测试具体结果

1. 市值类因子

• mc: 日个股总市值，个股的发行总股数与收盘价的乘积；
• _mclog: 日个股市值对数；
• _mcnonlinear: 非线性市值，市值因子的立方关于市值因子作正交化处理，得到的残差即为非线性市值因子； $$X^3 = \alpha + \beta X + \epsilon$$ 参考文献：Orr, D.J., Mashtaler, I., & Nagy, A (2012). The Barra China Equity Model (CNE5). MSCI BARRA.
• _circmc: 日个股流通市值，个股的流通股数与收盘价的乘积；
• _circ_mclog: 流通市值对数;
• _circ_to_total_mcratio: 流通市值占总市值比重;

size_factor = gf.get_size_factor(from_date='2009-12-31',to_date='2021-10-31',pool='liquid_perc70')
size_factor.set_index(['trade_date','stock_code'],inplace=True)
size_factor

		mc	mc_log	mc_nonlinear	circ_mc	circ_mc_log	circ_to_total_mc_ratio
trade_date	stock_code
2009-12-31	000001	7.567942e+07	18.142017	-0.884212	7.126066e+07	18.081855	0.941612
	000002	1.046436e+08	18.466070	-1.312490	1.043824e+08	18.463572	0.997504
	000005	5.504288e+06	15.521038	0.159761	5.500733e+06	15.520392	0.999354
	000006	5.746386e+06	15.564082	0.156153	5.589346e+06	15.536373	0.972671
	000009	1.197644e+07	16.298452	0.063289	1.084956e+07	16.199635	0.905908
...	...	...	...	...	...	...	...
2021-10-29	688779	4.516272e+07	17.625782	-0.241597	8.136354e+06	15.911853	0.180156
	688798	3.552566e+07	17.385766	-0.133597	6.843523e+06	15.738813	0.192636
	688819	3.961308e+07	17.494670	-0.179419	4.328712e+06	15.280781	0.109275
	688981	1.066930e+08	18.485466	-0.926438	1.029819e+08	18.450064	0.965217
	689009	4.510006e+06	15.321809	0.214607	2.835167e+06	14.857611	0.628639

250696 rows × 6 columns

总市值对数

mc_log_factor = size_factor[['mc_log']].rename(columns={'mc_log':'factor'})
fa_mc_log = fa.factor_analysis(factors=mc_log_factor,returns=returns)

fa_mc_log.quantile_returns_summ()

	t-stats	ann. return rate (%)	acc. return rate (%)	ann. volatility (%)	sharpe ratio	max drawdown (%)
quantiles
group 1	1.398638	13.615467	150.821639	31.237827	0.435865	38.167054
group 2	0.953467	8.861710	100.145220	30.426154	0.291253	45.417476
group 3	0.917918	8.030758	91.079090	28.743353	0.279395	47.597890
group 4	0.949985	7.671627	87.140957	26.572253	0.288708	52.290340
group 5	1.023024	6.474340	73.924161	20.932607	0.309295	39.182590
group longshort	0.885551	6.742618	76.897478	25.154809	0.268045	41.691550

fa_mc_log.quantile_returns_plot()

流通市值对数

circ_mc_log_factor = size_factor[['circ_mc_log']].rename(columns={'circ_mc_log':'factor'})
fa_circ_mc_log = fa.factor_analysis(factors=circ_mc_log_factor,returns=returns)

fa_circ_mc_log.quantile_returns_summ()

	t-stats	ann. return rate (%)	acc. return rate (%)	ann. volatility (%)	sharpe ratio	max drawdown (%)
quantiles
group 1	1.240611	12.122511	135.119336	31.550363	0.384227	42.820363
group 2	0.977465	9.172312	103.517761	30.678651	0.298980	46.438127
group 3	0.976543	8.604304	97.343589	28.876112	0.297973	46.135788
group 4	0.969733	7.972364	90.439575	27.016503	0.295092	48.785738
group 5	1.018341	6.438625	73.527807	20.916119	0.307831	39.523562
group longshort	0.689302	5.368181	61.591529	25.884174	0.207392	47.112967

fa_circ_mc_log.quantile_returns_plot()

非线性市值因子

mc_nonlinear_factor = size_factor[['mc_nonlinear']].rename(columns={'mc_nonlinear':'factor'})
fa_mc_nonlinear = fa.factor_analysis(factors=mc_nonlinear_factor,returns=returns)

fa_mc_nonlinear.quantile_returns_summ()

	t-stats	ann. return rate (%)	acc. return rate (%)	ann. volatility (%)	sharpe ratio	max drawdown (%)
quantiles
group 1	1.029060	6.800928	77.542825	21.828479	0.311562	39.980278
group 2	0.949380	7.678012	87.211072	26.610582	0.288532	52.576964
group 3	0.897505	7.840426	88.993461	28.723912	0.272958	47.403166
group 4	0.960404	8.940916	101.006082	30.466053	0.293471	45.816190
group 5	1.437242	8.321783	94.261593	18.998852	0.438015	25.421333
group longshort	0.395620	1.431782	16.718768	12.241886	0.116958	27.106548

fa_mc_nonlinear.quantile_returns_plot()

流通市值占比

circ_to_total_mc_ratio_factor = size_factor[['circ_to_total_mc_ratio']].rename(columns={'circ_to_total_mc_ratio':'factor'})
fa_circ_to_total_mc_ratio = fa.factor_analysis(factors=circ_to_total_mc_ratio_factor,returns=returns,industry_neutral=True)

fa_circ_to_total_mc_ratio.quantile_returns_summ()

	t-stats	ann. return rate (%)	acc. return rate (%)	ann. volatility (%)	sharpe ratio	max drawdown (%)
quantiles
group 1	0.985737	7.157147	81.478238	23.944366	0.298907	45.607187
group 2	1.003905	7.480553	85.040765	24.539014	0.304843	50.677281
group 3	0.761171	4.672898	53.778815	20.466886	0.228315	45.296074
group 4	1.526094	10.140229	113.971262	21.633986	0.468718	25.716442
group 5	0.997483	7.750176	88.003327	25.557382	0.303246	58.776632
group longshort	-0.241870	-0.553753	-6.525089	7.814972	-0.070858	40.363451

fa_circ_to_total_mc_ratio.quantile_returns_plot()

2. 波动率类因子

• _vol1m: 总波动率1（one-month total volatility），过去20个交易日的日度收益率波动率，其中剔除不满10个交易日的股票；
• _ido_vol1m: 特质波动率1（one-month idiosyncratic volatility），过去20个交易日个股超额收益率关于市场超额收益率正交化处理得到的残差标准差，其中剔除不满10个交易日的股票； $$r^i_t = \alpha^i + \beta^i_{mkt} MKT_t + \epsilon^i_t$$ 参考文献：Ang, A., Hodrick, R. J., Xing, Y., & Zhang, X. (2009). High Idiosyncratic Volatility and Low Returns: International and Further U.S. Evidence. Journal of Financial Economics, 91(1), 1-23.
• _vol1y: 总波动率2（twelve-month total volatility），过去252个交易日的日度收益率波动率，其中剔除不满120个交易日的股票；

• _ido_vol1y: 特质波动率2（twelve-month idiosyncratic volatility），过去252个交易日个股超额收益率关于市场超额收益率正交化处理得到的残差标准差，其中剔除不满120个交易日的股票；

• skew: 总偏度（total skewness)，过去252个交易日的日度收益率偏度，其中剔除不满120个交易日的股票；

• _idoskew: 特质偏度（idiosyncratic skewness），和特质波动率类似，不考虑总收益率能比风险因子解释的部分； </br> 参考文献：Boyer, B. H., Mitton, T., & Vorkink, K. (2010). Expected Idiosyncratic Skewness. Review of Financial Studies, 23(1), 169-202.</br>
• _conskew: 条件偏度（conditional skewness），过去252个交易日个股超额收益率关于市场超额收益率的平方回归得到的斜率系数，其中剔除不满120个交易日的股票； </br> 参考文献：Harvey, C. R., & Siddique, A. R. (2000). Conditional Skewness in Asset Pricing Tests. Journal of Finance, 55(3), 1263-1295.</br>

volatility_factor = gf.get_volatility_factor(from_date='2009-12-31',to_date='2021-10-31',pool='liquid_perc70')
volatility_factor.set_index(['trade_date','stock_code'],inplace=True)
volatility_factor

		vol_1m	vol_1y	ido_vol_1m	ido_vol_1y	skew	ido_skew	con_skew
trade_date	stock_code
2009-12-31	000001	0.023381	0.030132	0.016328	0.021933	0.607817	1.075634	-7.152257
	000002	0.022913	0.028345	0.015872	0.018598	0.130302	0.962938	-11.913605
	000005	0.032650	0.033516	0.026909	0.025574	0.273483	1.661326	-14.046154
	000006	0.028317	0.035414	0.022996	0.023873	-0.033927	0.391688	-12.340182
	000009	0.024583	0.036850	0.021914	0.026666	0.006678	0.863694	-15.874289
...	...	...	...	...	...	...	...	...
2021-10-29	688779	0.030279	NaN	NaN	NaN	NaN	NaN	NaN
	688798	0.027689	NaN	NaN	NaN	NaN	NaN	NaN
	688819	0.023869	0.033233	0.020941	0.031123	0.917616	1.209385	-26.581029
	688981	0.014825	0.025255	0.015726	0.024773	0.761047	1.092708	22.366436
	689009	0.034241	0.043204	0.039255	0.040675	0.486986	0.560439	-40.570108

250696 rows × 7 columns

总波动率 (最近一月)

vol_1m_factor = volatility_factor[['vol_1m']].rename(columns={'vol_1m':'factor'})
fa_vol_1m = fa.factor_analysis(factors=vol_1m_factor,returns=returns)

fa_vol_1m.quantile_returns_summ()

	t-stats	ann. return rate (%)	acc. return rate (%)	ann. volatility (%)	sharpe ratio	max drawdown (%)
quantiles
group 1	1.390388	7.793571	88.479505	18.434412	0.422773	29.990699
group 2	0.992024	7.302258	83.077951	24.259749	0.301003	37.717572
group 3	1.188357	9.480826	106.858916	26.048731	0.363965	46.253986
group 4	1.363331	11.628683	129.883192	27.597782	0.421363	36.578074
group 5	0.227050	2.138550	24.891937	31.758479	0.067338	72.907047
group longshort	0.820765	5.546495	63.587568	22.442749	0.247140	28.975416

fa_vol_1m.quantile_returns_plot()

总波动率（最近一年）

vol_1y_factor = volatility_factor[['vol_1y']].rename(columns={'vol_1y':'factor'})
fa_vol_1y = fa.factor_analysis(factors=vol_1y_factor,returns=returns)

fa_vol_1y.quantile_returns_summ()

	t-stats	ann. return rate (%)	acc. return rate (%)	ann. volatility (%)	sharpe ratio	max drawdown (%)
quantiles
group 1	1.295340	7.590868	86.253710	19.289313	0.393527	34.712859
group 2	1.151649	8.854485	100.066673	25.170516	0.351780	44.070652
group 3	0.980004	8.068595	91.493299	27.044828	0.298342	45.573449
group 4	0.295080	2.481838	28.843053	28.315469	0.087650	68.416735
group 5	-0.136588	-1.243591	-14.700536	31.177677	-0.039887	96.448599
group longshort	1.138422	8.936145	100.954246	25.688815	0.347861	24.994772

fa_vol_1y.quantile_returns_plot()

异质波动率（最近一月）

ido_vol_1m_factor = volatility_factor[['ido_vol_1m']].rename(columns={'ido_vol_1m':'factor'})
fa_ido_vol_1m = fa.factor_analysis(factors=ido_vol_1m_factor,returns=returns)

fa_ido_vol_1m.quantile_returns_summ()

	t-stats	ann. return rate (%)	acc. return rate (%)	ann. volatility (%)	sharpe ratio	max drawdown (%)
quantiles
group 1	1.082863	6.119681	69.982896	18.721520	0.326879	36.902883
group 2	1.222293	8.663638	97.989928	23.223565	0.373054	37.278878
group 3	1.528605	11.432177	127.793694	24.217914	0.472055	39.691252
group 4	0.992191	7.755407	88.060742	25.710458	0.301644	44.015804
group 5	0.063682	0.577869	6.773997	30.814125	0.018753	74.064608
group longshort	0.861525	5.512646	63.208899	21.253626	0.259374	30.370142

fa_ido_vol_1m.quantile_returns_plot()

异质波动率（最近一年）

ido_vol_1y_factor = volatility_factor[['ido_vol_1y']].rename(columns={'ido_vol_1y':'factor'})
fa_ido_vol_1y = fa.factor_analysis(factors=ido_vol_1y_factor,returns=returns)

fa_ido_vol_1y.quantile_returns_summ()

	t-stats	ann. return rate (%)	acc. return rate (%)	ann. volatility (%)	sharpe ratio	max drawdown (%)
quantiles
group 1	1.219591	7.484544	85.084677	20.209698	0.370344	37.352787
group 2	1.065323	7.801887	88.570744	24.084176	0.323942	39.662112
group 3	1.049672	8.109558	91.941576	25.373525	0.319607	50.519825
group 4	0.717770	6.153059	70.354342	28.394123	0.216702	51.998683
group 5	-0.084818	-0.764821	-9.020966	30.809738	-0.024824	87.534588
group longshort	1.026657	8.307506	94.105642	26.552953	0.312866	33.988191

fa_ido_vol_1y.quantile_returns_plot()

偏度

skew_factor = volatility_factor[['skew']].rename(columns={'skew':'factor'})
fa_skew = fa.factor_analysis(factors=skew_factor,returns=returns)

fa_skew.quantile_returns_summ()

	t-stats	ann. return rate (%)	acc. return rate (%)	ann. volatility (%)	sharpe ratio	max drawdown (%)
quantiles
group 1	1.349245	8.535281	96.591304	20.738142	0.411574	28.037534
group 2	1.072011	7.092757	80.767771	21.825366	0.324978	40.793522
group 3	1.011000	7.070847	80.525920	23.073165	0.306453	52.749602
group 4	0.947262	6.696871	76.390950	23.361169	0.286667	49.722503
group 5	0.872323	5.930377	67.874250	22.539826	0.263107	39.067870
group longshort	0.557971	2.470875	28.717054	14.909086	0.165729	29.771409

fa_skew.quantile_returns_plot()

异质偏度

ido_skew_factor = volatility_factor[['ido_skew']].rename(columns={'ido_skew':'factor'})
fa_ido_skew = fa.factor_analysis(factors=ido_skew_factor,returns=returns)

fa_ido_skew.quantile_returns_summ()

	t-stats	ann. return rate (%)	acc. return rate (%)	ann. volatility (%)	sharpe ratio	max drawdown (%)
quantiles
group 1	1.214858	9.086639	102.588391	24.462189	0.371456	29.565051
group 2	0.965377	6.987492	79.605432	23.887377	0.292518	47.767965
group 3	1.000714	6.787771	77.397239	22.404638	0.302963	37.996396
group 4	0.934279	6.197495	70.848667	21.967361	0.282123	43.460190
group 5	0.790031	5.559328	63.731103	23.368439	0.237899	50.283250
group longshort	0.616952	3.356662	38.857288	18.245002	0.183977	33.894420

fa_ido_skew.quantile_returns_plot()

条件偏度

con_skew_factor = volatility_factor[['con_skew']].rename(columns={'con_skew':'factor'})
fa_con_skew = fa.factor_analysis(factors=con_skew_factor,returns=returns)

fa_con_skew.quantile_returns_summ()

	t-stats	ann. return rate (%)	acc. return rate (%)	ann. volatility (%)	sharpe ratio	max drawdown (%)
quantiles
group 1	0.066441	0.584152	6.847449	29.854974	0.019566	66.851833
group 2	0.036664	0.290433	3.409045	26.935096	0.010783	62.227852
group 3	0.443266	3.531340	40.847534	26.694617	0.132287	54.504311
group 4	1.183831	8.720840	98.612732	24.130468	0.361404	39.243979
group 5	1.586474	9.686321	109.079600	19.917419	0.486324	33.379730
group longshort	1.318597	9.053815	102.232151	22.459396	0.403119	22.119254

fa_con_skew.quantile_returns_plot()

3. 流动性类因子

• _turn1m: 个股日换手率（one-month），过去20个交易日的日度换手率均值，其中剔除不满10个交易日的股票；
• _turn_std1m: 个股日换手率波动（one-month），过去20个交易日的日度换手率的标准差，其中剔除不满10个交易日的股票；
• _turn1y: 个股日换手率（twelve-month），过去252个交易日的日度换手率均值，其中剔除不满120个交易日的股票；
• _turn_std1y: 个股日换手率波动（twelve-month），过去252个交易日的日度换手率的标准差，其中剔除不满120个交易日的股票；
• _turnabn: 异常换手率（one-month abnormal turnover），过去20个交易日的日度换手率与过去252个交易日日度换手率的比值；
• _illiq1m: 非流动性因子（one-month illiquidity），过去20个交易日的日收益率绝对值除以日成交额的均值，其中剔除不满10个交易日的股票； $$ILLIQ^N_t = \frac{1}{N}\sum_{i=0}^{N-1}\frac{|R_{t-i}|}{Amount_{t-1}}$$ 参考文献：Amihud, Yakov, 2002, Illiquidity and stock returns: Cross-section and time series evidence, Journal of Financial Markets 5, 31–56.
• _illiq1y: 非流动行因子（twelve-month illiquidity），过去252个交易日的日收益率绝对值除以日成交额的均值，其中剔除不满120个交易日的股票；

liquidity_factor = gf.get_liquidity_factor(from_date='2009-12-31',to_date='2021-10-31',pool='liquid_perc70')
liquidity_factor.set_index(['trade_date','stock_code'],inplace=True)
liquidity_factor

		turn_1m	turn_std_1m	turn_1y	turn_std_1y	turn_abn	illiq_1m	illiq_1y
trade_date	stock_code
2009-12-31	000001	9.368108	5.240067	15.291751	9.395660	0.612625	2.887955e-11	3.037886e-11
	000002	16.892911	6.620091	19.389752	7.685814	0.871229	8.874766e-12	1.248956e-11
	000005	41.317234	17.894416	42.864445	34.987194	0.963905	1.161325e-10	2.746797e-10
	000006	24.276556	11.302615	29.452611	16.273596	0.824258	1.434729e-10	2.312247e-10
	000009	21.685049	6.760159	36.525848	21.814985	0.593690	8.117826e-11	1.081805e-10
...	...	...	...	...	...	...	...	...
2021-10-29	688779	61.461173	15.164703	NaN	NaN	NaN	4.199975e-11	NaN
	688798	14.120455	12.443404	NaN	NaN	NaN	2.192218e-10	NaN
	688819	25.927215	7.641897	54.252315	36.194348	0.477901	1.389233e-10	9.114412e-11
	688981	11.679183	5.572642	28.600970	18.708997	0.408349	9.217625e-12	8.793054e-12
	689009	240.100675	111.827613	487.062947	370.057493	0.492956	2.093390e-10	1.842303e-10

250696 rows × 7 columns

换手率（最近一月）

turn_1m_factor = liquidity_factor[['turn_1m']].rename(columns={'turn_1m':'factor'})
fa_turn_1m = fa.factor_analysis(factors=turn_1m_factor,returns=returns)

fa_turn_1m.quantile_returns_summ()

	t-stats	ann. return rate (%)	acc. return rate (%)	ann. volatility (%)	sharpe ratio	max drawdown (%)
quantiles
group 1	1.275586	7.419600	84.370089	19.160261	0.387239	33.248388
group 2	1.413675	11.226323	125.601165	25.737528	0.436185	44.226201
group 3	0.915188	7.763205	88.146320	27.900797	0.278243	46.709958
group 4	0.272076	2.447075	28.443492	30.284109	0.080804	69.510821
group 5	-0.429093	-4.092508	-49.028723	33.099497	-0.123643	101.688764
group longshort	1.596955	11.960025	133.398811	24.198138	0.494254	29.917020

fa_turn_1m.quantile_returns_plot()

换手率波动率（最近一月）

turn_std_1m_factor = liquidity_factor[['turn_std_1m']].rename(columns={'turn_std_1m':'factor'})
fa_turn_std_1m = fa.factor_analysis(factors=turn_std_1m_factor,returns=returns)

fa_turn_std_1m.quantile_returns_summ()

	t-stats	ann. return rate (%)	acc. return rate (%)	ann. volatility (%)	sharpe ratio	max drawdown (%)
quantiles
group 1	1.277648	7.374851	83.877475	19.017644	0.387790	32.581290
group 2	1.376906	10.775582	120.787332	25.412054	0.424034	42.028981
group 3	0.904695	7.546067	85.761254	27.460682	0.274795	52.976309
group 4	0.488848	4.355943	50.201458	29.748527	0.146426	66.640158
group 5	-0.903347	-8.021232	-97.936325	31.405951	-0.255405	120.961724
group longshort	2.310941	16.615841	181.813800	22.790853	0.729057	26.770884

fa_turn_std_1m.quantile_returns_plot()

换手率（最近一年）

turn_1y_factor = liquidity_factor[['turn_1y']].rename(columns={'turn_1y':'factor'})
fa_turn_1y = fa.factor_analysis(factors=turn_1y_factor,returns=returns)

fa_turn_1y.quantile_returns_summ()

	t-stats	ann. return rate (%)	acc. return rate (%)	ann. volatility (%)	sharpe ratio	max drawdown (%)
quantiles
group 1	1.218890	7.371642	83.842143	19.926011	0.369951	34.776106
group 2	1.141102	8.899263	100.553448	25.526718	0.348625	47.152602
group 3	0.545053	4.497377	51.799004	27.529959	0.163363	53.016015
group 4	0.549154	4.970753	57.131543	30.137324	0.164937	62.422538
group 5	0.004671	0.042529	0.499769	30.995586	0.001372	78.752224
group longshort	0.943649	7.326261	83.342374	25.584575	0.286355	38.560136

fa_turn_1y.quantile_returns_plot()

换手率波动率（最近一年）

turn_std_1y_factor = liquidity_factor[['turn_std_1y']].rename(columns={'turn_std_1y':'factor'})
fa_turn_std_1y = fa.factor_analysis(factors=turn_std_1y_factor,returns=returns)

fa_turn_std_1y.quantile_returns_summ()

	t-stats	ann. return rate (%)	acc. return rate (%)	ann. volatility (%)	sharpe ratio	max drawdown (%)
quantiles
group 1	1.355645	8.120766	92.064215	19.672857	0.412790	34.547792
group 2	1.153713	8.837373	99.880593	25.078753	0.352385	46.747214
group 3	0.505281	4.176001	48.166081	27.614086	0.151227	58.273022
group 4	0.383518	3.333855	38.597204	29.153648	0.114355	59.535594
group 5	-0.352888	-3.065206	-36.543593	29.998326	-0.102179	87.322344
group longshort	1.568547	11.508702	128.607808	23.751577	0.484545	38.485839

fa_turn_std_1y.quantile_returns_plot()

异常换手率

turn_abn_factor = liquidity_factor[['turn_abn']].rename(columns={'turn_abn':'factor'})
fa_turn_abn = fa.factor_analysis(factors=turn_abn_factor,returns=returns)

fa_turn_abn.quantile_returns_summ()

	t-stats	ann. return rate (%)	acc. return rate (%)	ann. volatility (%)	sharpe ratio	max drawdown (%)
quantiles
group 1	0.938714	6.353590	72.583645	22.398981	0.283655	44.834954
group 2	1.318741	8.827170	99.769635	21.916015	0.402773	39.213640
group 3	1.585334	10.623101	119.154792	21.772752	0.487908	30.109041
group 4	1.324481	9.478252	106.831075	23.365466	0.405652	31.873137
group 5	0.318777	2.665651	30.953673	28.128562	0.094767	58.617399
group longshort	0.620338	3.600087	41.629972	19.440172	0.185188	37.526980

fa_turn_abn.quantile_returns_plot()

非流动性（最近一月）

illiq_1m_factor = liquidity_factor[['illiq_1m']].rename(columns={'illiq_1m':'factor'})
fa_illiq_1m = fa.factor_analysis(factors=illiq_1m_factor,returns=returns)

fa_illiq_1m.quantile_returns_summ()

	t-stats	ann. return rate (%)	acc. return rate (%)	ann. volatility (%)	sharpe ratio	max drawdown (%)
quantiles
group 1	0.907570	5.795132	66.365647	21.182915	0.273576	41.513299
group 2	0.936817	7.132500	81.206337	25.110644	0.284043	51.758109
group 3	1.285905	10.231997	114.957981	25.897202	0.395100	38.796505
group 4	1.330629	11.171584	125.017518	27.216772	0.410467	39.383060
group 5	1.730542	15.648732	171.904854	28.775884	0.543814	29.657192
group longshort	1.367809	9.358872	105.539207	22.351728	0.418709	31.780758

fa_illiq_1m.quantile_returns_plot()

非流动性（最近一年）

illiq_1y_factor = liquidity_factor[['illiq_1y']].rename(columns={'illiq_1y':'factor'})
fa_illiq_1y = fa.factor_analysis(factors=illiq_1y_factor,returns=returns)

fa_illiq_1y.quantile_returns_summ()

	t-stats	ann. return rate (%)	acc. return rate (%)	ann. volatility (%)	sharpe ratio	max drawdown (%)
quantiles
group 1	0.987424	6.205410	70.936696	20.810859	0.298181	39.593304
group 2	0.891465	6.708638	76.521263	24.865694	0.269795	52.033292
group 3	1.126850	9.039417	102.075857	26.240950	0.344478	44.497033
group 4	1.258755	10.719337	120.185390	27.658776	0.387556	40.552622
group 5	1.310146	12.003218	133.856390	29.596616	0.405560	44.389677
group longshort	0.783385	5.486801	62.919695	23.266667	0.235822	38.745707

fa_illiq_1y.quantile_returns_plot()

4. Beta类因子

• beta: 市场Beta，过去252个交易日的个股超额收益率对市场收益超额收益率作回归得到的斜率系数，其中剔除不满120个交易日的股票； $$r^i_t = \alpha^i + \beta^i_{mkt} MKT_t + \epsilon^i_t$$
• _betadown: 下行Beta，下行风险为市场收益率低于某一临界收益率为条件计算的系统性风险,其中剔除过去252个交易日中不满120个交易天数的股票； $$\beta = \frac{cov(r_i,r_m|r_m<\mu_m)}{Var(r_m|r_m<\mu_m)}$$ 参考资料：Ang, A., Chen, J., & Xing, Y.(2006). Downside risk. Review of Financial Studies, 19(4), 1191-1239.
• _betaup: 上行Beta，上行风险为市场收益率高于某一临界收益率为条件计算的系统性风险,其中剔除过去252个交易日中不满120个交易天数的股票；
• _betarelative: 相对Beta，上行Beta与下行Beta的差值。

beta_factor = gf.get_beta_factor(from_date='2009-12-31',to_date='2021-10-31',pool='liquid_perc70')
beta_factor.set_index(['trade_date','stock_code'],inplace=True)
beta_factor

		beta	beta_up	beta_down	beta_relative
trade_date	stock_code
2009-12-31	000001	1.009846	0.643266	0.571294	0.071972
	000002	1.044442	0.706817	0.681236	0.025581
	000005	1.054034	0.258128	0.812633	-0.554506
	000006	1.268346	0.825271	0.768436	0.056834
	000009	1.254508	0.499687	0.928245	-0.428558
...	...	...	...	...	...
2021-10-29	688779	NaN	NaN	NaN	NaN
	688798	NaN	NaN	NaN	NaN
	688819	1.188440	0.303153	0.367037	-0.063884
	688981	0.498994	-0.155896	0.370523	-0.526419
	689009	1.453634	0.327101	0.562933	-0.235832

250696 rows × 4 columns

市场Beta

beta_mkt_factor = beta_factor[['beta']].rename(columns={'beta':'factor'})
fa_beta_mkt = fa.factor_analysis(factors=beta_mkt_factor,returns=returns)

fa_beta_mkt.quantile_returns_summ()

	t-stats	ann. return rate (%)	acc. return rate (%)	ann. volatility (%)	sharpe ratio	max drawdown (%)
quantiles
group 1	1.481018	8.592212	97.211836	19.014343	0.451881	33.440280
group 2	1.176691	9.064165	102.344488	25.195596	0.359752	48.948522
group 3	1.123959	8.991619	101.556851	26.174686	0.343523	38.154744
group 4	0.533483	4.380718	50.481447	27.411570	0.159813	52.490334
group 5	-0.175998	-1.557648	-18.439881	30.350962	-0.051321	90.704322
group longshort	1.515955	10.296559	115.651717	22.099795	0.465912	30.293591

fa_beta_mkt.quantile_returns_plot()

下行Beta

beta_down_factor = beta_factor[['beta_down']].rename(columns={'beta_down':'factor'})
fa_beta_down = fa.factor_analysis(factors=beta_down_factor,returns=returns)

fa_beta_down.quantile_returns_summ()

	t-stats	ann. return rate (%)	acc. return rate (%)	ann. volatility (%)	sharpe ratio	max drawdown (%)
quantiles
group 1	1.591906	9.599000	108.136426	19.677832	0.487808	33.028398
group 2	1.212834	9.141151	103.179808	24.644266	0.370924	37.703301
group 3	0.501367	3.883322	44.848592	25.912875	0.149861	55.781697
group 4	0.314966	2.518423	29.263411	26.914379	0.093572	52.849272
group 5	-0.062756	-0.515100	-6.068542	28.012381	-0.018388	78.300124
group longshort	1.540967	10.161958	114.204968	21.469125	0.473329	25.452989

fa_beta_down.quantile_returns_plot()

上行Beta

beta_up_factor = beta_factor[['beta_up']].rename(columns={'beta_up':'factor'})
fa_beta_up = fa.factor_analysis(factors=beta_up_factor,returns=returns)

fa_beta_up.quantile_returns_summ()

	t-stats	ann. return rate (%)	acc. return rate (%)	ann. volatility (%)	sharpe ratio	max drawdown (%)
quantiles
group 1	1.064173	7.005094	79.799872	21.722639	0.322479	35.220896
group 2	1.081545	6.801604	77.550305	20.771188	0.327454	39.877319
group 3	1.375199	9.404094	106.028728	22.334717	0.421053	40.998535
group 4	1.420294	10.315676	115.857062	23.630170	0.436547	38.295749
group 5	0.663889	5.590558	64.080327	27.960938	0.199942	45.346436
group longshort	0.247077	1.345683	15.719545	18.430242	0.073015	32.639894

fa_beta_up.quantile_returns_plot()

相对Beta

beta_relative_factor = beta_factor[['beta_relative']].rename(columns={'beta_relative':'factor'})
fa_beta_relative = fa.factor_analysis(factors=beta_relative_factor,returns=returns)

fa_beta_relative.quantile_returns_summ()

	t-stats	ann. return rate (%)	acc. return rate (%)	ann. volatility (%)	sharpe ratio	max drawdown (%)
quantiles
group 1	0.063877	0.518362	6.078085	27.564171	0.018806	64.900845
group 2	0.752882	5.578993	63.951014	24.606107	0.226732	49.590335
group 3	0.694776	4.678542	53.842426	22.449275	0.208405	56.404044
group 4	1.481175	9.669041	108.893006	21.296895	0.454012	37.982690
group 5	1.056885	7.463636	84.854660	23.257913	0.320907	34.523922
group longshort	1.102729	6.912485	78.776576	20.694306	0.334028	40.689706

fa_beta_relative.quantile_returns_plot()

5. 动量反转类因子

• _mom12m: 12个月动量（twelve-month momentum），个股第t-250交易日至第t-20交易日之间的累计日收益率，其中剔除交易天数不满110天的股票；
• _mom6m: 6个月动量（six-month momentum），个股第t-125交易日至第t-20交易日之间的累计日收益率，其中剔除交易天数不满50天的股票；
• _mom1m: 短期反转（short-term reversal），个股最近20个交易的累计日收益率，其中剔除交易天数不满10天的股票；
• imom: 特定动量（idiosyncratic momentum），个股第t-250交易日至第t-20交易日之间不能被大盘收益率解释部分的累计和；
• _momchg: 动量变化，个股第t-120交易日至第t-20个交易日之间的动量减去第t-250交易日至第t-120个交易日之间的动量；

mom_factor = gf.get_momentum_factor(from_date='2009-12-31',to_date='2021-10-31',pool='liquid_perc70')
mom_factor.set_index(['trade_date','stock_code'],inplace=True)
mom_factor

		mom_1m	mom_6m	mom_12m	imom	mom_chg
trade_date	stock_code
2009-12-31	000001	0.017536	0.060668	1.259420	-0.017959	-0.689300
	000002	-0.066493	-0.196948	0.489375	0.045655	-0.410984
	000005	-0.101491	0.313726	1.233333	0.116102	0.083371
	000006	-0.131135	-0.088112	1.063435	0.106806	-0.886501
	000009	-0.140845	-0.060812	1.761628	0.161363	-1.148737
...	...	...	...	...	...	...
2021-10-29	688779	-0.071032	NaN	NaN	NaN	NaN
	688798	-0.094711	NaN	NaN	NaN	NaN
	688819	-0.089182	0.017123	0.042573	0.066399	NaN
	688981	0.018505	-0.026127	-0.056897	-0.028073	0.046861
	689009	-0.195981	0.205324	0.115623	0.181284	0.263038

250696 rows × 5 columns

12个月动量

mom_12m_factor = mom_factor[['mom_12m']].rename(columns={'mom_12m':'factor'})
fa_mom_12m = fa.factor_analysis(factors=mom_12m_factor,returns=returns)

fa_mom_12m.quantile_returns_summ()

	t-stats	ann. return rate (%)	acc. return rate (%)	ann. volatility (%)	sharpe ratio	max drawdown (%)
quantiles
group 1	0.106664	0.837978	9.811436	26.646253	0.031448	62.462070
group 2	0.418732	2.926489	33.942796	23.481945	0.124627	61.877714
group 3	0.502383	3.274838	37.923935	21.867602	0.149758	38.265861
group 4	1.455907	9.666119	108.861450	21.660236	0.446261	28.972413
group 5	1.025411	7.593134	86.278617	24.374059	0.311525	46.811255
group longshort	1.102512	6.703755	76.467181	20.091596	0.333660	64.222693

fa_mom_12m.quantile_returns_plot()

六个月动量

mom_6m_factor = mom_factor[['mom_6m']].rename(columns={'mom_6m':'factor'})
fa_mom_6m = fa.factor_analysis(factors=mom_6m_factor,returns=returns)

fa_mom_6m.quantile_returns_summ()

	t-stats	ann. return rate (%)	acc. return rate (%)	ann. volatility (%)	sharpe ratio	max drawdown (%)
quantiles
group 1	0.647082	5.188345	59.575301	26.670389	0.194536	47.283391
group 2	0.800377	5.716759	65.490616	23.703191	0.241181	42.958161
group 3	1.038901	6.778038	77.289531	21.551079	0.314510	36.275891
group 4	0.812778	5.453893	62.551366	22.293981	0.244635	38.077517
group 5	1.122732	8.577287	97.049185	25.040238	0.342540	44.785387
group longshort	0.561019	3.235404	37.473884	19.349693	0.167207	91.670806

fa_mom_6m.quantile_returns_plot()

一个月动量/短期反转

mom_1m_factor = mom_factor[['mom_1m']].rename(columns={'mom_1m':'factor'})
fa_mom_1m = fa.factor_analysis(factors=mom_1m_factor,returns=returns)

fa_mom_1m.quantile_returns_summ()

	t-stats	ann. return rate (%)	acc. return rate (%)	ann. volatility (%)	sharpe ratio	max drawdown (%)
quantiles
group 1	1.460095	12.141562	135.320908	26.847654	0.452239	29.674777
group 2	1.100619	7.955305	90.252690	23.754483	0.334897	36.170803
group 3	1.539560	11.079304	124.032995	23.337980	0.474733	27.945473
group 4	1.483165	10.281388	115.488727	22.556556	0.455805	37.621066
group 5	0.451821	3.556602	41.135100	26.373547	0.134855	65.094671
group longshort	1.195095	8.314845	94.185807	22.829977	0.364207	26.061225

fa_mom_1m.quantile_returns_plot()

特定动量

imom_factor = mom_factor[['imom']].rename(columns={'imom':'factor'})
fa_imom = fa.factor_analysis(factors=imom_factor,returns=returns)

fa_imom.quantile_returns_summ()

	t-stats	ann. return rate (%)	acc. return rate (%)	ann. volatility (%)	sharpe ratio	max drawdown (%)
quantiles
group 1	0.490319	3.847615	44.443263	26.257312	0.146535	66.976273
group 2	1.078078	6.894398	78.576620	21.113767	0.326536	40.551519
group 3	1.166800	7.937065	90.052831	22.357512	0.355007	44.094379
group 4	1.486700	10.276821	115.439658	22.493360	0.456882	25.921273
group 5	1.409480	11.139178	124.671873	25.623129	0.434731	28.916217
group longshort	1.100871	7.043917	80.228610	21.111327	0.333656	35.749658

fa_imom.quantile_returns_plot()

动量变化

mom_chg_factor = mom_factor[['mom_chg']].rename(columns={'mom_chg':'factor'})
fa_mom_chg = fa.factor_analysis(factors=mom_chg_factor,returns=returns)

fa_mom_chg.quantile_returns_summ()

	t-stats	ann. return rate (%)	acc. return rate (%)	ann. volatility (%)	sharpe ratio	max drawdown (%)
quantiles
group 1	1.024597	7.978973	90.511973	25.590301	0.311797	33.755689
group 2	1.224430	8.601506	97.313105	23.022901	0.373607	30.532712
group 3	1.346123	9.026727	101.938088	21.936850	0.411487	37.979675
group 4	0.675931	4.510601	51.948265	22.263384	0.202602	53.614477
group 5	0.780584	5.624236	64.456833	23.920582	0.235121	51.755750
group longshort	0.462799	2.239504	26.055140	16.308854	0.137318	26.783360

fa_mom_chg.quantile_returns_plot()

summ_dict = {'总市值对数':[0.885551,6.742618,76.897478,25.154809,0.268045,41.691550],
'流通市值对数':[0.689302,5.368181,61.591529,25.884174,0.207392,47.112967],
'非线性市值':[0.395620,1.431782,16.718768,12.241886,0.116958,27.106548],
'流通市值占比':[-0.241870,-0.553753,-6.525089,7.814972,-0.070858,40.363451],
'总波动率（最近一月）':[0.820765,5.546495,63.587568,22.442749,0.247140,28.975416],
'总波动率（最近一年）':[1.138422,8.936145,100.954246,25.688815,0.347861,24.994772],
'特定波动率（最近一月）':[0.861525,5.512646,63.208899,21.253626,0.259374,30.370142],
'特定波动率（最近一年）':[1.026657,8.307506,94.105642,26.552953,0.312866,33.988191],
'偏度':[0.557971,2.470875,28.717054,14.909086,0.165729,29.771409],
'特定偏度':[0.616952,3.356662,38.857288,18.245002,0.183977,33.894420],
'条件偏度':[1.318597,9.053815,102.232151,22.459396,0.403119,22.119254],
'换手率（最近一月）':[1.596955,11.960025,133.398811,24.198138,0.494254,29.917020],
'换手率波动率（最近一月）':[2.310941,16.615841,181.813800,22.790853,0.729057,26.770884],
'换手率（最近一年）':[0.943649,7.326261,83.342374,25.584575,0.286355,38.560136],
'换手率波动率（最近一年）':[1.568547,11.508702,128.607808,23.751577,0.484545,38.485839],
'异常换手率':[0.620338,3.600087,41.629972,19.440172,0.185188,37.526980],
'非流动性(最近一月)':[1.367809,9.358872,105.539207,22.351728,0.418709,31.780758],
'非流动性（最近一年）':[0.783385,5.486801,62.919695,23.266667,0.235822,38.745707],
'市场Beta':[1.515955,10.296559,115.651717,22.099795,0.465912,30.293591],
'下行Beta':[1.540967,10.161958,114.204968,21.469125,0.473329,25.452989],
'上行Beta':[0.247077,1.345683,15.719545,18.430242,0.073015,32.639894],
'相对Beta':[1.102729,6.912485,78.776576,20.694306,0.334028,40.689706],
'动量（最近一年）':[1.102512,6.703755,76.467181,20.091596,0.333660,64.222693],
'动量（最近六月）':[0.561019,3.235404,37.473884,19.349693,0.167207,91.670806],
'短期反转':[1.195095,8.314845,94.185807,22.829977,0.364207,26.061225],
'特定动量':[1.100871,7.043917,80.228610,21.111327,0.333656,35.749658],
'动量变化':[0.462799,2.239504,26.055140,16.308854,0.137318,26.783360]}

summ_df = pd.DataFrame.from_dict(summ_dict, orient='index',columns=['t值','年化收益率(%)','累计收益率(%)','年化波动率(%)','夏普比率','最大回测(%)'])

指标计算：\ 夏普比率（年化）：$R_{mean}$为区间内平均收益率，$R_f$为无风险收益率，$\sigma_{R}$为区间内收益波动率，$N$为$\sqrt{250}$或$\sqrt{52}$或$\sqrt{12}$。 $$Sharpe_{annual} = (\frac{R_{mean}-R_f}{\sigma_{R}})\times N$$ 年化收益率：$R_{mean}$为区间内平均收益率，$N$为计算周期天数。 $$R_{annual} = [(1+R_{mean})^{\frac{365}{N}}-1]\times 100\%$$ 年化波动率：$r_{i}$为收益率，$R_{mean}$为区间内平均收益率，$n$为$250$或$52$或$12$。 $$V_{annual} = \sqrt{\frac{\sum_i^N(r_i-R_{mean})^2}{N}}\times \sqrt{n}$$