本研究内容参考海通证券研究报告《选股因子系列研究(十七)——选股因子的正交》内容，具体研报可参考【研报分享】海通证券：选股因子的正交
近年来，随着投资者对于因子选股体系研究的深入，选股因子值的处理也在逐渐细化，本文将主要对于选股因子的正交进行分析讨论。之所以讨论因子的正交是因为在传统的多因子模型中，选取的因子之间往往存在着相关性，而这种相关性并不稳定，且相关性的存在会复杂因子权重的分配。 对于等权分配因子权重的多因子模型，由于因子之间相关性的存在，模型可能实际上对于某一因子有更高的暴露（例如，市值因子）。 对于权重优化的模型，相关性的影响可能会更大。因此，本文考虑在构建因子的时候对于相关性进行剔除从而达到更为可控的因子暴露。
研报中主要分为三部分。第一部分对于因子正交的必要性以及正交过程中的相关处理方式进行了说明。 第二部分回测对比了正交多因子模型与原始多因子模型的历史表现。第三部分对于正交顺序的确定进行了讨论。
本研究主要参考第一部分的处理方法，对第二部分内容进行了实证，按照这个思路，展开研究，下面是研究的内容分布：
1）因子数据获取：
设置股票池，获取指定时间范围的月度因子数据，按照研报思路，我们直接获取了聚宽因子库中的因子数据，并加入行业因子，按日期将因子值存入字典，记录保存了原始因子值，方便进行计算构造正交因子。
2）因子数据处理：
将计算出来的因子值按日期遍历获取，根据需要进行数据处理
在T期因子值中加入T+1期收益值，方便因子分析统计
3）因子统计分析：
针对每期截面进行因子IC统计
汇总为时间序列上的IC数据，进行展示
4）分组回测分析：
根据所选的因子，在每个调仓日进行股票排序，分层进行收益净值观察
根据所选因子，在每个调仓日进行股票排序，进行多头组合收益分析
1）时间范围：
2014.6 ～ 2019.6
2）研究指数：
中证500
3）股票池：
中证500指数成分股
剔除 ST、停牌、涨跌停、上市不满 6 个月
月初调仓
4）费用设置：
暂无交易成本设置
本文参考研报中关于选股因子正交的讨论，通过使用正交选股因子来得到更加可控的因子暴露，我们采取研报中给出的参考顺序进行了正交化处理，通过实际组合的构建以及初步回测， 相比于原始因子收益及夏普都有所提升。 在三因子与八因子两种模型中，对因子IC均有提升，在多头组合中也得到了了印证。
#导入需要的库、定义需要用到的工具函数#工具函数import timefrom datetime import datetime, timedeltafrom jqdata import *import numpy as npimport pandas as pdimport mathfrom statsmodels import regressionimport statsmodels.api as smimport matplotlib.pyplot as pltimport datetimefrom scipy import statsfrom sklearn.linear_model import LinearRegression as LRfrom jqfactor import *import warnings warnings.filterwarnings('ignore') plt.style.use('ggplot')#输入起止日期，返回所有自然日日期def get_date_list(begin_date, end_date):dates = []dt = datetime.strptime(begin_date,"%Y-%m-%d")date = begin_date[:]while date <= end_date:dates.append(date)dt += timedelta(days=1)date = dt.strftime("%Y-%m-%d")return dates#获取日期列表def get_tradeday_list(start,end,frequency=None,count=None):if count != None:df = get_price('000001.XSHG',end_date=end,count=count)else:df = get_price('000001.XSHG',start_date=start,end_date=end)if frequency == None or frequency =='day':return df.indexelse:df['year-month'] = [str(i)[0:7] for i in df.index]if frequency == 'month':return df.drop_duplicates('year-month').indexelif frequency == 'quarter':df['month'] = [str(i)[5:7] for i in df.index]df = df[(df['month']=='01') | (df['month']=='04') | (df['month']=='07') | (df['month']=='10') ]return df.drop_duplicates('year-month').indexelif frequency =='halfyear':df['month'] = [str(i)[5:7] for i in df.index]df = df[(df['month']=='01') | (df['month']=='06')]return df.drop_duplicates('year-month').index #输入开始日期和结束日期，返回每周第一个交易日def get_weekday(s_date,d_date):df = get_price('000001.XSHG',start_date=s_date,end_date=d_date)dt_list = []for d1,d2 in zip(df.index[:-1],df.index[1:]):d_1 = datetime.datetime(int(str(d1)[:4]),int(str(d1)[5:7]),int(str(d1)[8:10]))d_2 = datetime.datetime(int(str(d2)[:4]),int(str(d2)[5:7]),int(str(d2)[8:10]))weekday1 = d_1.strftime("%w")weekday2 = d_2.strftime("%w")interday = (d_2 - d_1).daysif (int(weekday1) >= int(weekday2)) or interday>7:dt_list.append(str(d2)[:10])return dt_list def ret_se(start_date='2018-6-1',end_date='2018-7-1',stock_pool=None,weight=0):pool = stock_poolif len(pool) != 0:#得到股票的历史价格数据df = get_price(list(pool),start_date=start_date,end_date=end_date,fields=['close']).closedf = df.dropna(axis=1)#获取列表中的股票流通市值对数值df_mkt = get_fundamentals(query(valuation.code,valuation.circulating_market_cap).filter(valuation.code.in_(df.columns)))df_mkt.index = df_mkt['code'].valuesfact_se =pd.Series(df_mkt['circulating_market_cap'].values,index = df_mkt['code'].values)fact_se = np.log(fact_se)else:df = get_price('000001.XSHG',start_date=start_date,end_date=end_date,fields=['close'])df['v'] = [1]*len(df)del df['close']#相当于昨天的百分比变化pct = df.pct_change()+1pct.iloc[0,:] = 1if weight == 0:#等权重平均收益结果se = pct.cumsum(axis=1).iloc[:,-1]/pct.shape[1]return seelse:#按权重的方式计算se = (pct*fact_se).cumsum(axis=1).iloc[:,-1]/sum(fact_se)return se#获取所有分组pctdef get_all_pct(pool_dict,trade_list,groups=5):num = 1for s,e in zip(trade_list[:-1],trade_list[1:]):stock_list = pool_dict[s]stock_num = len(stock_list)//groupsif num == 0:pct_se_list = []for i in range(groups):pct_se_list.append(ret_se(start_date=s,end_date=e,stock_pool=stock_list[i*stock_num:(i+1)*stock_num]))pct_df1 = pd.concat(pct_se_list,axis=1)pct_df1.columns = range(groups)pct_df = pd.concat([pct_df,pct_df1],axis=0)else:pct_se_list = []for i in range(groups):pct_se_list.append(ret_se(start_date=s,end_date=e,stock_pool=stock_list[i*stock_num:(i+1)*stock_num]))pct_df = pd.concat(pct_se_list,axis=1) pct_df.columns = range(groups)num = 0return pct_dfdef tradedays_before(date,count):#获取指定交易日往前推count天交易日date = get_price('000001.XSHG',end_date=date,count=count+1).index[0]return datedef ShiftTradingDay(date,shift):# 获取所有的交易日，返回一个包含所有交易日的 list,元素值为 datetime.date 类型.tradingday = get_all_trade_days()# 得到date之后shift天那一天在列表中的行标号 返回一个数date = datetime.date(int(str(date)[:4]),int(str(date)[5:7]),int(str(date)[8:10]))shiftday_index = list(tradingday).index(date)+shift# 根据行号返回该日日期 为datetime.date类型return tradingday[shiftday_index] #进行新股、St股过滤，返回筛选后的股票def filter_stock(stockList,date,days=21*3,skip_paused=1,limit=0):#日频策略加入开盘涨停过滤#去除上市距beginDate不足3个月的股票def delect_stop(stocks,beginDate,n=days):stockList=[]beginDate = datetime.datetime.strptime(beginDate, "%Y-%m-%d")for stock in stocks:start_date=get_security_info(stock).start_dateif start_date<(beginDate-datetime.timedelta(days=n)).date():stockList.append(stock)return stockList#剔除ST股st_data=get_extras('is_st',stockList, count = 1,end_date=date)stockList = [stock for stock in stockList if not st_data[stock][0]]#剔除当天停牌股if skip_paused == 1:paused_df = get_price(stockList,end_date=date,count=1,fields=['paused'])['paused'].Tpaused_df.columns = ['paused']paused_df = paused_df[paused_df['paused']==0]stockList = paused_df.index#新股及退市股票stockList=delect_stop(stockList,date)#剔除开盘涨停股票if limit == 1:#如果需要收盘涨跌停可以改字段即可df = get_price(stockList,end_date=date,fields=['open','high_limit','low_limit'],count=1).iloc[:,0,:]df['h_limit']=(df['open']==df['high_limit'])df['l_limit']=(df['open']==df['low_limit'])stockList = [df.index[i] for i in range(len(df)) if not (df.h_limit[i] or df.l_limit[i])] #过滤涨跌停股票return stockList#设置股票池（指数成分股）index = '000905.XSHG' #设置股票池，和对比基准，这里是中证500#设置统计起止日期date_start = '2014-05-01'date_end = '2019-07-1'#获取统计期内交易日列表、用于计算因子数据date_list = get_tradeday_list(start=date_start,end=date_end,frequency='month',count=None)#获取回测日期间的所有交易日date_list
DatetimeIndex(['2014-05-05', '2014-06-03', '2014-07-01', '2014-08-01', '2014-09-01', '2014-10-08', '2014-11-03', '2014-12-01', '2015-01-05', '2015-02-02', '2015-03-02', '2015-04-01', '2015-05-04', '2015-06-01', '2015-07-01', '2015-08-03', '2015-09-01', '2015-10-08', '2015-11-02', '2015-12-01', '2016-01-04', '2016-02-01', '2016-03-01', '2016-04-01', '2016-05-03', '2016-06-01', '2016-07-01', '2016-08-01', '2016-09-01', '2016-10-10', '2016-11-01', '2016-12-01', '2017-01-03', '2017-02-03', '2017-03-01', '2017-04-05', '2017-05-02', '2017-06-01', '2017-07-03', '2017-08-01', '2017-09-01', '2017-10-09', '2017-11-01', '2017-12-01', '2018-01-02', '2018-02-01', '2018-03-01', '2018-04-02', '2018-05-02', '2018-06-01', '2018-07-02', '2018-08-01', '2018-09-03', '2018-10-08', '2018-11-01', '2018-12-03', '2019-01-02', '2019-02-01', '2019-03-01', '2019-04-01', '2019-05-06', '2019-06-03', '2019-07-01'], dtype='datetime64[ns]', freq=None)
根据研报中提到的因子，我们直接通过聚宽因子库获取，后面会提到行业因子数据手动计算加入
#查询个股所在行业函数代码（申万一级） ,为中性化函数的子函数 def get_industry_code_from_security(security,date=None):industry_index=get_industries(name='sw_l1').indexfor i in range(0,len(industry_index)):try:index = get_industry_stocks(industry_index[i],date=date).index(security)return industry_index[i]except:continuereturn u'未找到' #为股票池添加行业标记,return df格式 ,为中性化函数的子函数 def get_industry_exposure(stock_list,date=None):df = pd.DataFrame(index=get_industries(name='sw_l1').index, columns=stock_list)for stock in stock_list:try:df[stock][get_industry_code_from_security(stock,date)] = 1except:print('报错')continuereturn df.fillna(0)#将NaN赋为0#计算并保存因子值数据#因子获取 市值因子、反转因子、换手率因子def get_3_factor(stocks_list,date1='2019-06-01',date2='2019-07-01'):date2 = str(date2)[:10]date1 = str(date1)[:10]df = get_fundamentals(query(valuation.code,valuation.market_cap).filter(valuation.code.in_(stocks_list)),date=date2)df.index = df['code'].valuesdel df['code']df = log(df)q = query(valuation.turnover_ratio).filter(valuation.code.in_(stocks_list))df3 = get_fundamentals_continuously(q, end_date=date2, count=30)['turnover_ratio']se_tur = log(df3[df3.index>=date1].mean())df1 = get_price(stocks_list,start_date=date1,end_date=date2,fields=['close'])['close']se_pct = df1.iloc[-1,:]/df1.iloc[0,:]-1df['tur'] = se_turdf['pct'] = se_pctreturn df#计算并保存因子值数据#八个风格因子def get_8_factor(stocks_list,date='2019-06-01'):factors = ['size','momentum','liquidity','residual_volatility','book_to_price_ratio','beta','earnings_yield','leverage']#取值函数f_dict = get_factor_values(stocks_list , factors=factors,end_date=date,count=1)df = pd.concat([f_dict[factor] for factor in factors],axis=0)df.index = factorsreturn df.Tstocks_list = ['000001.XSHE','600000.XSHG']get_8_factor(stocks_list,date=date_list[0])
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| size | momentum | liquidity | residual_volatility | book_to_price_ratio | beta | earnings_yield | leverage | |
|---|---|---|---|---|---|---|---|---|
| code | ||||||||
| 000001.XSHE | 0.614343 | -0.315892 | 1.428474 | -0.347846 | 1.168728 | 0.455703 | 2.851955 | 0.220709 |
| 600000.XSHG | 0.839260 | 0.184742 | 1.572740 | -0.349360 | 1.359600 | 0.180290 | 2.851955 | 0.011776 |
#循环日期列表，进行因子值记录，按字典的方式存储#进行因子值计算factor_3_dict = {}factor_8_dict= {}#循环时间列表获取原始因子数据组成dictfor date1,date2 in zip(date_list[:-1],date_list[1:]):end_date=str(date2)[:10]print('正在计算 {} 因子数据......'.format(end_date))stocks_list = get_index_stocks(index,date=end_date)#获取指定日期成分股列表stocks_list = filter_stock(stocks_list,end_date,days=183,limit=1)#进行股票筛选stocks_list = filter_stock(stocks_list,str(date1)[:10],days=183,limit=1)#进行股票筛选factor_3_dict[end_date] = get_3_factor(stocks_list,date1=date1,date2=end_date)factor_8_dict[end_date] = get_8_factor(stocks_list,date=end_date)正在计算 2014-06-03 因子数据...... 正在计算 2014-07-01 因子数据...... 正在计算 2014-08-01 因子数据...... 正在计算 2014-09-01 因子数据...... 正在计算 2014-10-08 因子数据...... 正在计算 2014-11-03 因子数据...... 正在计算 2014-12-01 因子数据...... 正在计算 2015-01-05 因子数据...... 正在计算 2015-02-02 因子数据...... 正在计算 2015-03-02 因子数据...... 正在计算 2015-04-01 因子数据...... 正在计算 2015-05-04 因子数据...... 正在计算 2015-06-01 因子数据...... 正在计算 2015-07-01 因子数据...... 正在计算 2015-08-03 因子数据...... 正在计算 2015-09-01 因子数据...... 正在计算 2015-10-08 因子数据...... 正在计算 2015-11-02 因子数据...... 正在计算 2015-12-01 因子数据...... 正在计算 2016-01-04 因子数据...... 正在计算 2016-02-01 因子数据...... 正在计算 2016-03-01 因子数据...... 正在计算 2016-04-01 因子数据...... 正在计算 2016-05-03 因子数据...... 正在计算 2016-06-01 因子数据...... 正在计算 2016-07-01 因子数据...... 正在计算 2016-08-01 因子数据...... 正在计算 2016-09-01 因子数据...... 正在计算 2016-10-10 因子数据...... 正在计算 2016-11-01 因子数据...... 正在计算 2016-12-01 因子数据...... 正在计算 2017-01-03 因子数据...... 正在计算 2017-02-03 因子数据...... 正在计算 2017-03-01 因子数据...... 正在计算 2017-04-05 因子数据...... 正在计算 2017-05-02 因子数据...... 正在计算 2017-06-01 因子数据...... 正在计算 2017-07-03 因子数据...... 正在计算 2017-08-01 因子数据...... 正在计算 2017-09-01 因子数据...... 正在计算 2017-10-09 因子数据...... 正在计算 2017-11-01 因子数据...... 正在计算 2017-12-01 因子数据...... 正在计算 2018-01-02 因子数据...... 正在计算 2018-02-01 因子数据...... 正在计算 2018-03-01 因子数据...... 正在计算 2018-04-02 因子数据...... 正在计算 2018-05-02 因子数据...... 正在计算 2018-06-01 因子数据...... 正在计算 2018-07-02 因子数据...... 正在计算 2018-08-01 因子数据...... 正在计算 2018-09-03 因子数据...... 正在计算 2018-10-08 因子数据...... 正在计算 2018-11-01 因子数据...... 正在计算 2018-12-03 因子数据...... 正在计算 2019-01-02 因子数据...... 正在计算 2019-02-01 因子数据...... 正在计算 2019-03-01 因子数据...... 正在计算 2019-04-01 因子数据...... 正在计算 2019-05-06 因子数据...... 正在计算 2019-06-03 因子数据...... 正在计算 2019-07-01 因子数据......
进行因子值数据处理、如有必要可进行去极值、标准化、中性化
加入收益数据：将T期因子值中加入T~T+1的收益数据进行记录
参考研报中给出的中性化顺序、
#数据清洗、包括去极值、标准化、中性化等,并加入y值import time t1 = time.time()factor_3_y_dict = {}factor_8_y_dict = {}for date_1,date_2 in zip(date_list[1:-1],date_list[2:]):d1 = ShiftTradingDay(date_1,1) #往后推一天d2 = ShiftTradingDay(date_2,1)print('开始整理 {} 数据...'.format(str(date_1)[:10]))factor_3_df = factor_3_dict[str(date_1)[:10]] #根据字典存储的日期格式不同进行不同设置factor_8_df = factor_8_dict[str(date_1)[:10]] #根据字典存储的日期格式不同进行不同设置pool = list(factor_3_df.index)#计算指数涨跌幅df_1 = get_price(index,end_date=d1,fields=['open'],count = 1)['open']df_2 = get_price(index,end_date=d2,fields=['open'],count = 1)['open']index_pct = df_2.values[0]/df_1.values[0] - 1#具体数值#计算各股票涨跌幅df_1 = get_price(pool,end_date=d1,fields=['open'],count = 1)['open']df_2 = get_price(pool,end_date=d2,fields=['open'],count = 1)['open']df_3 = pd.concat([df_1,df_2],axis=0).T #进行合并stock_pct = df_3.iloc[:,1]/df_3.iloc[:,0] - 1 #计算pct，series#对数据进行处理、标准化、去极值、中性化factor_3_df = winsorize_med(factor_3_df, scale=3, inclusive=True, inf2nan=True, axis=0) #中位数去极值处理factor_8_df = winsorize_med(factor_8_df, scale=3, inclusive=True, inf2nan=True, axis=0) #中位数去极值处理factor_3_df = standardlize(factor_3_df, inf2nan=True, axis=0) #对每列做标准化处理factor_8_df = standardlize(factor_8_df, inf2nan=True, axis=0) #对每列做标准化处理#factor_df['pct_alpha'] = stock_pct-index_pctfactor_3_df['y'] = stock_pctfactor_8_df['y'] = stock_pct#进行正交因子记录factor_list = ['size','momentum','liquidity','residual_volatility','book_to_price_ratio','beta','earnings_yield','leverage']factor_new_list = []#先对市值因子进行行业中性化for factor in ['market_cap','tur','pct']:if factor == 'market_cap':factor_3_df[factor+'_'] = neutralize(factor_3_df[factor], how=['sw_l1'], date=str(date_1)[:10], axis=0,fillna='sw_l1')#中性化factor_new_list.append(factor+'_')else:#对factor正交X = factor_3_df[factor_new_list]y = factor_3_df[factor]reg = LR().fit(X,y)factor_3_df[factor+'_'] = y - reg.predict(X)factor_new_list.append(factor+'_')factor_3_y_dict[str(date_1)[:10]] = factor_3_dffactor_new_list = []#先对市值因子进行行业中性化for factor in factor_list:if factor == 'size':factor_8_df['size'+'_'] = neutralize(factor_8_df['size'], how=['sw_l1'], date=str(date_1)[:10], axis=0,fillna='sw_l1')#中性化factor_new_list.append('size_')else:#对factor正交X = factor_8_df[factor_new_list]y = factor_8_df[factor]reg = LR().fit(X,y)factor_8_df[factor+'_'] = y - reg.predict(X)factor_new_list.append(factor+'_')factor_8_y_dict[str(date_1)[:10]] = factor_8_dft2 = time.time()print('计算数据耗时：{0}'.format(t2-t1))print(factor_3_y_dict[str(date_1)[:10]].shape)开始整理 2014-06-03 数据... 开始整理 2014-07-01 数据... 开始整理 2014-08-01 数据... 开始整理 2014-09-01 数据... 开始整理 2014-10-08 数据... 开始整理 2014-11-03 数据... 开始整理 2014-12-01 数据... 开始整理 2015-01-05 数据... 开始整理 2015-02-02 数据... 开始整理 2015-03-02 数据... 开始整理 2015-04-01 数据... 开始整理 2015-05-04 数据... 开始整理 2015-06-01 数据... 开始整理 2015-07-01 数据... 开始整理 2015-08-03 数据... 开始整理 2015-09-01 数据... 开始整理 2015-10-08 数据... 开始整理 2015-11-02 数据... 开始整理 2015-12-01 数据... 开始整理 2016-01-04 数据... 开始整理 2016-02-01 数据... 开始整理 2016-03-01 数据... 开始整理 2016-04-01 数据... 开始整理 2016-05-03 数据... 开始整理 2016-06-01 数据... 开始整理 2016-07-01 数据... 开始整理 2016-08-01 数据... 开始整理 2016-09-01 数据... 开始整理 2016-10-10 数据... 开始整理 2016-11-01 数据... 开始整理 2016-12-01 数据... 开始整理 2017-01-03 数据... 开始整理 2017-02-03 数据... 开始整理 2017-03-01 数据... 开始整理 2017-04-05 数据... 开始整理 2017-05-02 数据... 开始整理 2017-06-01 数据... 开始整理 2017-07-03 数据... 开始整理 2017-08-01 数据... 开始整理 2017-09-01 数据... 开始整理 2017-10-09 数据... 开始整理 2017-11-01 数据... 开始整理 2017-12-01 数据... 开始整理 2018-01-02 数据... 开始整理 2018-02-01 数据... 开始整理 2018-03-01 数据... 开始整理 2018-04-02 数据... 开始整理 2018-05-02 数据... 开始整理 2018-06-01 数据... 开始整理 2018-07-02 数据... 开始整理 2018-08-01 数据... 开始整理 2018-09-03 数据... 开始整理 2018-10-08 数据... 开始整理 2018-11-01 数据... 开始整理 2018-12-03 数据... 开始整理 2019-01-02 数据... 开始整理 2019-02-01 数据... 开始整理 2019-03-01 数据... 开始整理 2019-04-01 数据... 开始整理 2019-05-06 数据... 开始整理 2019-06-03 数据... 计算数据耗时：58.29415845870972 (482, 7)
factor_3_y_dict[str(date_1)[:10]].head(3)
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| market_cap | tur | pct | y | market_cap_ | tur_ | pct_ | |
|---|---|---|---|---|---|---|---|
| 000006.XSHE | -1.183287 | -0.773171 | -0.051458 | 0.050943 | -1.270898 | -0.972542 | 0.125768 |
| 000008.XSHE | -0.447743 | -0.513199 | -0.511732 | 0.026385 | -0.292191 | -0.559036 | -0.481746 |
| 000009.XSHE | -0.155374 | 0.102236 | -0.413471 | 0.031690 | 0.104927 | 0.118697 | -0.426872 |
IC统计
根据IC值计算等权多因子组合打分
接下来的研究中，我们分别对于三因子与八个风格因子做如下分类进行研究
| （因子模型）\（因子处理） | 原始因子 | 正交因子 |
|---|---|---|
| 等权多因子模型 | factor_a | factor_b |
| 最大化收益预期 | factor_c | factor_d |
#3因子#记录IC值#统计记录IC值ic_df = pd.DataFrame()for d in date_list[1:-1]:d = str(d)[:10]ic_df[d] = (factor_3_y_dict[d].corr()).loc[:,'y']#记录ic的均值，这里取5期均值作为型号函数参数ic_mean = ic_df.rolling(5,axis=1).mean()ic_mean.iloc[:,:4] = ic_df.iloc[:,:4]sign_df = sign(ic_mean)#等权多因子模型factor_3_list = ['market_cap','tur','pct']factor_3_list_ = ['market_cap_','tur_','pct_']for d1,d2 in zip(date_list[1:-2],date_list[2:-1]):d1,d2 = str(d1)[:10],str(d2)[:10]factor_df_ = factor_3_y_dict[d1]factor_df = factor_3_y_dict[d2]#等权factor_df['factor_a'] = np.dot(factor_df[factor_3_list],sign_df[d1][factor_3_list])factor_df['factor_b'] = np.dot(factor_df[factor_3_list_],sign_df[d1][factor_3_list_])#预测值X_ = factor_df_[factor_3_list+['y']]X_ = X_.dropna()reg = LR(fit_intercept=False).fit(X_[factor_3_list],X_['y'])X = factor_df[factor_3_list]factor_df['factor_c'] = reg.predict(X)#预测值X_ = factor_df_[factor_3_list_+['y']]X_ = X_.dropna()reg = LR(fit_intercept=False).fit(X_[factor_3_list_],X_['y'])X = factor_df[factor_3_list_]factor_df['factor_d'] = reg.predict(X)factor_3_y_dict[d2] = factor_df
#8因子#记录IC值#统计记录IC值ic_df = pd.DataFrame()for d in date_list[1:-1]:d = str(d)[:10]ic_df[d] = (factor_8_y_dict[d].corr()).loc[:,'y']#记录ic的均值，这里取5期均值作为型号函数参数ic_mean = ic_df.rolling(5,axis=1).mean()ic_mean.iloc[:,:4] = ic_df.iloc[:,:4]sign_df = sign(ic_mean)#等权多因子模型factor_8_list = ['size','momentum','liquidity','residual_volatility','book_to_price_ratio','beta','earnings_yield','leverage']factor_8_list_ = [factor+'_' for factor in factor_8_list]for d1,d2 in zip(date_list[1:-2],date_list[2:-1]):d1,d2 = str(d1)[:10],str(d2)[:10]factor_df_ = factor_8_y_dict[d1]factor_df = factor_8_y_dict[d2]#等权factor_df['factor_a'] = np.dot(factor_df[factor_8_list],sign_df[d1][factor_8_list])factor_df['factor_b'] = np.dot(factor_df[factor_8_list_],sign_df[d1][factor_8_list_])#预测值X_ = factor_df_[factor_8_list+['y']]X_ = X_.dropna()reg = LR(fit_intercept=False).fit(X_[factor_8_list],X_['y'])X = factor_df[factor_8_list]factor_df['factor_c'] = reg.predict(X)#预测值X_ = factor_df_[factor_8_list_+['y']]X_ = X_.dropna()reg = LR(fit_intercept=False).fit(X_[factor_8_list_],X_['y'])X = factor_df[factor_8_list_]factor_df['factor_d'] = reg.predict(X)factor_8_y_dict[d2] = factor_df
在下面的内容中，我们将对所有因子IC值进行统计记录，并记录各因子值IC均值、IC标准差、IC最小值、IC最大值、负IC占比
并将IC值与累计IC进行统计展示
#统计记录IC值ic_df = pd.DataFrame()for d in date_list[2:-1]:d = str(d)[:10]ic_df[d] = (factor_3_y_dict[d].corr()).loc[:,'y']#所有因子信息统计如下factor_alg = ['factor_a','factor_b','factor_c','factor_d']for factor in factor_alg:ic_ = ic_df.Tic_df_temp = ic_df.T[factor]tab_ic = pd.DataFrame()for year in range(2014,2020):#表格统计ic_temp = ic_[(ic_.index>(str(year)+'-01-01')) & (ic_.index<(str(year+1)+'-01-01'))]tab_ic[str(year)] = [ic_temp[factor].mean(),ic_temp[factor].std(),ic_temp[factor].min(),ic_temp[factor].max(),round(sum(ic_temp[factor]<0)/len(ic_temp),4)]tab_ic['所有年份'] = [ic_[factor].mean(),ic_[factor].std(),ic_[factor].min(),ic_[factor].max(),round(sum(ic_[factor]<0)/len(ic_),4)]tab_ic.index=['IC均值','IC标准差',"IC最小值","IC最大值","负IC占比"]print('========================因子：{} IC统计信息如下======================'.format(factor))tab_ic = tab_ic.Tif factor != 'y':tab_ic['IC_IR'] = tab_ic['IC均值']/tab_ic['IC标准差']print(tab_ic)#进行IC值展示ic_df_temp1 = ic_df.T[[factor]]ic_df_temp1['ic_sum'] = ic_df_temp1[factor].cumsum()ic_df_temp1.plot(use_index=False,y=[factor,'ic_sum'],secondary_y=['ic_sum'],figsize=(9,5))plt.show()========================因子：factor_a IC统计信息如下====================== IC均值 IC标准差 IC最小值 IC最大值 负IC占比 IC_IR 2014 -0.017538 0.124705 -0.246621 0.089271 0.5000 -0.140638 2015 0.071137 0.173595 -0.391035 0.312932 0.1667 0.409786 2016 0.053121 0.137648 -0.162805 0.278617 0.3333 0.385920 2017 0.048078 0.125649 -0.177519 0.253278 0.2500 0.382635 2018 0.030171 0.163429 -0.273895 0.236523 0.3333 0.184612 2019 -0.024473 0.164221 -0.273033 0.183985 0.5000 -0.149026 所有年份 0.036300 0.147268 -0.391035 0.312932 0.3167 0.246489
========================因子：factor_b IC统计信息如下====================== IC均值 IC标准差 IC最小值 IC最大值 负IC占比 IC_IR 2014 0.027131 0.054115 -0.042642 0.098155 0.3333 0.501354 2015 0.070938 0.159593 -0.347438 0.312901 0.1667 0.444492 2016 0.046544 0.140073 -0.175027 0.212870 0.2500 0.332284 2017 0.031378 0.134259 -0.220017 0.243917 0.2500 0.233715 2018 0.052601 0.121627 -0.206282 0.234303 0.2500 0.432474 2019 -0.034569 0.164682 -0.287688 0.153701 0.5000 -0.209914 所有年份 0.039548 0.133809 -0.347438 0.312901 0.2667 0.295558
========================因子：factor_c IC统计信息如下====================== IC均值 IC标准差 IC最小值 IC最大值 负IC占比 IC_IR 2014 0.040188 0.119786 -0.176964 0.184186 0.1667 0.335499 2015 0.055830 0.190043 -0.431224 0.262616 0.2500 0.293779 2016 0.032703 0.129978 -0.172952 0.221127 0.3333 0.251604 2017 -0.007106 0.168578 -0.319850 0.251916 0.5833 -0.042154 2018 -0.047817 0.145440 -0.249650 0.205273 0.6667 -0.328773 2019 -0.018378 0.216746 -0.341112 0.168363 0.3333 -0.084790 所有年份 0.008903 0.160522 -0.431224 0.262616 0.4167 0.055464
========================因子：factor_d IC统计信息如下====================== IC均值 IC标准差 IC最小值 IC最大值 负IC占比 IC_IR 2014 0.072537 0.054451 -0.000394 0.156377 0.1667 1.332152 2015 0.054744 0.196954 -0.449488 0.289851 0.2500 0.277956 2016 0.023425 0.139099 -0.254416 0.206825 0.3333 0.168408 2017 -0.003378 0.164517 -0.332777 0.240672 0.5000 -0.020531 2018 -0.051295 0.141295 -0.252695 0.199002 0.6667 -0.363031 2019 -0.028938 0.217763 -0.349407 0.161143 0.3333 -0.132886 所有年份 0.009059 0.160229 -0.449488 0.289851 0.4000 0.056541
以上是针对三因子进行因子正交的结果统计，通过因子IC计算，获得如下信息：
将原始因子进行正交，且在等权分组下IC值最高，也就是factor_b表现最好
两种因子模型中，正交因子IC值均大于原始因子IC
等权多因子模型因子IC远超最大化收益预期因子IC
#统计记录IC值ic_df = pd.DataFrame()for d in date_list[2:-1]:d = str(d)[:10]ic_df[d] = (factor_8_y_dict[d].corr()).loc[:,'y']#所有因子信息统计如下factor_alg = ['factor_a','factor_b','factor_c','factor_d']for factor in factor_alg:ic_ = ic_df.Tic_df_temp = ic_df.T[factor]tab_ic = pd.DataFrame()for year in range(2014,2020):#表格统计ic_temp = ic_[(ic_.index>(str(year)+'-01-01')) & (ic_.index<(str(year+1)+'-01-01'))]tab_ic[str(year)] = [ic_temp[factor].mean(),ic_temp[factor].std(),ic_temp[factor].min(),ic_temp[factor].max(),round(sum(ic_temp[factor]<0)/len(ic_temp),4)]tab_ic['所有年份'] = [ic_[factor].mean(),ic_[factor].std(),ic_[factor].min(),ic_[factor].max(),round(sum(ic_[factor]<0)/len(ic_),4)]tab_ic.index=['IC均值','IC标准差',"IC最小值","IC最大值","负IC占比"]print('========================因子：{} IC统计信息如下======================'.format(factor))tab_ic = tab_ic.Tif factor != 'y':tab_ic['IC_IR'] = tab_ic['IC均值']/tab_ic['IC标准差']print(tab_ic)#进行IC值展示ic_df_temp1 = ic_df.T[[factor]]ic_df_temp1['ic_sum'] = ic_df_temp1[factor].cumsum()ic_df_temp1.plot(use_index=False,y=[factor,'ic_sum'],secondary_y=['ic_sum'],figsize=(9,5))plt.show()========================因子：factor_a IC统计信息如下====================== IC均值 IC标准差 IC最小值 IC最大值 负IC占比 IC_IR 2014 0.050919 0.197914 -0.154034 0.274019 0.5000 0.257277 2015 -0.037982 0.135574 -0.236333 0.163321 0.5833 -0.280160 2016 0.075084 0.150006 -0.169020 0.310844 0.2500 0.500541 2017 0.054524 0.113728 -0.187793 0.239862 0.2500 0.479421 2018 0.010294 0.189112 -0.338846 0.222067 0.4167 0.054433 2019 -0.063888 0.115252 -0.206008 0.080114 0.6667 -0.554333 所有年份 0.019087 0.153365 -0.338846 0.310844 0.4167 0.124454
========================因子：factor_b IC统计信息如下====================== IC均值 IC标准差 IC最小值 IC最大值 负IC占比 IC_IR 2014 0.117090 0.150642 -0.042009 0.293220 0.3333 0.777278 2015 -0.029352 0.133764 -0.290880 0.216595 0.5000 -0.219428 2016 0.061530 0.109532 -0.116220 0.296168 0.2500 0.561755 2017 0.025427 0.132253 -0.174656 0.273113 0.4167 0.192261 2018 0.018354 0.129832 -0.198739 0.175450 0.4167 0.141368 2019 -0.022994 0.096336 -0.169612 0.074829 0.5000 -0.238680 所有年份 0.024602 0.129089 -0.290880 0.296168 0.4000 0.190580
========================因子：factor_c IC统计信息如下====================== IC均值 IC标准差 IC最小值 IC最大值 负IC占比 IC_IR 2014 0.133941 0.237370 -0.071692 0.497230 0.5000 0.564270 2015 -0.042432 0.165020 -0.433392 0.206798 0.5000 -0.257134 2016 0.072190 0.110240 -0.075665 0.225292 0.3333 0.654838 2017 0.072251 0.124198 -0.096468 0.269312 0.3333 0.581744 2018 -0.012845 0.165180 -0.321072 0.240996 0.5833 -0.077767 2019 -0.021236 0.229861 -0.373027 0.199288 0.3333 -0.092386 所有年份 0.029103 0.167597 -0.433392 0.497230 0.4333 0.173650
========================因子：factor_d IC统计信息如下====================== IC均值 IC标准差 IC最小值 IC最大值 负IC占比 IC_IR 2014 0.146349 0.214446 -0.055401 0.477480 0.5000 0.682451 2015 -0.036516 0.158761 -0.416434 0.210858 0.4167 -0.230003 2016 0.070505 0.110067 -0.092411 0.234537 0.3333 0.640558 2017 0.075719 0.123733 -0.101036 0.247039 0.4167 0.611954 2018 -0.013557 0.161304 -0.315654 0.243071 0.5833 -0.084044 2019 -0.021096 0.241235 -0.384796 0.192966 0.3333 -0.087448 所有年份 0.031756 0.164851 -0.416434 0.477480 0.4333 0.192632
以上是针对八个风格因子进行因子正交的结果统计，通过因子IC计算，获得如下信息：
最大化收益预期模型下，且进行因子正交的表现最好，五年IC均值为0.0318，也就是factor_d分组
和三因子的测试效果一样，两种因子模型中，正交因子IC值均大于原始因子IC值
在八个风格因子的测试中，最大化收益预期模型要优于等权多因子模型
多头收益
分组收益
接下来，我们将对所有因子值进行分组收益统计，并记录各分组总收益、年化收益、夏普率、最大回撤、每日收益情况
并将分组年化收益进行统计展示
factor_alg = ['factor_a','factor_b','factor_c','factor_d']factor_3_alg_dict = {}def get_risk_index(se): #输入每日收益变化，从零算起return_se = se.cumprod()-1total_returns = return_se[-1]total_an_returns = ((1+total_returns)**(250/len(return_se))-1)sharpe = (total_an_returns-0.025)/(np.std(se)*np.sqrt(250))returns_mean = round(se.mean()-1,6)*100ret = return_se.dropna()ret = ret+1maxdown_list = []for i in range(1,len(ret)):low = min(ret[i:])high = max(ret[0:i]) if high>low:#print(high,low)maxdown_list.append((high-low)/high)#print((high-low)/high)else:maxdown_list.append(0)max_drawdown = max(maxdown_list)#print('策略运行时间：{} 至 {}'.format(str(return_se.index[0])[:10],str(return_se.index[-1])[:10]))total_returns = str(round(total_returns*100,2))+'%'total_an_returns = str(round(total_an_returns*100,2))+'%'sharpe = str(round(sharpe,2))max_drawdown = str(round(max_drawdown*100,2))+'%'return total_returns,total_an_returns,sharpe,max_drawdown,returns_meanfor factor in factor_alg:#获取因子值组成dffactor_df = pd.DataFrame()for d in date_list[2:-1]:d = str(d)[:10]factor_df[d] = factor_3_y_dict[d].loc[:,factor]factor_df =factor_df.Trev = 1fe= 0.00#开始hold_num = 50pct_adj = 1backtest_list = get_tradeday_list(start=factor_df.index[0],end=factor_df.index[-1],count=None)return_alpha_df = pd.DataFrame()return_index_df = pd.DataFrame()return_df = pd.DataFrame()trade_record_df = pd.DataFrame()#中间变量pool_temp_bf = []tur = 0tur_list = []trade = 0mark = 0year = str(backtest_list[0])[:4]for d1,d2 in zip(backtest_list[:-1],backtest_list[1:]):d1_ = ShiftTradingDay(d1,1) #往后推一天d2_ = ShiftTradingDay(d2,1)d1 = str(d1)[:10]d2 = str(d2)[:10]#调仓日获取最新股票列表if d1 in factor_df.index:#print('===触发调仓===')trade = 1#获取头部股票#print('{}进行调仓操作'.format(str(d1_)[:10]))df_temp = factor_df.loc[d1,:].sort_values(ascending=True) #mo默认从小到大排序df_temp = df_temp.dropna()if rev == 0:pool_temp = df_temp.index[:hold_num]else:pool_temp = df_temp.index[-hold_num:]#trade_record_df[str(d1_)[:10]] = pool_temptur_temp = len([stock for stock in pool_temp if stock not in pool_temp_bf])/len(pool_temp) #换手率tur_list.append(tur_temp)#print换手率bif str(d1)[:4] == year:tur += tur_tempelse:#print('{} 年持仓交易换手率为： {}'.format(year,round(tur,2)))tur = 0year = str(d1)[:4]pool_temp_bf = pool_tempif pct_adj == 1: #常规的方法#计算组合收益df1 = get_price(list(pool_temp),end_date=d1_,count=1,fields=['open'])['open'] #index为日期，columns为股票名称df1 = df1.dropna(axis=1) #去掉NAN值，删除列df2 = get_price(list(df1.columns),end_date=d2_,count=1,fields=['open'])['open']ret = (df2.values/df1.values).mean() #计算组合收益均值#调仓是减去手续费if trade == 1:ret = ret*(1-tur_temp*fe)trade = 0#计算同期指数收益率df_index1 = get_price('000905.XSHG',end_date=d1_,count=1,fields=['open'])['open']df_index2 = get_price('000905.XSHG',end_date=d2_,count=1,fields=['open'])['open']index_ret = df_index2.values[-1]/df_index1.values[-1]if pct_adj == 2: #常规的方法#计算组合收益df1 = get_price(list(pool_temp),end_date=d1,count=1,fields=['close'])['close'] #index为日期，columns为股票名称df1 = df1.dropna(axis=1) #去掉NAN值，删除列df2 = get_price(list(df1.columns),end_date=d2,count=1,fields=['close'])['close']ret = (df2.values/df1.values).mean() #计算组合收益均值#调仓是减去手续费if trade == 1:ret = ret*(1-tur_temp*fe)trade = 0#计算同期指数收益率df_index1 = get_price('000905.XSHG',end_date=d1,count=1,fields=['close'])['close']df_index2 = get_price('000905.XSHG',end_date=d2,count=1,fields=['close'])['close']index_ret = df_index2.values[-1]/df_index1.values[-1]if pct_adj == 3: #设置指定时间点#计算组合收益df1 = get_price(list(pool_temp),end_date=str(d1_)[:10]+' 14:56:00',frequency='1m',count=1,fields=['close'])['close'] #index为日期，columns为股票名称df1 = df1.dropna(axis=1) #去掉NAN值，删除列df2 = get_price(list(df1.columns),end_date=str(d2_)[:10]+' 14:50:00',frequency='1m',count=1,fields=['close'])['close']ret = (df2.values/df1.values).mean() #计算组合收益均值#调仓是减去手续费if trade == 1:ret = ret*(1-tur_temp*fe)trade = 0#计算同期指数收益率df_index1 = get_price('000905.XSHG',end_date=str(d1_)[:10]+' 14:56:00',count=1,frequency='1m',fields=['close'])['close']df_index2 = get_price('000905.XSHG',end_date=str(d2_)[:10]+' 14:50:00',count=1,frequency='1m',fields=['close'])['close']index_ret = df_index2.values[-1]/df_index1.values[-1]if pct_adj == 4: #有重叠模型if mark ==0:#首次pool_old = []pool_new = pool_temp#计算组合日内收益df1 = get_price(list(pool_new),end_date=str(d1_)[:10],count=1,fields=['open'])['open'] #index为日期，columns为股票名称df1 = df1.dropna(axis=1) #去掉NAN值，删除列df2 = get_price(list(df1.columns),end_date=str(d1_)[:10],count=1,fields=['close'])['close']ret1 = (df2.values/df1.values).mean() #计算组合收益均值#整体收益ret = (0.5+ret1/2)#调仓是减去手续费if trade == 1:ret = ret*(1-0.5*tur_temp*fe)trade = 0#计算同期指数收益率df_index1 = get_price('000905.XSHG',end_date=str(d1)[:10],count=1,fields=['close'])['close']df_index2 = get_price('000905.XSHG',end_date=str(d2)[:10],count=1,fields=['close'])['close']index_ret = df_index2.values[-1]/df_index1.values[-1]mark = 1else:#多次pool_old = pool_newpool_new = pool_temp#计算组合日内收益df1 = get_price(list(pool_new)+list(pool_old),end_date=str(d1_)[:10],count=1,fields=['open'])['open'] #index为日期，columns为股票名称df1 = df1.dropna(axis=1) #去掉NAN值，删除列df2 = get_price(list(df1.columns),end_date=str(d1_)[:10],count=1,fields=['close'])['close']ret1 = (df2.values/df1.values).mean() #计算组合收益均值#计算组合日间收益df1 = get_price(list(pool_old),end_date=str(d1)[:10],count=1,fields=['close'])['close'] #index为日期，columns为股票名称df1 = df1.dropna(axis=1) #去掉NAN值，删除列df2 = get_price(list(df1.columns),end_date=str(d2)[:10],count=1,fields=['open'])['open']ret2 = (df2.values/df1.values).mean() #计算组合收益均值#整体收益ret = ret1*(0.5+ret2/2)#调仓是减去手续费if trade == 1:ret = ret*(1-0.5*tur_temp*fe)trade = 0#计算同期指数收益率df_index1 = get_price('000905.XSHG',end_date=str(d1)[:10],count=1,fields=['close'])['close']df_index2 = get_price('000905.XSHG',end_date=str(d2)[:10],count=1,fields=['close'])['close']index_ret = df_index2.values[-1]/df_index1.values[-1]return_alpha_df[d1] = [ret-index_ret] #记录超额收益return_df[d1] = [ret] #记录组合收益return_index_df[d1] = [index_ret] #记录基准收益return_df = return_df.Treturn_alpha_df = return_alpha_df.Treturn_index_df = return_index_df.Treturn_all_df = pd.concat([return_df,return_alpha_df+1,return_index_df],axis=1)return_all_df.columns = ['ret','alpha','index']#进行调仓股票记录trade_record_df.to_csv('trade_record.csv')summary = pd.DataFrame(index=['总收益','年化收益','夏普率','最大回撤','每日收益%'])summary['ret'] = get_risk_index(return_all_df['ret'])summary['alpha']=get_risk_index(return_all_df['alpha'])summary['index']=get_risk_index(return_all_df['index'])summary = summary.Tyear_list = list(set([int(i[:4]) for i in return_all_df.index]))for year in year_list:return_year_df = return_all_df[(return_all_df.index<str(year)+'-12-31') & (return_all_df.index>str(year)+'-01-01')]summary[year] = round(return_year_df.cumprod().iloc[-1,:]*100-100,2).valuesprint('=====策略运行时间：{} 至 {}====='.format(str(return_all_df.index[0])[:10],str(return_all_df.index[-1])[:10]))print('测试因子为{} 调仓均换手率为：{}'.format(factor,round(np.mean(tur_list),3)))factor_3_alg_dict[factor] = summaryprint(summary)=====策略运行时间：2014-07-01 至 2019-05-31===== 测试因子为factor_a 调仓均换手率为：0.644 总收益 年化收益 夏普率 最大回撤 ... 2018 2019 2014 2015 ret 121.37% 18.01% 0.44 46.08% ... -26.35 23.19 34.41 84.41 alpha 88.32% 14.1% 1.31 12.1% ... 12.24 4.74 -0.64 36.56 index 22.71% 4.36% 0.06 65.85% ... -34.75 17.33 35.14 41.29 [3 rows x 11 columns] =====策略运行时间：2014-07-01 至 2019-05-31===== 测试因子为factor_b 调仓均换手率为：0.654 总收益 年化收益 夏普率 最大回撤 ... 2018 2019 2014 2015 ret 115.45% 17.34% 0.42 46.09% ... -26.86 19.14 36.21 92.93 alpha 83.11% 13.43% 1.27 9.37% ... 11.51 1.23 0.79 42.68 index 22.71% 4.36% 0.06 65.85% ... -34.75 17.33 35.14 41.29 [3 rows x 11 columns] =====策略运行时间：2014-07-01 至 2019-05-31===== 测试因子为factor_c 调仓均换手率为：0.781 总收益 年化收益 夏普率 最大回撤 ... 2018 2019 2014 2015 ret 69.69% 11.65% 0.25 53.45% ... -36.33 13.69 36.22 80.42 alpha 45.45% 8.12% 0.58 12.5% ... -2.75 -3.09 0.87 34.38 index 22.71% 4.36% 0.06 65.85% ... -34.75 17.33 35.14 41.29 [3 rows x 11 columns] =====策略运行时间：2014-07-01 至 2019-05-31===== 测试因子为factor_d 调仓均换手率为：0.776 总收益 年化收益 夏普率 最大回撤 ... 2018 2019 2014 2015 ret 60.55% 10.37% 0.22 57.05% ... -35.56 12.35 40.87 79.55 alpha 36.97% 6.77% 0.46 12.61% ... -1.68 -4.26 4.34 33.29 index 22.71% 4.36% 0.06 65.85% ... -34.75 17.33 35.14 41.29 [3 rows x 11 columns]
factor_alg = ['factor_a','factor_b','factor_c','factor_d']factor_8_alg_dict = {}for factor in factor_alg:#获取因子值组成dffactor_df = pd.DataFrame()for d in date_list[2:-1]:d = str(d)[:10]factor_df[d] = factor_8_y_dict[d].loc[:,factor]factor_df =factor_df.Trev = 1fe= 0.00#开始hold_num = 50pct_adj = 1backtest_list = get_tradeday_list(start=factor_df.index[0],end=factor_df.index[-1],count=None)return_alpha_df = pd.DataFrame()return_index_df = pd.DataFrame()return_df = pd.DataFrame()trade_record_df = pd.DataFrame()#中间变量pool_temp_bf = []tur = 0tur_list = []trade = 0mark = 0year = str(backtest_list[0])[:4]for d1,d2 in zip(backtest_list[:-1],backtest_list[1:]):d1_ = ShiftTradingDay(d1,1) #往后推一天d2_ = ShiftTradingDay(d2,1)d1 = str(d1)[:10]d2 = str(d2)[:10]#调仓日获取最新股票列表if d1 in factor_df.index:#print('===触发调仓===')trade = 1#获取头部股票#print('{}进行调仓操作'.format(str(d1_)[:10]))df_temp = factor_df.loc[d1,:].sort_values(ascending=True) #mo默认从小到大排序df_temp = df_temp.dropna()if rev == 0:pool_temp = df_temp.index[:hold_num]else:pool_temp = df_temp.index[-hold_num:]#trade_record_df[str(d1_)[:10]] = pool_temptur_temp = len([stock for stock in pool_temp if stock not in pool_temp_bf])/len(pool_temp) #换手率tur_list.append(tur_temp)#print换手率bif str(d1)[:4] == year:tur += tur_tempelse:#print('{} 年持仓交易换手率为： {}'.format(year,round(tur,2)))tur = 0year = str(d1)[:4]pool_temp_bf = pool_tempif pct_adj == 1: #常规的方法#计算组合收益df1 = get_price(list(pool_temp),end_date=d1_,count=1,fields=['open'])['open'] #index为日期，columns为股票名称df1 = df1.dropna(axis=1) #去掉NAN值，删除列df2 = get_price(list(df1.columns),end_date=d2_,count=1,fields=['open'])['open']ret = (df2.values/df1.values).mean() #计算组合收益均值#调仓是减去手续费if trade == 1:ret = ret*(1-tur_temp*fe)trade = 0#计算同期指数收益率df_index1 = get_price('000905.XSHG',end_date=d1_,count=1,fields=['open'])['open']df_index2 = get_price('000905.XSHG',end_date=d2_,count=1,fields=['open'])['open']index_ret = df_index2.values[-1]/df_index1.values[-1]if pct_adj == 2: #常规的方法#计算组合收益df1 = get_price(list(pool_temp),end_date=d1,count=1,fields=['close'])['close'] #index为日期，columns为股票名称df1 = df1.dropna(axis=1) #去掉NAN值，删除列df2 = get_price(list(df1.columns),end_date=d2,count=1,fields=['close'])['close']ret = (df2.values/df1.values).mean() #计算组合收益均值#调仓是减去手续费if trade == 1:ret = ret*(1-tur_temp*fe)trade = 0#计算同期指数收益率df_index1 = get_price('000905.XSHG',end_date=d1,count=1,fields=['close'])['close']df_index2 = get_price('000905.XSHG',end_date=d2,count=1,fields=['close'])['close']index_ret = df_index2.values[-1]/df_index1.values[-1]if pct_adj == 3: #设置指定时间点#计算组合收益df1 = get_price(list(pool_temp),end_date=str(d1_)[:10]+' 14:56:00',frequency='1m',count=1,fields=['close'])['close'] #index为日期，columns为股票名称df1 = df1.dropna(axis=1) #去掉NAN值，删除列df2 = get_price(list(df1.columns),end_date=str(d2_)[:10]+' 14:50:00',frequency='1m',count=1,fields=['close'])['close']ret = (df2.values/df1.values).mean() #计算组合收益均值#调仓是减去手续费if trade == 1:ret = ret*(1-tur_temp*fe)trade = 0#计算同期指数收益率df_index1 = get_price('000905.XSHG',end_date=str(d1_)[:10]+' 14:56:00',count=1,frequency='1m',fields=['close'])['close']df_index2 = get_price('000905.XSHG',end_date=str(d2_)[:10]+' 14:50:00',count=1,frequency='1m',fields=['close'])['close']index_ret = df_index2.values[-1]/df_index1.values[-1]if pct_adj == 4: #有重叠模型if mark ==0:#首次pool_old = []pool_new = pool_temp#计算组合日内收益df1 = get_price(list(pool_new),end_date=str(d1_)[:10],count=1,fields=['open'])['open'] #index为日期，columns为股票名称df1 = df1.dropna(axis=1) #去掉NAN值，删除列df2 = get_price(list(df1.columns),end_date=str(d1_)[:10],count=1,fields=['close'])['close']ret1 = (df2.values/df1.values).mean() #计算组合收益均值#整体收益ret = (0.5+ret1/2)#调仓是减去手续费if trade == 1:ret = ret*(1-0.5*tur_temp*fe)trade = 0#计算同期指数收益率df_index1 = get_price('000905.XSHG',end_date=str(d1)[:10],count=1,fields=['close'])['close']df_index2 = get_price('000905.XSHG',end_date=str(d2)[:10],count=1,fields=['close'])['close']index_ret = df_index2.values[-1]/df_index1.values[-1]mark = 1else:#多次pool_old = pool_newpool_new = pool_temp#计算组合日内收益df1 = get_price(list(pool_new)+list(pool_old),end_date=str(d1_)[:10],count=1,fields=['open'])['open'] #index为日期，columns为股票名称df1 = df1.dropna(axis=1) #去掉NAN值，删除列df2 = get_price(list(df1.columns),end_date=str(d1_)[:10],count=1,fields=['close'])['close']ret1 = (df2.values/df1.values).mean() #计算组合收益均值#计算组合日间收益df1 = get_price(list(pool_old),end_date=str(d1)[:10],count=1,fields=['close'])['close'] #index为日期，columns为股票名称df1 = df1.dropna(axis=1) #去掉NAN值，删除列df2 = get_price(list(df1.columns),end_date=str(d2)[:10],count=1,fields=['open'])['open']ret2 = (df2.values/df1.values).mean() #计算组合收益均值#整体收益ret = ret1*(0.5+ret2/2)#调仓是减去手续费if trade == 1:ret = ret*(1-0.5*tur_temp*fe)trade = 0#计算同期指数收益率df_index1 = get_price('000905.XSHG',end_date=str(d1)[:10],count=1,fields=['close'])['close']df_index2 = get_price('000905.XSHG',end_date=str(d2)[:10],count=1,fields=['close'])['close']index_ret = df_index2.values[-1]/df_index1.values[-1]return_alpha_df[d1] = [ret-index_ret] #记录超额收益return_df[d1] = [ret] #记录组合收益return_index_df[d1] = [index_ret] #记录基准收益return_df = return_df.Treturn_alpha_df = return_alpha_df.Treturn_index_df = return_index_df.Treturn_all_df = pd.concat([return_df,return_alpha_df+1,return_index_df],axis=1)return_all_df.columns = ['ret','alpha','index']#进行调仓股票记录trade_record_df.to_csv('trade_record.csv')summary = pd.DataFrame(index=['总收益','年化收益','夏普率','最大回撤','每日收益%'])summary['ret'] = get_risk_index(return_all_df['ret'])summary['alpha']=get_risk_index(return_all_df['alpha'])summary['index']=get_risk_index(return_all_df['index'])summary = summary.Tyear_list = list(set([int(i[:4]) for i in return_all_df.index]))for year in year_list:return_year_df = return_all_df[(return_all_df.index<str(year)+'-12-31') & (return_all_df.index>str(year)+'-01-01')]summary[year] = round(return_year_df.cumprod().iloc[-1,:]*100-100,2).valuesprint('=====策略运行时间：{} 至 {}====='.format(str(return_all_df.index[0])[:10],str(return_all_df.index[-1])[:10]))print('测试因子为{} 调仓均换手率为：{}'.format(factor,round(np.mean(tur_list),3)))factor_8_alg_dict[factor] = summaryprint(summary)=====策略运行时间：2014-07-01 至 2019-05-31===== 测试因子为factor_a 调仓均换手率为：0.473 总收益 年化收益 夏普率 最大回撤 ... 2018 2019 2014 2015 ret 85.61% 13.75% 0.32 51.12% ... -27.04 16.53 42.42 49.23 alpha 57.48% 9.92% 0.78 15.0% ... 11.21 -0.69 5.44 9.55 index 22.71% 4.36% 0.06 65.85% ... -34.75 17.33 35.14 41.29 [3 rows x 11 columns] =====策略运行时间：2014-07-01 至 2019-05-31===== 测试因子为factor_b 调仓均换手率为：0.517 总收益 年化收益 夏普率 最大回撤 ... 2018 2019 2014 2015 ret 96.73% 15.14% 0.35 49.37% ... -27.21 18.30 51.54 57.48 alpha 68.45% 11.48% 1.01 12.27% ... 11.15 0.83 12.21 16.30 index 22.71% 4.36% 0.06 65.85% ... -34.75 17.33 35.14 41.29 [3 rows x 11 columns] =====策略运行时间：2014-07-01 至 2019-05-31===== 测试因子为factor_c 调仓均换手率为：0.767 总收益 年化收益 夏普率 最大回撤 ... 2018 2019 2014 2015 ret 102.76% 15.87% 0.37 52.72% ... -29.91 13.02 64.64 38.90 alpha 74.17% 12.25% 0.95 20.67% ... 7.32 -3.65 22.00 3.21 index 22.71% 4.36% 0.06 65.85% ... -34.75 17.33 35.14 41.29 [3 rows x 11 columns] =====策略运行时间：2014-07-01 至 2019-05-31===== 测试因子为factor_d 调仓均换手率为：0.768 总收益 年化收益 夏普率 最大回撤 ... 2018 2019 2014 2015 ret 108.42% 16.53% 0.39 50.17% ... -29.99 12.34 60.68 44.77 alpha 77.49% 12.7% 1.04 18.08% ... 7.20 -4.14 18.99 6.70 index 22.71% 4.36% 0.06 65.85% ... -34.75 17.33 35.14 41.29 [3 rows x 11 columns]
f_list = ['factor_a','factor_b','factor_c','factor_d']mark = 1for f in f_list:if mark == 1:result = factor_8_alg_dict[f].loc['alpha',:]mark = 0else:result_temp = factor_8_alg_dict[f].loc['alpha',:]result = pd.concat([result,result_temp],axis=1)result.columns = ['等权模型-原始因子','等权模型-正交因子','回归模型-原始因子','回归模型-正交因子']result.T
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| 总收益 | 年化收益 | 夏普率 | 最大回撤 | 每日收益% | 2016 | 2017 | 2018 | 2019 | 2014 | 2015 | |
|---|---|---|---|---|---|---|---|---|---|---|---|
| 等权模型-原始因子 | 57.48% | 9.92% | 0.78 | 15.0% | 0.0397 | 12.18 | 10.63 | 11.21 | -0.69 | 5.44 | 9.55 |
| 等权模型-正交因子 | 68.45% | 11.48% | 1.01 | 12.27% | 0.0451 | 13.46 | 2.19 | 11.15 | 0.83 | 12.21 | 16.3 |
| 回归模型-原始因子 | 74.17% | 12.25% | 0.95 | 20.67% | 0.0484 | 19.45 | 11.41 | 7.32 | -3.65 | 22 | 3.21 |
| 回归模型-正交因子 | 77.49% | 12.7% | 1.04 | 18.08% | 0.0497 | 18.36 | 14.11 | 7.2 | -4.14 | 18.99 | 6.7 |
我们选取某一期因子数据进行相关性检查，八个风格因子在处理前后的秩相关系数矩阵如下表所示
#这里对八个风格因子相关性进行统计展示factors = ['size','momentum','liquidity','residual_volatility','book_to_price_ratio','beta','earnings_yield','leverage']factors_ = [f+'_' for f in factors]import seaborn as snsdf = factor_8_y_dict[list(factor_8_y_dict.keys())[-1]][factors].corr(method='spearman')fig = plt.figure(figsize= (12,8))ax = fig.add_subplot(111)ax = sns.heatmap(df,annot=True,annot_kws={'size':9,'weight':'bold'})df = factor_8_y_dict[list(factor_8_y_dict.keys())[-1]][factors_].corr(method='spearman')fig = plt.figure(figsize= (12,8))ax = fig.add_subplot(111)ax = sns.heatmap(df,annot=True,annot_kws={'size':9,'weight':'bold'})正交处理后，因子之间的相关性基本上达到了零
本文参考研报中关于选股因子正交的讨论，通过使用正交选股因子来得到更加可控的因子暴露，我们采取研报中给出的参考顺序进行了正交化处理，通过实际组合的构建以及初步回测， 相比于原始因子收益及夏普都有所提升。 在三因子与八因子两种模型中，对因子IC均有提升，在多头组合中也得到了了印证。
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