投資組合的收益率與風險

1 不同相關系數下投資組合標準差隨投資比例變動的情況
- 1.1 設定calc_mean函式為采用的投資組合方式
- 1.2 以x/50為權重（其中x屬于0到50）進行投資組合（其實就是0到1中間等距抽權重）
- 1.3 計算不同相關系數的股票組合對應收益值
- 1.4 不同相關系數均值和標準差關系圖
2 Markowitz模型實作
- 2.1 獲取各只股票日線行情資料
- 2.2 計算每只股票的日收益率（個股回報率）并將其合并
- 2.3 了解各股票的日收益率及累計收益率時序圖
- 2.4 了解各股票之間的相關性
- 2.5 定義MeanVariance類，通過輸入收益率序列計算最優資產比例，繪制最小方差前緣曲線
  - 2.5.1 定義MeanVariance類及類內函式
  - 2.5.2 呼叫minvar函式計算最小方差
  - 2.5.3 呼叫frontierCurve繪制效率前沿曲線
  - 2.5.4 將資料拆分為訓練和測驗資料，輸出根據訓練資料計算的效率前沿曲線
  - 2.5.5 給定收益率下，計算方差最小時對應的五種股票的比例權重
  - 2.5.6 繪制收益率曲線
  - 2.5.7 與隨機生成的組合進行比較
3 Black-Litterman模型
- 3.1 創建blacklitterman函式，計算后驗收益期望及協方差
- 3.2 創建blminVar函式，輸出最優資產配比
  - 3.2.1 看不懂就拆開看的：
  - 3.2.2 帶例子計算結果去啦！

不同相關系數下投資組合標準差隨投資比例變動的情況

import  numpy  as np
import pandas as pd
import matplotlib.pyplot as plt
import matplotlib
%matplotlib inline

設定calc_mean函式為采用的投資組合方式

def calc_mean(frac):
    return (0.08* frac+0.15*(1-frac))

0.08* (1/50)+0.15*(1-(1/50))

0.14859999999999998

以x/50為權重（其中x屬于0到50）進行投資組合（其實就是0到1中間等距抽權重）

mean=list(map(calc_mean,[x/50 for x in range(51)]))
mean

[0.15,
 0.14859999999999998,
 0.1472,
 0.14579999999999999,
 0.1444,
 0.14300000000000002,
 0.1416,
 0.1402,
 0.1388,
 0.1374,
 0.136,
 0.1346,
 0.13319999999999999,
 0.1318,
 0.13040000000000002,
 0.129,
 0.1276,
 0.12619999999999998,
 0.1248,
 0.1234,
 0.122,
 0.12060000000000001,
 0.1192,
 0.1178,
 0.1164,
 0.11499999999999999,
 0.1136,
 0.1122,
 0.1108,
 0.1094,
 0.108,
 0.1066,
 0.1052,
 0.1038,
 0.10239999999999999,
 0.101,
 0.0996,
 0.09820000000000001,
 0.0968,
 0.0954,
 0.094,
 0.0926,
 0.0912,
 0.0898,
 0.0884,
 0.08700000000000001,
 0.0856,
 0.08420000000000001,
 0.0828,
 0.0814,
 0.08]

[x/50 for x in range(51)] #0-1之間組合資料

[0.0,
 0.02,
 0.04,
 0.06,
 0.08,
 0.1,
 0.12,
 0.14,
 0.16,
 0.18,
 0.2,
 0.22,
 0.24,
 0.26,
 0.28,
 0.3,
 0.32,
 0.34,
 0.36,
 0.38,
 0.4,
 0.42,
 0.44,
 0.46,
 0.48,
 0.5,
 0.52,
 0.54,
 0.56,
 0.58,
 0.6,
 0.62,
 0.64,
 0.66,
 0.68,
 0.7,
 0.72,
 0.74,
 0.76,
 0.78,
 0.8,
 0.82,
 0.84,
 0.86,
 0.88,
 0.9,
 0.92,
 0.94,
 0.96,
 0.98,
 1.0]

計算不同相關系數的股票組合對應收益值

公式為（0.12x+0.25（1-x））的完全平方展開式，其中交叉項還乘以了相關系數，0.12和0.25分別為兩種股票的收益率，x和（1-x）為標準差（或者權重，這里還沒弄懂），最終得值為均值，

import math
sd_mat=np.array([list(map(lambda x :math.sqrt( (x**2)*0.12**2 \
                                              + ((1-x)**2)*0.25**2\
                                              +   2*x*(1-x)*(-1.5+i*0.5)*0.12*0.25)
                          ,[x/50 for x in range(51)])) for  i  in range(1,6)])   #range表示左閉右開區間
sd_mat

array([[0.25      , 0.2426    , 0.2352    , 0.2278    , 0.2204    ,
        0.213     , 0.2056    , 0.1982    , 0.1908    , 0.1834    ,
        0.176     , 0.1686    , 0.1612    , 0.1538    , 0.1464    ,
        0.139     , 0.1316    , 0.1242    , 0.1168    , 0.1094    ,
        0.102     , 0.0946    , 0.0872    , 0.0798    , 0.0724    ,
        0.065     , 0.0576    , 0.0502    , 0.0428    , 0.0354    ,
        0.028     , 0.0206    , 0.0132    , 0.0058    , 0.0016    ,
        0.009     , 0.0164    , 0.0238    , 0.0312    , 0.0386    ,
        0.046     , 0.0534    , 0.0608    , 0.0682    , 0.0756    ,
        0.083     , 0.0904    , 0.0978    , 0.1052    , 0.1126    ,
        0.12      ],
       [0.25      , 0.24380886, 0.23763636, 0.231484  , 0.22535341,
        0.21924644, 0.2131651 , 0.20711166, 0.20108864, 0.19509885,
        0.18914545, 0.18323198, 0.17736245, 0.17154137, 0.16577382,
        0.16006561, 0.15442331, 0.14885443, 0.1433675 , 0.13797232,
        0.13268007, 0.12750357, 0.1224575 , 0.11755867, 0.11282624,
        0.10828204, 0.10395076, 0.0998601 , 0.09604082, 0.09252654,
        0.08935323, 0.08655842, 0.08417981, 0.08225351, 0.08081188,
        0.07988116, 0.07947931, 0.07961432, 0.0802835 , 0.08147368,
        0.08316249, 0.08532034, 0.08791268, 0.09090237, 0.09425158,
        0.09792344, 0.10188307, 0.10609826, 0.11053977, 0.11518142,
        0.12      ],
       [0.25      , 0.24501175, 0.240048  , 0.23511027, 0.23020026,
        0.22531977, 0.22047077, 0.21565537, 0.21087589, 0.20613481,
        0.20143485, 0.19677896, 0.19217034, 0.18761247, 0.18310915,
        0.17866449, 0.17428299, 0.16996953, 0.16572942, 0.16156844,
        0.15749286, 0.15350948, 0.14962567, 0.14584937, 0.14218917,
        0.13865425, 0.13525443, 0.13200015, 0.12890244, 0.12597285,
        0.12322337, 0.12066632, 0.11831416, 0.11617934, 0.11427406,
        0.11260995, 0.11119784, 0.11004744, 0.10916703, 0.10856316,
        0.10824047, 0.10820148, 0.10844648, 0.10897357, 0.10977869,
        0.11085576, 0.11219697, 0.11379297, 0.11563321, 0.11770624,
        0.12      ],
       [0.25      , 0.24620877, 0.24243564, 0.23868146, 0.23494714,
        0.23123365, 0.227542  , 0.22387327, 0.22022861, 0.21660923,
        0.21301643, 0.20945157, 0.2059161 , 0.20241156, 0.19893959,
        0.19550192, 0.19210039, 0.18873696, 0.1854137 , 0.18213281,
        0.17889662, 0.1757076 , 0.17256836, 0.16948168, 0.16645047,
        0.16347783, 0.160567  , 0.1577214 , 0.15494464, 0.15224047,
        0.14961283, 0.14706584, 0.14460373, 0.14223094, 0.13995199,
        0.13777155, 0.13569436, 0.13372524, 0.13186903, 0.13013055,
        0.12851459, 0.12702582, 0.12566877, 0.12444774, 0.12336677,
        0.12242957, 0.12163947, 0.12099934, 0.12051158, 0.12017803,
        0.12      ],
       [0.25      , 0.2474    , 0.2448    , 0.2422    , 0.2396    ,
        0.237     , 0.2344    , 0.2318    , 0.2292    , 0.2266    ,
        0.224     , 0.2214    , 0.2188    , 0.2162    , 0.2136    ,
        0.211     , 0.2084    , 0.2058    , 0.2032    , 0.2006    ,
        0.198     , 0.1954    , 0.1928    , 0.1902    , 0.1876    ,
        0.185     , 0.1824    , 0.1798    , 0.1772    , 0.1746    ,
        0.172     , 0.1694    , 0.1668    , 0.1642    , 0.1616    ,
        0.159     , 0.1564    , 0.1538    , 0.1512    , 0.1486    ,
        0.146     , 0.1434    , 0.1408    , 0.1382    , 0.1356    ,
        0.133     , 0.1304    , 0.1278    , 0.1252    , 0.1226    ,
        0.12      ]])

sd_mat.shape

(5, 51)

不同相關系數均值和標準差關系圖

label為相關系數，橫軸為標準差，縱軸為均值，

plt.plot(sd_mat[0,:],mean,label="-1")
plt.plot(sd_mat[1,:],mean,label="-0.5")
plt.plot(sd_mat[2,:],mean,label="0")
plt.plot(sd_mat[3,:],mean,label="0.5")
plt.plot(sd_mat[4,:],mean,label="1")
plt.legend(loc="upper left")

<matplotlib.legend.Legend at 0x18896d0b7c0>

在這里插入圖片描述

Markowitz模型實作

先匯入股票，本次實作使用股票為600004、600015、600023、600033、600183，分別對應白云機場、華夏銀行、浙能電力、福建高速和生益科技股票，

目前我國000或002開頭的就是深證的，600開頭的是上證的，300開頭的是創業板zhi 200開頭的是深圳B股,900開頭的是上海B股，

獲取各只股票日線行情資料

import tushare as ts
pro = ts.pro_api('4c1fa508ab60e554d221c55a47dfa557a6c7bfd0c239b45657c2262d')
df = pro.daily(ts_code='600004.SH', start_date='20200101', end_date='20201231')
df.head()

	ts_code	trade_date	open	high	low	close	pre_close	change	pct_chg	vol	amount
0	600004.SH	20201231	13.80	14.30	13.70	14.13	13.63	0.50	3.6684	186855.09	261417.827
1	600004.SH	20201230	13.36	13.72	13.25	13.63	13.37	0.26	1.9447	105098.32	142205.693
2	600004.SH	20201229	13.18	13.61	13.18	13.37	13.27	0.10	0.7536	97057.08	130418.052
3	600004.SH	20201228	13.43	13.45	13.17	13.27	13.48	-0.21	-1.5579	120737.86	160222.485
4	600004.SH	20201225	13.25	13.50	13.22	13.48	13.35	0.13	0.9738	57026.12	76510.480

byjc = df.set_index(["trade_date"])
byjc.index = pd.to_datetime(byjc.index)
byjc.head(10)

	ts_code	open	high	low	close	pre_close	change	pct_chg	vol	amount
trade_date
2020-12-31	600004.SH	13.80	14.30	13.70	14.13	13.63	0.50	3.6684	186855.09	261417.827
2020-12-30	600004.SH	13.36	13.72	13.25	13.63	13.37	0.26	1.9447	105098.32	142205.693
2020-12-29	600004.SH	13.18	13.61	13.18	13.37	13.27	0.10	0.7536	97057.08	130418.052
2020-12-28	600004.SH	13.43	13.45	13.17	13.27	13.48	-0.21	-1.5579	120737.86	160222.485
2020-12-25	600004.SH	13.25	13.50	13.22	13.48	13.35	0.13	0.9738	57026.12	76510.480
2020-12-24	600004.SH	13.35	13.41	13.18	13.35	13.35	0.00	0.0000	78080.01	104002.222
2020-12-23	600004.SH	13.39	13.46	13.25	13.35	13.35	0.00	0.0000	122316.53	163204.891
2020-12-22	600004.SH	13.96	13.96	13.31	13.35	14.12	-0.77	-5.4533	256419.53	348439.957
2020-12-21	600004.SH	14.05	14.15	13.63	14.12	14.21	-0.09	-0.6334	128751.81	179205.692
2020-12-18	600004.SH	14.43	14.43	14.15	14.21	14.43	-0.22	-1.5246	82641.45	117739.517

data = pro.daily(ts_code='600015.SH', start_date='20200101', end_date='20201231')
hxyh = data.set_index(["trade_date"])
hxyh.index=pd.to_datetime(hxyh.index) #時間型別
hxyh.head(10)

	ts_code	open	high	low	close	pre_close	change	pct_chg	vol	amount
trade_date
2020-12-31	600015.SH	6.17	6.28	6.17	6.25	6.19	0.06	0.9693	323628.00	202126.611
2020-12-30	600015.SH	6.14	6.19	6.12	6.19	6.15	0.04	0.6504	171216.96	105291.236
2020-12-29	600015.SH	6.14	6.17	6.13	6.15	6.14	0.01	0.1629	138161.26	84991.588
2020-12-28	600015.SH	6.16	6.18	6.12	6.14	6.17	-0.03	-0.4862	142068.40	87339.651
2020-12-25	600015.SH	6.15	6.21	6.15	6.17	6.17	0.00	0.0000	166727.73	102964.436
2020-12-24	600015.SH	6.18	6.22	6.14	6.17	6.18	-0.01	-0.1618	109642.01	67734.194
2020-12-23	600015.SH	6.18	6.19	6.13	6.18	6.18	0.00	0.0000	151969.90	93657.059
2020-12-22	600015.SH	6.23	6.24	6.16	6.18	6.24	-0.06	-0.9615	175320.62	108670.014
2020-12-21	600015.SH	6.23	6.26	6.20	6.24	6.23	0.01	0.1605	131370.60	81852.468
2020-12-18	600015.SH	6.23	6.27	6.21	6.23	6.24	-0.01	-0.1603	150797.28	94042.457

data = pro.daily(ts_code='600023.SH', start_date='20200101', end_date='20201231')
zndl = data.set_index(["trade_date"])
zndl.index=pd.to_datetime(zndl.index) #時間型別
zndl.head(10)

	ts_code	open	high	low	close	pre_close	change	pct_chg	vol	amount
trade_date
2020-12-31	600023.SH	3.64	3.66	3.62	3.63	3.64	-0.01	-0.2747	276557.88	100496.614
2020-12-30	600023.SH	3.63	3.69	3.62	3.64	3.64	0.00	0.0000	345081.00	126011.396
2020-12-29	600023.SH	3.76	3.77	3.63	3.64	3.75	-0.11	-2.9333	486175.37	179125.733
2020-12-28	600023.SH	3.65	3.81	3.64	3.75	3.63	0.12	3.3058	812157.21	304098.705
2020-12-25	600023.SH	3.60	3.77	3.60	3.63	3.60	0.03	0.8333	802186.21	294034.916
2020-12-24	600023.SH	3.66	3.66	3.59	3.60	3.66	-0.06	-1.6393	216392.19	78215.857
2020-12-23	600023.SH	3.63	3.67	3.62	3.66	3.63	0.03	0.8264	246516.04	89848.931
2020-12-22	600023.SH	3.70	3.71	3.62	3.63	3.71	-0.08	-2.1563	236203.13	86417.953
2020-12-21	600023.SH	3.72	3.73	3.68	3.71	3.74	-0.03	-0.8021	306758.67	113636.876
2020-12-18	600023.SH	3.70	3.78	3.69	3.74	3.68	0.06	1.6304	496335.82	185874.480

data = pro.daily(ts_code='600033.SH', start_date='20200101', end_date='20201231')
fjgs = data.set_index(["trade_date"])
fjgs.index=pd.to_datetime(fjgs.index) #時間型別
fjgs.head(10)

	ts_code	open	high	low	close	pre_close	change	pct_chg	vol	amount
trade_date
2020-12-31	600033.SH	2.63	2.64	2.61	2.63	2.64	-0.01	-0.3788	66428.48	17454.118
2020-12-30	600033.SH	2.62	2.65	2.61	2.64	2.62	0.02	0.7634	64786.08	17069.822
2020-12-29	600033.SH	2.61	2.64	2.60	2.62	2.61	0.01	0.3831	61694.88	16166.056
2020-12-28	600033.SH	2.62	2.63	2.60	2.61	2.63	-0.02	-0.7605	47187.00	12331.493
2020-12-25	600033.SH	2.59	2.63	2.59	2.63	2.60	0.03	1.1538	57316.73	14985.076
2020-12-24	600033.SH	2.62	2.62	2.59	2.60	2.61	-0.01	-0.3831	37202.50	9677.080
2020-12-23	600033.SH	2.62	2.63	2.60	2.61	2.61	0.00	0.0000	35652.00	9312.229
2020-12-22	600033.SH	2.65	2.65	2.61	2.61	2.66	-0.05	-1.8797	36789.00	9663.675
2020-12-21	600033.SH	2.64	2.66	2.63	2.66	2.65	0.01	0.3774	39729.19	10508.296
2020-12-18	600033.SH	2.64	2.66	2.63	2.65	2.64	0.01	0.3788	48981.25	12971.882

data = pro.daily(ts_code='600183.SH', start_date='20200101', end_date='20201231')
sykj = data.set_index(["trade_date"])
sykj.index=pd.to_datetime(sykj.index) #時間型別
sykj.head(10)

	ts_code	open	high	low	close	pre_close	change	pct_chg	vol	amount
trade_date
2020-12-31	600183.SH	28.20	28.48	27.70	28.16	28.09	0.07	0.2492	236546.60	666296.114
2020-12-30	600183.SH	27.60	28.44	27.52	28.09	27.72	0.37	1.3348	298485.52	837217.068
2020-12-29	600183.SH	28.05	28.11	27.38	27.72	28.16	-0.44	-1.5625	274469.65	762046.593
2020-12-28	600183.SH	27.30	28.66	27.26	28.16	27.50	0.66	2.4000	368864.23	1038064.670
2020-12-25	600183.SH	25.54	27.64	25.53	27.50	25.53	1.97	7.7164	405867.59	1091263.537
2020-12-24	600183.SH	25.53	26.28	25.48	25.53	25.48	0.05	0.1962	218026.21	562524.467
2020-12-23	600183.SH	26.35	26.38	25.00	25.48	26.03	-0.55	-2.1129	420599.35	1067254.221
2020-12-22	600183.SH	26.90	27.00	26.00	26.03	27.18	-1.15	-4.2311	237254.71	627783.299
2020-12-21	600183.SH	26.83	27.71	26.63	27.18	27.00	0.18	0.6667	276529.00	753021.804
2020-12-18	600183.SH	27.07	27.58	26.80	27.00	26.85	0.15	0.5587	220284.43	598219.499

計算每只股票的日收益率（個股回報率）并將其合并

import ffn
byjc_Dretwd=ffn.to_returns(byjc.close)
hxyh_Dretwd=ffn.to_returns(hxyh.close)
zndl_Dretwd=ffn.to_returns(zndl.close)
fjgs_Dretwd=ffn.to_returns(fjgs.close)
sykj_Dretwd=ffn.to_returns(sykj.close)

sh_return=pd.concat([fjgs_Dretwd,zndl_Dretwd,sykj_Dretwd,hxyh_Dretwd,byjc_Dretwd],axis=1) #重組為一個df
sh_return.columns = ['fjgs','zndl','sykj','hxyh','byjc'] #重命名列名
sh_return=sh_return.dropna()#dropna函式用來洗掉有缺失值的行
sh_return.head()

	fjgs	zndl	sykj	hxyh	byjc
trade_date
2020-12-30	0.003802	0.002755	-0.002486	-0.009600	-0.035386
2020-12-29	-0.007576	0.000000	-0.013172	-0.006462	-0.019076
2020-12-28	-0.003817	0.030220	0.015873	-0.001626	-0.007479
2020-12-25	0.007663	-0.032000	-0.023438	0.004886	0.015825
2020-12-24	-0.011407	-0.008264	-0.071636	0.000000	-0.009644

了解各股票的日收益率及累計收益率時序圖

sh_return.plot()
plt.title('Daily Return of 5 sStocks(2020)')
plt.legend(loc='lower center',bbox_to_anchor=(0.5,-0.3),
          ncol=5,fancybox=True,shadow=True)
plt.show()

<ipython-input-17-18e69f52f319>:5: UserWarning: Matplotlib is currently using agg, which is a non-GUI backend, so cannot show the figure.
  plt.show()

在這里插入圖片描述

cumreturn=(1+sh_return).cumprod()
cumreturn.plot()
plt.title('Cumulative Return of 5 Stocks(2020)')
plt.show()

<ipython-input-18-ccd1c3bea7db>:4: UserWarning: Matplotlib is currently using agg, which is a non-GUI backend, so cannot show the figure.
  plt.show()

在這里插入圖片描述

了解各股票之間的相關性

sh_return.corr()

	fjgs	zndl	sykj	hxyh	byjc
fjgs	1.000000	0.675856	0.363203	0.642483	0.450363
zndl	0.675856	1.000000	0.318658	0.608911	0.358668
sykj	0.363203	0.318658	1.000000	0.307890	0.295727
hxyh	0.642483	0.608911	0.307890	1.000000	0.424358
byjc	0.450363	0.358668	0.295727	0.424358	1.000000

若股票之間的相關性太高，投資組合降低風險的效果就比較有限，從香港系數矩陣可以看出，五只股票之間都是正相關，福建高速和浙能電力、華夏銀行相關性最高，

定義MeanVariance類，通過輸入收益率序列計算最優資產比例，繪制最小方差前緣曲線

定義MeanVariance類及類內函式

import ffn
from scipy import linalg
class MeanVariance:
    
    #定義構造器,傳入收益率資料(dataframe格式的每日收益率)
    def __init__(self,returns): #初始化資料集合，五種股票資料
        self.returns=returns
        
    #定義最小化方差的函式,即求解二次規劃
    def minVar(self,goalRet): #計算最小方差
        covs=np.array(self.returns.cov())
        means=np.array(self.returns.mean())
        L1=np.append(np.append(covs.swapaxes(0,1),[means],0),
                     [np.ones(len(means))],0).swapaxes(0,1)
        L2=list(np.ones(len(means)))
        L2.extend([0,0])
        L3=list(means)
        L3.extend([0,0])
        L4=np.array([L2,L3])
        L=np.append(L1,L4,0)
        results=linalg.solve(L,np.append(np.zeros(len(means)),[1,goalRet],0))
        return(np.array([list(self.returns.columns),results[:-2]]))
    
    #定義繪制最小方差前緣曲線函式
    def frontierCurve(self): #繪圖，根據線性求解
        goals=[x/500000 for x in range(-100,4000)]
        variances=list(map(lambda x: self.calVar(self.minVar(x)[1,:].astype(np.float)),goals))
        plt.plot(variances,goals)  #方差-收益率圖
        
    #給定各資產的比例,計算收益率的均值
    def meanRet(self,fracs): #fracs概率
        meanRisky=ffn.to_returns(self.returns).mean()
        assert len(meanRisky)==len(fracs), 'Length of fractions must be equal to number of assets'
        return(np.sum(np.multiply(meanRisky,np.array(fracs))))
    
    #給定各資產的比例,計算收益率方差
    def calVar(self,fracs):
        return(np.dot(np.dot(fracs,self.returns.cov()),fracs))

呼叫minvar函式計算最小方差

minvar=MeanVariance(sh_return)

呼叫frontierCurve繪制效率前沿曲線

minvar.frontierCurve() #橫軸為方差，縱軸為收益，曲線為收益方差最低點

在這里插入圖片描述

將資料拆分為訓練和測驗資料，輸出根據訓練資料計算的效率前沿曲線

sh_return.shape

(242, 5)

train_set=sh_return[0:121]   
test_set=sh_return[122:242] #訓練資料和測驗資料，各匯入一半
varMinmizer=MeanVariance(train_set)
varMinmizer.frontierCurve() #收益方差最低點

在這里插入圖片描述

給定收益率下，計算方差最小時對應的五種股票的比例權重

goal_return=0.003
protfolio_weight=varMinmizer.minVar(goal_return) #計算最小方差.根據五種股票
protfolio_weight #權重，五種股票的比例權重

array([['fjgs', 'zndl', 'sykj', 'hxyh', 'byjc'],
       ['-0.185777320912347', '-1.8333107604295968',
        '0.38673711936434396', '2.0333149700802164',
        '0.5990359918973837']], dtype='<U32')

test_return=np.dot(test_set,np.array([protfolio_weight[1,:].astype(np.float)]).swapaxes(0,1)) 
#按照交換x,y
test_return

array([[-0.11011845],
       [-0.02524191],
       [-0.06059084],
       [-0.00483673],
       [-0.00067331],
       [ 0.00451267],
       [-0.02368934],
       [ 0.02203717],
       [ 0.00173678],
       [ 0.07425185],
       [ 0.0112505 ],
       [-0.01023086],
       [-0.04548689],
       [ 0.04493778],
       [-0.02015694],
       [ 0.0052846 ],
       [ 0.00265628],
       [ 0.02267791],
       [ 0.0288354 ],
       [-0.00508686],
       [ 0.02599153],
       [ 0.02081656],
       [-0.00166454],
       [-0.04485105],
       [-0.03813144],
       [-0.04204255],
       [ 0.03486829],
       [-0.04028191],
       [ 0.00842363],
       [ 0.01696757],
       [ 0.06047486],
       [ 0.03047909],
       [-0.05145005],
       [-0.00333348],
       [-0.00292845],
       [ 0.00730291],
       [ 0.02302764],
       [ 0.00071038],
       [ 0.01599063],
       [-0.02301472],
       [ 0.05399119],
       [ 0.05057536],
       [ 0.00619487],
       [-0.04426579],
       [-0.06304755],
       [ 0.02011673],
       [ 0.04067394],
       [-0.02014949],
       [-0.00400891],
       [-0.0259005 ],
       [-0.01740082],
       [-0.05066975],
       [ 0.03218413],
       [ 0.02201851],
       [-0.02564261],
       [ 0.02496331],
       [ 0.01314226],
       [-0.01007401],
       [-0.02022558],
       [-0.02382847],
       [-0.00250703],
       [-0.01666069],
       [-0.01190292],
       [ 0.01046496],
       [ 0.03835301],
       [ 0.03398579],
       [ 0.0005996 ],
       [-0.04287169],
       [-0.02749323],
       [ 0.06616573],
       [-0.00028395],
       [ 0.05502029],
       [ 0.0366752 ],
       [ 0.03932765],
       [ 0.08592724],
       [ 0.02159489],
       [ 0.01792505],
       [ 0.00881541],
       [-0.04477628],
       [ 0.03570067],
       [ 0.03264928],
       [-0.00825414],
       [ 0.00851066],
       [-0.01358265],
       [-0.04444564],
       [ 0.00871176],
       [-0.0079298 ],
       [ 0.04009519],
       [-0.00403245],
       [-0.01284608],
       [-0.01690251],
       [-0.04568924],
       [ 0.00241797],
       [ 0.0133465 ],
       [-0.0304876 ],
       [-0.03241099],
       [ 0.00303069],
       [-0.00297659],
       [-0.00146255],
       [-0.00240845],
       [-0.0395943 ],
       [-0.01543629],
       [ 0.03707392],
       [ 0.00505044],
       [-0.0290022 ],
       [ 0.05648995],
       [-0.01158704],
       [ 0.00279889],
       [-0.00393927],
       [ 0.00092292],
       [ 0.01125273],
       [-0.00371833],
       [ 0.03248409],
       [-0.0327072 ],
       [-0.03644614],
       [-0.0076972 ],
       [ 0.01118346],
       [-0.00150503],
       [ 0.00326623],
       [ 0.00645175]])

sim_weight=np.random.uniform(0,1,(100,5)) #亂數
sim_weight

array([[9.02596959e-01, 3.76262930e-01, 6.78788501e-01, 3.72752382e-01,
        3.81890155e-01],
       [4.61790022e-01, 2.50318083e-01, 8.12363330e-01, 9.47705004e-01,
        6.54625324e-01],
       [7.70635263e-01, 6.78646675e-01, 5.35714827e-01, 4.40542592e-02,
        5.79451488e-01],
       [7.94560717e-01, 3.91893060e-02, 1.84737034e-01, 8.96622279e-01,
        4.55253890e-01],
       [5.00623474e-01, 4.57421136e-01, 9.37412800e-01, 4.68915861e-01,
        2.51780445e-01],
       [6.10727677e-01, 9.10018989e-01, 1.90229137e-01, 5.89624002e-01,
        7.50811768e-01],
       [6.54119584e-01, 6.99277911e-01, 7.86371064e-01, 5.42726325e-01,
        5.25777733e-01],
       [3.57751269e-01, 7.62158579e-01, 5.33726920e-01, 3.58773657e-01,
        2.33096611e-01],
       [4.93000589e-01, 6.86923780e-01, 4.68621878e-01, 5.60846914e-01,
        9.08581075e-01],
       [7.04448567e-01, 4.81023531e-01, 2.95615051e-01, 2.24994103e-01,
        4.09386928e-01],
       [7.75254913e-03, 5.32295178e-01, 8.22935438e-01, 1.13852844e-01,
        6.70073088e-01],
       [2.79925781e-01, 1.57646996e-01, 4.30745258e-01, 7.75570703e-02,
        7.57233696e-02],
       [9.02327119e-01, 6.22353094e-01, 8.11022610e-01, 4.79416372e-01,
        9.90680610e-01],
       [5.28365437e-03, 7.60598096e-02, 3.11953117e-01, 3.50564099e-01,
        2.50126713e-01],
       [4.09351464e-01, 4.05636701e-01, 8.53661068e-01, 8.72152555e-01,
        9.30888148e-01],
       [7.17377715e-01, 9.43990271e-01, 3.77244832e-01, 4.73779134e-01,
        5.35254976e-01],
       [8.19747596e-01, 8.36042977e-01, 8.14826653e-01, 2.83596123e-01,
        2.33435627e-01],
       [8.10657368e-01, 2.04881553e-01, 9.76210748e-01, 6.77514916e-01,
        2.41308170e-02],
       [5.06362334e-01, 7.48858420e-02, 8.69922564e-01, 1.36639804e-02,
        1.39033752e-01],
       [1.53885649e-01, 5.30735655e-01, 9.70589007e-01, 4.72322755e-01,
        3.93527157e-01],
       [1.17698436e-01, 9.84057538e-01, 9.50760636e-01, 6.81740321e-01,
        6.91331760e-01],
       [4.76974660e-01, 8.12390566e-01, 2.17269527e-01, 9.33557049e-01,
        5.12890057e-01],
       [6.65764616e-01, 5.91170479e-01, 4.83041600e-01, 8.15889943e-01,
        5.79378415e-01],
       [4.22279247e-01, 4.55583133e-01, 7.80749390e-01, 7.90695717e-01,
        7.44457541e-02],
       [8.33391878e-01, 8.61807069e-01, 9.47168723e-03, 5.56376255e-01,
        3.55746683e-01],
       [5.99938911e-01, 4.84690799e-01, 7.51076755e-01, 2.79942344e-01,
        8.95771536e-01],
       [1.65167861e-02, 1.03481429e-01, 8.87673006e-01, 4.59212157e-01,
        4.87966300e-01],
       [2.70083716e-01, 8.58539156e-01, 2.52079363e-02, 8.33757013e-01,
        2.72905216e-01],
       [7.50730234e-01, 4.24462497e-04, 3.26366654e-01, 2.58576867e-01,
        1.30843726e-01],
       [1.29889095e-01, 8.90247465e-01, 4.14531222e-01, 1.26835523e-01,
        1.13266528e-02],
       [1.39842913e-01, 5.86007597e-01, 2.93179565e-01, 4.46639656e-01,
        5.45572753e-02],
       [1.96100798e-01, 4.81756392e-01, 8.17861476e-01, 8.62922569e-01,
        6.94755944e-02],
       [8.80579877e-01, 2.77329884e-01, 1.09251298e-01, 7.67789095e-01,
        8.58970487e-01],
       [6.48493753e-01, 9.72395101e-01, 3.32044412e-02, 8.25528293e-01,
        8.37446628e-01],
       [2.70624530e-01, 8.58610165e-01, 9.51243666e-02, 3.32908942e-01,
        4.65119505e-01],
       [3.44186845e-01, 6.20875263e-01, 6.47787000e-01, 9.41466289e-01,
        8.88133838e-02],
       [6.96415284e-01, 3.35618259e-01, 4.27412104e-01, 9.75705624e-01,
        9.98000317e-01],
       [4.35619177e-01, 3.87558779e-01, 4.30763422e-01, 9.25248547e-01,
        9.57756296e-02],
       [9.57884243e-01, 2.11188490e-01, 5.44391353e-01, 7.41643153e-01,
        8.12112030e-01],
       [4.20178450e-01, 3.69513387e-02, 3.34522980e-01, 1.50243105e-01,
        3.11842687e-02],
       [2.49210170e-01, 6.01143933e-01, 5.96449615e-01, 6.67530386e-01,
        1.98877734e-01],
       [8.66697603e-01, 1.67607911e-01, 5.18357829e-01, 1.80723852e-01,
        3.64400552e-01],
       [8.51683579e-01, 2.28259511e-01, 4.94088371e-01, 8.87069298e-02,
        4.05412532e-01],
       [4.52325481e-02, 6.82542923e-01, 2.48142239e-01, 4.91822233e-01,
        1.76566522e-01],
       [1.76382700e-01, 4.23572994e-01, 1.86778371e-01, 6.42219544e-01,
        6.63508978e-01],
       [6.11881870e-01, 8.90490557e-01, 9.94668782e-01, 9.46196757e-01,
        4.34194946e-01],
       [5.02852239e-01, 1.98142332e-01, 9.92453904e-01, 8.84549444e-01,
        6.97299807e-01],
       [8.65473471e-01, 4.50734526e-01, 2.88710480e-01, 8.24001155e-01,
        8.24163231e-01],
       [2.52135339e-01, 1.52863848e-01, 8.61560440e-01, 1.92514934e-01,
        8.44152804e-01],
       [1.30846531e-01, 2.02477494e-01, 8.41907758e-01, 2.72048612e-01,
        2.79161559e-01],
       [5.22543328e-01, 9.79903944e-01, 7.57297551e-01, 9.09711783e-01,
        8.11010876e-01],
       [3.90452171e-01, 4.04869166e-01, 4.10778467e-01, 5.38810790e-02,
        7.20165821e-01],
       [9.84090706e-01, 2.07825930e-02, 3.73142851e-01, 4.66086568e-01,
        3.01294420e-01],
       [2.96729994e-02, 7.22559447e-01, 3.25238703e-01, 5.20593100e-01,
        2.81266789e-01],
       [6.45034069e-01, 8.88655388e-01, 7.98535281e-01, 9.18093455e-01,
        5.51861958e-01],
       [6.17507555e-01, 6.53052173e-01, 8.76951611e-01, 4.23447372e-01,
        8.88272806e-01],
       [9.95110802e-01, 8.13853611e-01, 9.42655235e-01, 4.41823485e-01,
        1.32271916e-02],
       [7.45223475e-01, 8.34551563e-01, 1.08675841e-01, 4.24253511e-01,
        8.11314020e-01],
       [9.22853995e-01, 8.24845800e-01, 3.35043686e-01, 1.88414328e-01,
        7.77752679e-02],
       [4.79855679e-01, 6.58275935e-02, 2.87447223e-01, 4.38889243e-02,
        1.55655620e-01],
       [9.71216934e-01, 8.30405436e-01, 3.09952015e-01, 7.86804698e-01,
        6.75085450e-02],
       [4.05749690e-01, 1.39407459e-01, 7.80232674e-01, 9.65163821e-01,
        1.01830685e-01],
       [3.20528051e-01, 5.39637812e-02, 4.31657841e-01, 7.04632230e-02,
        5.40182605e-02],
       [4.51025449e-01, 6.24396996e-01, 2.17317856e-01, 6.91048568e-01,
        3.27145505e-01],
       [5.78734756e-02, 5.66975138e-01, 5.82714729e-01, 1.06343643e-02,
        8.73370778e-01],
       [1.99935573e-01, 8.08797242e-01, 5.42644344e-01, 3.62700167e-01,
        8.10791718e-01],
       [7.87148319e-01, 7.49812561e-01, 6.93030256e-02, 6.96712770e-01,
        3.50987536e-01],
       [4.12114459e-01, 6.69651141e-01, 4.42083535e-01, 6.51143854e-01,
        2.09044025e-01],
       [4.57205547e-01, 4.53447780e-01, 4.41328214e-01, 3.19826298e-01,
        6.95390510e-01],
       [2.76607663e-01, 7.45829743e-01, 8.76821099e-01, 9.08213010e-01,
        4.98635096e-01],
       [6.12872530e-01, 8.77373005e-02, 6.52744603e-01, 1.77231628e-02,
        3.63441882e-01],
       [9.55249114e-01, 8.62395856e-01, 6.22376413e-01, 1.45106388e-01,
        5.74500790e-01],
       [5.05321770e-01, 1.72383345e-01, 2.69803510e-01, 9.48454018e-01,
        8.18452610e-01],
       [3.50867963e-01, 4.29409449e-01, 7.50936406e-01, 3.59995051e-01,
        9.35785501e-01],
       [1.49625448e-01, 1.45928612e-02, 8.11472733e-01, 9.26829363e-01,
        1.66884799e-01],
       [6.99032463e-02, 8.09651763e-01, 3.97792919e-01, 8.07733356e-01,
        6.42889670e-01],
       [3.21057772e-01, 9.68237260e-01, 8.70586733e-01, 2.91539429e-01,
        9.20640741e-01],
       [7.87248426e-01, 3.53537253e-01, 2.95357885e-01, 8.69106856e-01,
        7.34115519e-01],
       [2.36478799e-01, 3.40149684e-01, 9.44648843e-01, 7.53158760e-01,
        1.06725521e-01],
       [6.08081572e-01, 4.12868708e-01, 1.23856045e-01, 7.60754627e-01,
        6.86373032e-01],
       [7.15315473e-01, 2.17327945e-01, 1.65380585e-01, 1.33889168e-01,
        9.76392372e-01],
       [3.42413401e-01, 8.21412746e-01, 8.93184528e-01, 2.97280317e-01,
        3.79123005e-01],
       [2.93882121e-01, 5.44256489e-01, 5.56119146e-01, 6.85895129e-01,
        4.18436783e-02],
       [5.54351561e-01, 1.43035494e-01, 9.83685259e-01, 7.92416601e-01,
        1.81446608e-01],
       [8.02655646e-01, 6.99615383e-02, 8.49461656e-01, 3.91742126e-01,
        2.36464094e-01],
       [3.36669649e-02, 1.34884405e-01, 7.68615141e-01, 7.88732161e-01,
        8.07690867e-01],
       [6.91802860e-01, 4.60674563e-01, 2.91990705e-02, 3.55472558e-01,
        2.97092808e-01],
       [2.87012974e-01, 8.56598445e-01, 2.24723853e-01, 7.49230662e-01,
        4.55577780e-01],
       [6.61091320e-01, 1.15149507e-01, 4.02977806e-01, 8.95355549e-01,
        4.27400442e-01],
       [1.61653341e-01, 6.80827584e-01, 3.56344842e-01, 8.68873642e-01,
        8.27962997e-01],
       [5.81998497e-01, 2.72759624e-02, 7.98603526e-01, 6.36773965e-01,
        1.06708038e-01],
       [9.67964595e-01, 3.97669431e-01, 8.13862210e-02, 1.26654237e-01,
        3.89938429e-01],
       [6.69173975e-01, 1.26097567e-02, 4.72127236e-01, 1.78969329e-01,
        9.95198099e-01],
       [1.99196882e-01, 4.07419375e-01, 1.08011725e-01, 4.70669873e-01,
        2.59156493e-01],
       [5.36425977e-01, 9.75941413e-02, 6.99387359e-01, 7.08227556e-01,
        1.70702509e-01],
       [8.35400787e-01, 6.86454909e-02, 3.37686524e-01, 9.10780025e-01,
        7.16111389e-01],
       [2.89169565e-01, 4.92159303e-01, 6.06209542e-01, 7.16603968e-01,
        1.19856973e-01],
       [8.21844583e-01, 5.62624705e-01, 9.10118730e-01, 8.33129636e-01,
        9.55516226e-01],
       [8.68937084e-01, 9.50778274e-01, 9.84988311e-01, 5.21978793e-01,
        7.38793945e-01],
       [7.94385085e-01, 6.24590473e-01, 4.61838436e-01, 6.29618835e-01,
        5.34655742e-01]])

test_return=pd.DataFrame(test_return,index=test_set.index) #新建dataframe
test_return

	0
trade_date
2020-07-03	-0.110118
2020-07-02	-0.025242
2020-07-01	-0.060591
2020-06-30	-0.004837
2020-06-29	-0.000673
...	...
2020-01-08	-0.007697
2020-01-07	0.011183
2020-01-06	-0.001505
2020-01-03	0.003266
2020-01-02	0.006452

120 rows × 1 columns

test_cum_return=(1+test_return).cumprod()#累積收益
test_cum_return.head

<bound method NDFrame.head of                    0
trade_date          
2020-07-03  0.889882
2020-07-02  0.867419
2020-07-01  0.814862
2020-06-30  0.810920
2020-06-29  0.810374
...              ...
2020-01-08  0.965167
2020-01-07  0.975961
2020-01-06  0.974492
2020-01-03  0.977675
2020-01-02  0.983983

[120 rows x 1 columns]>

test_cum_return.index

DatetimeIndex(['2020-07-03', '2020-07-02', '2020-07-01', '2020-06-30',
               '2020-06-29', '2020-06-24', '2020-06-23', '2020-06-22',
               '2020-06-19', '2020-06-18',
               ...
               '2020-01-15', '2020-01-14', '2020-01-13', '2020-01-10',
               '2020-01-09', '2020-01-08', '2020-01-07', '2020-01-06',
               '2020-01-03', '2020-01-02'],
              dtype='datetime64[ns]', name='trade_date', length=120, freq=None)

test_cum_return.columns = ['cum_return'] #重命名列名
test_cum_return

	cum_return
trade_date
2020-07-03	0.889882
2020-07-02	0.867419
2020-07-01	0.814862
2020-06-30	0.810920
2020-06-29	0.810374
...	...
2020-01-08	0.965167
2020-01-07	0.975961
2020-01-06	0.974492
2020-01-03	0.977675
2020-01-02	0.983983

120 rows × 1 columns

繪制收益率曲線

plt.plot(test_cum_return.index,test_cum_return)

[<matplotlib.lines.Line2D at 0x1889ad79250>]

在這里插入圖片描述

與隨機生成的組合進行比較

sim_weight=np.random.uniform(0,1,(100,5))  #（0，1）之間生成亂數，大小是（100，5）
sim_weight=np.apply_along_axis(lambda x:x /sum(x),1,sim_weight)   
#權重，numpy.apply_along_axis()函式回傳的是一個根據func()函式以及維度axis運算后得到的陣列.
sim_weight

array([[2.15710380e-01, 3.36014900e-02, 3.52812998e-01, 2.25394003e-02,
        3.75335732e-01],
       [1.58004653e-01, 2.29000886e-02, 2.25653116e-01, 2.54353241e-01,
        3.39088901e-01],
       [2.46635746e-01, 1.97933264e-01, 2.93933362e-01, 2.26955925e-01,
        3.45417023e-02],
       [1.81360931e-01, 2.40309226e-01, 1.99632515e-02, 1.76374715e-01,
        3.81991875e-01],
       [1.89561391e-01, 1.80771066e-01, 2.26772421e-01, 2.73908729e-01,
        1.28986392e-01],
       [2.84803939e-01, 6.36540873e-02, 1.30749020e-01, 2.03368025e-01,
        3.17424929e-01],
       [3.19401286e-01, 5.96941721e-02, 3.47614496e-01, 2.45560529e-01,
        2.77295172e-02],
       [1.50899206e-01, 2.27189539e-01, 2.58833824e-01, 8.99617418e-02,
        2.73115689e-01],
       [1.95500520e-01, 7.36123151e-02, 2.98103862e-06, 6.27570996e-01,
        1.03313187e-01],
       [2.08077300e-01, 2.12013901e-01, 2.51080153e-01, 3.17070738e-01,
        1.17579076e-02],
       [2.17765162e-01, 1.08443799e-01, 2.78651418e-01, 2.47894727e-01,
        1.47244895e-01],
       [1.95987198e-01, 1.54514812e-01, 2.07100145e-01, 2.33745196e-01,
        2.08652650e-01],
       [3.15280429e-01, 1.01903038e-01, 3.12310770e-01, 8.91078002e-02,
        1.81397963e-01],
       [2.37775282e-01, 1.70584380e-01, 2.58668719e-01, 3.08281958e-01,
        2.46896611e-02],
       [1.35432702e-01, 1.50142874e-01, 8.79858084e-02, 3.25280372e-01,
        3.01158244e-01],
       [9.48712818e-04, 3.11365673e-01, 1.06820413e-01, 2.64695497e-01,
        3.16169704e-01],
       [1.40243201e-01, 1.18591964e-01, 2.18570743e-01, 2.61465156e-01,
        2.61128936e-01],
       [1.64520440e-01, 3.44380420e-01, 2.51611086e-01, 1.66548599e-01,
        7.29394541e-02],
       [2.84951705e-01, 2.31736686e-01, 1.68303753e-01, 6.93825076e-02,
        2.45625348e-01],
       [1.96861615e-02, 2.44749740e-01, 5.07177341e-01, 1.02352289e-01,
        1.26034469e-01],
       [1.85485303e-01, 1.54990916e-01, 2.70442691e-01, 1.92948783e-01,
        1.96132306e-01],
       [2.50392802e-01, 3.48561942e-01, 4.09345075e-02, 2.15747002e-01,
        1.44363747e-01],
       [2.37950955e-01, 2.59599786e-01, 1.52431301e-01, 1.57300240e-01,
        1.92717719e-01],
       [2.19107407e-01, 1.25430955e-01, 2.77723211e-01, 1.38552750e-01,
        2.39185677e-01],
       [1.77089302e-01, 2.33276958e-01, 3.28293098e-01, 2.15310392e-01,
        4.60302494e-02],
       [2.55165676e-01, 2.84403926e-01, 1.13054630e-01, 1.67431827e-02,
        3.30632585e-01],
       [1.16642459e-01, 2.41868153e-01, 1.25568317e-01, 1.22613475e-01,
        3.93307595e-01],
       [2.86751792e-02, 1.46461087e-02, 4.22284580e-01, 1.08888568e-01,
        4.25505564e-01],
       [2.16435319e-01, 1.99630958e-01, 1.04932277e-01, 2.34668889e-01,
        2.44332557e-01],
       [2.50149591e-01, 2.87753083e-02, 3.24471163e-01, 2.78963962e-01,
        1.17639976e-01],
       [7.03347549e-02, 3.50697129e-01, 3.11758845e-01, 7.37654094e-02,
        1.93443862e-01],
       [1.35150010e-01, 1.63345906e-01, 2.69017254e-01, 2.10693778e-01,
        2.21793052e-01],
       [2.01212678e-01, 3.84996871e-01, 1.86379373e-01, 4.33139626e-02,
        1.84097116e-01],
       [3.09692458e-01, 6.53743845e-02, 2.11675699e-01, 1.84087741e-01,
        2.29169717e-01],
       [5.99411870e-02, 1.70114724e-01, 6.62921057e-02, 3.46750361e-01,
        3.56901622e-01],
       [2.23905659e-01, 1.55867394e-01, 2.08600894e-01, 1.94978637e-01,
        2.16647417e-01],
       [2.03086684e-01, 2.65281317e-01, 1.10597786e-01, 4.21024096e-01,
        1.01169359e-05],
       [2.43043492e-02, 2.06083107e-01, 3.37943170e-01, 2.43808012e-01,
        1.87861362e-01],
       [1.55071671e-01, 2.06030798e-01, 1.74062446e-01, 2.11290972e-01,
        2.53544112e-01],
       [5.86474461e-02, 4.41831496e-01, 2.52952511e-02, 4.23126216e-01,
        5.10995910e-02],
       [9.94975503e-02, 2.76636397e-01, 1.07207563e-01, 2.71420752e-01,
        2.45237738e-01],
       [2.29005892e-01, 2.89867826e-01, 5.58590928e-02, 1.51555992e-01,
        2.73711196e-01],
       [1.43747173e-01, 8.27803954e-02, 3.19485984e-01, 3.03883091e-01,
        1.50103357e-01],
       [2.75732323e-01, 1.29558909e-01, 1.63272991e-01, 2.99053295e-01,
        1.32382481e-01],
       [1.64526630e-01, 2.57521161e-01, 2.86481651e-01, 2.33509333e-01,
        5.79612248e-02],
       [6.34696266e-02, 2.19750011e-01, 2.72246965e-01, 2.85904176e-01,
        1.58629222e-01],
       [3.60572520e-01, 6.45109386e-02, 4.49786430e-02, 2.24713503e-01,
        3.05224395e-01],
       [1.34454684e-02, 1.94850081e-01, 3.01170712e-01, 3.01571049e-01,
        1.88962689e-01],
       [6.53210956e-02, 4.54132965e-01, 1.58957712e-01, 2.12879541e-01,
        1.08708686e-01],
       [7.65133979e-02, 2.29623966e-02, 1.94773977e-01, 2.57611700e-01,
        4.48138529e-01],
       [7.10028706e-03, 1.76159234e-01, 3.41841761e-01, 2.37419476e-01,
        2.37479242e-01],
       [2.01947698e-01, 1.73420997e-02, 4.03626199e-01, 2.72095535e-01,
        1.04988468e-01],
       [6.87892632e-02, 3.06799052e-01, 3.01944539e-01, 4.00451750e-02,
        2.82421970e-01],
       [2.27605475e-01, 2.42849226e-01, 3.48084101e-02, 1.68129285e-01,
        3.26607605e-01],
       [2.90479254e-01, 2.74752356e-01, 1.17176961e-01, 4.48938588e-02,
        2.72697570e-01],
       [2.40863650e-01, 8.53837457e-02, 7.72600590e-02, 2.37088894e-01,
        3.59403651e-01],
       [2.16620651e-01, 2.13497347e-01, 1.92780456e-01, 1.48951225e-01,
        2.28150320e-01],
       [1.68058333e-01, 3.61103135e-01, 1.09495019e-01, 2.86961973e-01,
        7.43815394e-02],
       [1.43299482e-01, 3.24870407e-01, 6.68362081e-02, 1.06270787e-01,
        3.58723116e-01],
       [1.93693122e-01, 3.28493561e-01, 1.17629308e-01, 3.32925482e-01,
        2.72585273e-02],
       [1.31238234e-01, 2.90987611e-01, 5.04308708e-02, 1.37452008e-01,
        3.89891276e-01],
       [3.20489444e-01, 1.27198019e-01, 3.18005768e-02, 3.03340522e-01,
        2.17171438e-01],
       [1.82661938e-01, 2.66020119e-01, 2.72516025e-01, 2.80374056e-02,
        2.50764513e-01],
       [3.95109126e-02, 2.27522271e-01, 1.48717548e-01, 3.14956277e-01,
        2.69292991e-01],
       [2.19056591e-01, 7.26045899e-02, 4.44426722e-01, 2.29366900e-02,
        2.40975407e-01],
       [2.59742063e-01, 2.95591668e-02, 5.08163842e-02, 1.75721814e-01,
        4.84160573e-01],
       [3.95285792e-01, 7.01380246e-02, 2.86333364e-01, 1.39871373e-01,
        1.08371446e-01],
       [2.74824695e-01, 6.30446266e-03, 2.10454587e-01, 2.14509417e-01,
        2.93906838e-01],
       [4.30142190e-01, 6.84748065e-02, 2.52081589e-01, 1.69448731e-01,
        7.98526834e-02],
       [4.23252875e-03, 2.24854782e-01, 3.24988744e-01, 3.29064622e-01,
        1.16859324e-01],
       [2.86516002e-01, 3.38568082e-01, 1.95953733e-01, 5.77201515e-02,
        1.21242032e-01],
       [2.52018486e-01, 1.30107025e-01, 2.16385880e-01, 2.51224181e-01,
        1.50264428e-01],
       [8.73392189e-02, 1.65495600e-01, 3.54225451e-01, 3.13233931e-01,
        7.97057990e-02],
       [2.29582252e-01, 3.33487817e-01, 7.13499342e-02, 1.35469401e-01,
        2.30110596e-01],
       [1.10334826e-02, 8.23627540e-02, 2.64219338e-01, 3.50534353e-01,
        2.91850072e-01],
       [2.51429396e-01, 1.08662457e-01, 2.37057162e-01, 2.25474778e-01,
        1.77376207e-01],
       [1.17829206e-01, 4.00904842e-02, 2.66774305e-01, 2.83143358e-01,
        2.92162648e-01],
       [1.22817097e-01, 6.62502141e-02, 3.23229286e-01, 1.73243087e-01,
        3.14460315e-01],
       [1.97963547e-01, 1.53187502e-01, 9.15982708e-02, 9.74238156e-02,
        4.59826865e-01],
       [1.63329768e-01, 2.52927873e-01, 8.48656786e-02, 2.85387407e-01,
        2.13489273e-01],
       [2.49089727e-01, 1.11324427e-01, 4.29936058e-01, 1.37002074e-01,
        7.26477143e-02],
       [2.82091585e-01, 2.16096986e-02, 1.97555562e-01, 2.52726967e-01,
        2.46016187e-01],
       [1.47518090e-01, 2.69419100e-01, 3.18056620e-01, 1.94893723e-01,
        7.01124660e-02],
       [5.26515083e-02, 2.79188405e-02, 4.10848226e-01, 1.75515007e-01,
        3.33066418e-01],
       [2.00436836e-01, 1.90147381e-01, 2.57453882e-01, 8.39497499e-02,
        2.68012151e-01],
       [5.34156737e-02, 3.55650593e-02, 3.98793566e-01, 3.34770108e-01,
        1.77455593e-01],
       [1.48785472e-01, 1.38299321e-01, 2.04166875e-01, 1.77291874e-01,
        3.31456457e-01],
       [6.31350973e-02, 3.00511024e-01, 7.92409052e-02, 3.23628905e-01,
        2.33484068e-01],
       [4.30981494e-02, 4.63168024e-01, 1.18329907e-01, 3.28276115e-01,
        4.71278041e-02],
       [2.92287901e-01, 2.65500202e-01, 1.69560284e-01, 2.19350264e-01,
        5.33013490e-02],
       [2.07227809e-01, 3.08249831e-01, 2.59191788e-01, 1.50275489e-01,
        7.50550827e-02],
       [2.63637285e-01, 1.78688209e-01, 6.10027610e-02, 3.18891618e-01,
        1.77780127e-01],
       [2.66101585e-01, 1.35994431e-01, 2.66853208e-01, 2.06925616e-01,
        1.24125161e-01],
       [3.98594221e-01, 7.20453832e-02, 5.43301947e-02, 1.20640837e-01,
        3.54389364e-01],
       [3.32397799e-01, 8.57398533e-02, 8.93782341e-02, 1.16078791e-01,
        3.76405322e-01],
       [3.12067107e-01, 1.43370430e-01, 2.96921812e-01, 9.30800499e-02,
        1.54560602e-01],
       [1.48366564e-01, 2.23040459e-01, 2.24621396e-01, 3.05071330e-01,
        9.89002509e-02],
       [2.52870783e-01, 7.50960949e-02, 6.44838403e-02, 3.66138716e-01,
        2.41410566e-01],
       [1.84012108e-01, 2.63814905e-02, 1.93513118e-01, 2.61234936e-01,
        3.34858347e-01],
       [1.13036969e-01, 2.18235168e-01, 2.39444596e-01, 6.05908522e-02,
        3.68692414e-01]])

sim_return=np.dot(test_set,sim_weight.swapaxes(0,1)) #np二維陣列資料型別
sim_return=pd.DataFrame(sim_return,index=test_cum_return.index) #轉化為pandas dataFrame
sim_sum_return=(1+sim_return).cumprod() #累計收益
plt.plot(sim_sum_return) #綜合繪圖

[<matplotlib.lines.Line2D at 0x1889e3c0be0>,
 <matplotlib.lines.Line2D at 0x1889e288ac0>,
 <matplotlib.lines.Line2D at 0x1889e2886a0>,
 <matplotlib.lines.Line2D at 0x1889e288d00>,
 <matplotlib.lines.Line2D at 0x1889e288040>,
 <matplotlib.lines.Line2D at 0x1889e288f70>,
 <matplotlib.lines.Line2D at 0x1889e288f40>,
 <matplotlib.lines.Line2D at 0x1889e2885b0>,
 <matplotlib.lines.Line2D at 0x1889e288790>,
 <matplotlib.lines.Line2D at 0x1889e288ca0>,
 <matplotlib.lines.Line2D at 0x1889e3c0040>,
 <matplotlib.lines.Line2D at 0x1889e288610>,
 <matplotlib.lines.Line2D at 0x1889e288730>,
 <matplotlib.lines.Line2D at 0x1889e288940>,
 <matplotlib.lines.Line2D at 0x1889e2888e0>,
 <matplotlib.lines.Line2D at 0x1889e288250>,
 <matplotlib.lines.Line2D at 0x1889e288280>,
 <matplotlib.lines.Line2D at 0x1889e288490>,
 <matplotlib.lines.Line2D at 0x1889e288430>,
 <matplotlib.lines.Line2D at 0x1889e2880a0>,
 <matplotlib.lines.Line2D at 0x1889e316670>,
 <matplotlib.lines.Line2D at 0x1889e316640>,
 <matplotlib.lines.Line2D at 0x1889e316b20>,
 <matplotlib.lines.Line2D at 0x1889e316ac0>,
 <matplotlib.lines.Line2D at 0x1889e316fa0>,
 <matplotlib.lines.Line2D at 0x1889e316eb0>,
 <matplotlib.lines.Line2D at 0x1889e316c10>,
 <matplotlib.lines.Line2D at 0x1889e3168b0>,
 <matplotlib.lines.Line2D at 0x1889e316130>,
 <matplotlib.lines.Line2D at 0x1889e316160>,
 <matplotlib.lines.Line2D at 0x1889e3165b0>,
 <matplotlib.lines.Line2D at 0x1889e316730>,
 <matplotlib.lines.Line2D at 0x1889e316880>,
 <matplotlib.lines.Line2D at 0x1889e316940>,
 <matplotlib.lines.Line2D at 0x1889e291190>,
 <matplotlib.lines.Line2D at 0x1889e291280>,
 <matplotlib.lines.Line2D at 0x1889e291bb0>,
 <matplotlib.lines.Line2D at 0x1889e291fa0>,
 <matplotlib.lines.Line2D at 0x1889e291f40>,
 <matplotlib.lines.Line2D at 0x1889e291100>,
 <matplotlib.lines.Line2D at 0x1889e291040>,
 <matplotlib.lines.Line2D at 0x1889e291b20>,
 <matplotlib.lines.Line2D at 0x1889e291a90>,
 <matplotlib.lines.Line2D at 0x1889e291eb0>,
 <matplotlib.lines.Line2D at 0x1889e291760>,
 <matplotlib.lines.Line2D at 0x1889e291880>,
 <matplotlib.lines.Line2D at 0x1889e2917f0>,
 <matplotlib.lines.Line2D at 0x1889e2919d0>,
 <matplotlib.lines.Line2D at 0x1889e291370>,
 <matplotlib.lines.Line2D at 0x1889e2914c0>,
 <matplotlib.lines.Line2D at 0x1889e291430>,
 <matplotlib.lines.Line2D at 0x1889e291610>,
 <matplotlib.lines.Line2D at 0x1889e2911f0>,
 <matplotlib.lines.Line2D at 0x1889e23bb50>,
 <matplotlib.lines.Line2D at 0x1889e23ba60>,
 <matplotlib.lines.Line2D at 0x1889e23b760>,
 <matplotlib.lines.Line2D at 0x1889e23b3a0>,
 <matplotlib.lines.Line2D at 0x1889e23b1f0>,
 <matplotlib.lines.Line2D at 0x1889e23ba30>,
 <matplotlib.lines.Line2D at 0x1889e23bb80>,
 <matplotlib.lines.Line2D at 0x1889e23bca0>,
 <matplotlib.lines.Line2D at 0x1889e23b4f0>,
 <matplotlib.lines.Line2D at 0x1889e23b490>,
 <matplotlib.lines.Line2D at 0x1889e23bd90>,
 <matplotlib.lines.Line2D at 0x1889e23bac0>,
 <matplotlib.lines.Line2D at 0x1889debf100>,
 <matplotlib.lines.Line2D at 0x1889debfbb0>,
 <matplotlib.lines.Line2D at 0x1889debfbe0>,
 <matplotlib.lines.Line2D at 0x1889debfca0>,
 <matplotlib.lines.Line2D at 0x1889debfe50>,
 <matplotlib.lines.Line2D at 0x1889debff70>,
 <matplotlib.lines.Line2D at 0x1889debfcd0>,
 <matplotlib.lines.Line2D at 0x1889e4adfd0>,
 <matplotlib.lines.Line2D at 0x1889e4adeb0>,
 <matplotlib.lines.Line2D at 0x1889ccaf790>,
 <matplotlib.lines.Line2D at 0x1889ccafe80>,
 <matplotlib.lines.Line2D at 0x1889ccaf550>,
 <matplotlib.lines.Line2D at 0x1889d14ec40>,
 <matplotlib.lines.Line2D at 0x1889d14e910>,
 <matplotlib.lines.Line2D at 0x1889d14e2e0>,
 <matplotlib.lines.Line2D at 0x1889d14e130>,
 <matplotlib.lines.Line2D at 0x1889d14e0d0>,
 <matplotlib.lines.Line2D at 0x1889d14eee0>,
 <matplotlib.lines.Line2D at 0x1889d14eb20>,
 <matplotlib.lines.Line2D at 0x1889d14e580>,
 <matplotlib.lines.Line2D at 0x1889d14ee50>,
 <matplotlib.lines.Line2D at 0x1889d14e9a0>,
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 <matplotlib.lines.Line2D at 0x1889d14e970>,
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 <matplotlib.lines.Line2D at 0x1889d14e880>,
 <matplotlib.lines.Line2D at 0x1889d14e6d0>,
 <matplotlib.lines.Line2D at 0x1889d6d7d00>,
 <matplotlib.lines.Line2D at 0x1889d6d7fa0>,
 <matplotlib.lines.Line2D at 0x1889d6d7f40>,
 <matplotlib.lines.Line2D at 0x1889d6d7b80>,
 <matplotlib.lines.Line2D at 0x1889d6d79a0>,
 <matplotlib.lines.Line2D at 0x1889d6d75e0>,
 <matplotlib.lines.Line2D at 0x1889d6d7130>,
 <matplotlib.lines.Line2D at 0x1889d6d7f10>]

在這里插入圖片描述

plt.plot(test_cum_return.index,test_cum_return,color="green")##收益率曲線

[<matplotlib.lines.Line2D at 0x1889e75bd00>]

在這里插入圖片描述

經比較發現，我們用MeanVariance得到的收益率曲線處于所有隨機生成組合的中上部，

Black-Litterman模型

定義函式

創建blacklitterman函式，計算后驗收益期望及協方差

def blacklitterman(returns,tau, P, Q): #協方差
  mu=returns.mean()
  sigma=returns.cov()
  pi1=mu
  ts = tau * sigma
  Omega = np.dot(np.dot(P,ts),P.T) * np.eye(Q.shape[0])
  middle = linalg.inv(np.dot(np.dot(P,ts),P.T) + Omega)  
  er = np.expand_dims(pi1,axis=0).T + np.dot(np.dot(np.dot(ts,P.T),middle),
                      (Q - np.expand_dims(np.dot(P,pi1.T),axis=1)))
  posteriorSigma = sigma + ts - np.dot(ts.dot(P.T).dot(middle).dot(P),ts)
  return [er, posteriorSigma]

繼續延用前面五只股票資產分配的例子，zip里要加上投資者的個人觀點進行分析，現在假設某股票分析師認為白云機場、華夏銀行、浙能電力、生益科技四只股票的日均收益率將達到0.3%；兩只交通類股票白云機場和福建高速的日均收益將比浙能電力高0.1%，以此為根據構建個人觀點，

下面將構建投資人的個人觀點，構建資產選擇矩陣P，假設分析師認為：

前四只股票日均收益率為日均0.3%
q1只交通股日均收益比浙能電力高0.1%

pick1=np.array([1,0,1,1,1])
pick1

array([1, 0, 1, 1, 1])

q1=np.array([0.003*4])
q1

array([0.012])

pick2=np.array([0.5,0.5,0,0,-1])
pick2

array([ 0.5,  0.5,  0. ,  0. , -1. ])

q2=np.array([0.001])
q2

array([0.001])

P=np.array([pick1,pick2])
P

array([[ 1. ,  0. ,  1. ,  1. ,  1. ],
       [ 0.5,  0.5,  0. ,  0. , -1. ]])

Q=np.array([q1,q2])
Q

array([[0.012],
       [0.001]])

blacklitterman函式輸出值res第一個內容為后驗分布期望，第二個內容為后驗分布協方差
blacklitterman函式輸入值第一個為股票歷史收益率，第二個為主觀觀點相對于先驗資訊的比重，第三、四個為代表投資人的看法，

res=blacklitterman(sh_return,0.1,P,Q)

res

[array([[0.00145304],
        [0.0012935 ],
        [0.00171238],
        [0.00159785],
        [0.00166382]]),
           fjgs      zndl      sykj      hxyh      byjc
 fjgs  0.000138  0.000114  0.000134  0.000093  0.000133
 zndl  0.000114  0.000211  0.000145  0.000108  0.000132
 sykj  0.000134  0.000145  0.001076  0.000118  0.000234
 hxyh  0.000093  0.000108  0.000118  0.000154  0.000131
 byjc  0.000133  0.000132  0.000234  0.000131  0.000643]

p_mean=pd.DataFrame(res[0],index=sh_return.columns,columns=['posterior_mean'])
p_mean

	posterior_mean
fjgs	0.001453
zndl	0.001294
sykj	0.001712
hxyh	0.001598
byjc	0.001664

以上就是五只股票的后驗收益期望值

res[1]

	fjgs	zndl	sykj	hxyh	byjc
fjgs	0.000138	0.000114	0.000134	0.000093	0.000133
zndl	0.000114	0.000211	0.000145	0.000108	0.000132
sykj	0.000134	0.000145	0.001076	0.000118	0.000234
hxyh	0.000093	0.000108	0.000118	0.000154	0.000131
byjc	0.000133	0.000132	0.000234	0.000131	0.000643

創建blminVar函式，輸出最優資產配比

以上就是五只股票的后驗分布協方差

得到了后驗收益的期望值和協方差之后，我們就可以利用Markowitz模型進行資產的配置，我們定義新的函式blminVar()以求解資產配置權重，

輸入變數有blacklitterman函式輸出值（blres）和投資人的目標收益率（goalRet），
輸出值為各只股票的資產配比，

def blminVar(blres,goalRet): #輸出最優資產配比
        covs=np.array(blres[1])
        means=np.array(blres[0])
        L1=np.append(np.append((covs.swapaxes(0,1)),[means.flatten()],0),
                               [np.ones(len(means))],0).swapaxes(0,1)
        L2=list(np.ones(len(means)))
        L2.extend([0,0])
        L3=list(means)
        L3=means
        #L3.extend([0,0])
        L3=np.append(L3,0)
        L3=np.append(L3,0)
        L4=np.array([L2,L3])
        L=np.append(L1,L4,0)
        results=linalg.solve(L,np.append(np.zeros(len(means)),[1,goalRet],0))
        return(pd.DataFrame(results[:-2],
                            index=blres[1].columns,columns=['p_weight']))

看不懂就拆開看的：

means=np.array(res[0])
means

array([[0.00145304],
       [0.0012935 ],
       [0.00171238],
       [0.00159785],
       [0.00166382]])

covs=np.array(res[1])
covs

array([[1.38431847e-04, 1.14441282e-04, 1.33778102e-04, 9.26090407e-05,
        1.33487719e-04],
       [1.14441282e-04, 2.10899253e-04, 1.45080724e-04, 1.08488731e-04,
        1.32170134e-04],
       [1.33778102e-04, 1.45080724e-04, 1.07565619e-03, 1.18352813e-04,
        2.34291648e-04],
       [9.26090407e-05, 1.08488731e-04, 1.18352813e-04, 1.53747653e-04,
        1.31375380e-04],
       [1.33487719e-04, 1.32170134e-04, 2.34291648e-04, 1.31375380e-04,
        6.43349060e-04]])

len(means)

np.zeros(len(means))

array([0., 0., 0., 0., 0.])

np.append(np.zeros(len(means)),[1,0.75/280],0)

array([0.        , 0.        , 0.        , 0.        , 0.        ,
       1.        , 0.00267857])

 L1=np.append(np.append((covs.swapaxes(0,1)),[means.flatten()],0),
                               [np.ones(len(means))],0).swapaxes(0,1)
L1

array([[1.38431847e-04, 1.14441282e-04, 1.33778102e-04, 9.26090407e-05,
        1.33487719e-04, 1.45304284e-03, 1.00000000e+00],
       [1.14441282e-04, 2.10899253e-04, 1.45080724e-04, 1.08488731e-04,
        1.32170134e-04, 1.29350239e-03, 1.00000000e+00],
       [1.33778102e-04, 1.45080724e-04, 1.07565619e-03, 1.18352813e-04,
        2.34291648e-04, 1.71238140e-03, 1.00000000e+00],
       [9.26090407e-05, 1.08488731e-04, 1.18352813e-04, 1.53747653e-04,
        1.31375380e-04, 1.59785088e-03, 1.00000000e+00],
       [1.33487719e-04, 1.32170134e-04, 2.34291648e-04, 1.31375380e-04,
        6.43349060e-04, 1.66382178e-03, 1.00000000e+00]])

L2=list(np.ones(len(means)))
L2.extend([0,0])
#L3=list(means)
L3=means
#L3.extend([0,0])
L3=np.append(L3,0)
L3=np.append(L3,0)
L3

array([0.00145304, 0.0012935 , 0.00171238, 0.00159785, 0.00166382,
       0.        , 0.        ])

L4=np.array([L2,L3])
L=np.append(L1,L4,0)
L3

array([0.00145304, 0.0012935 , 0.00171238, 0.00159785, 0.00166382,
       0.        , 0.        ])

results=linalg.solve(L,np.append(np.zeros(len(means)),[1,0.75/252],0))
results

array([-2.28108358e-01, -4.11299682e+00,  5.06477940e-01,  4.29626690e+00,
        5.38360342e-01, -1.99335214e+00,  2.86120684e-03])

帶例子計算結果去啦！

blminVar(res,0.75/252)  #年收益率為75%，一年252天是交易日

	p_weight
fjgs	-0.228108
zndl	-4.112997
sykj	0.506478
hxyh	4.296267
byjc	0.538360

blminVar(res,0.75/280) #最優資產配置，0.75期望收益，280

	p_weight
fjgs	-0.071785
zndl	-3.272995
sykj	0.403138
hxyh	3.516868
byjc	0.424774

blminVar(res,0.15/280)

	p_weight
fjgs	1.053747
zndl	2.775015
sykj	-0.340909
hxyh	-2.094806
byjc	-0.393046

以上就是各種配比，做完啦！！！！晚安好夢！

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標籤：python

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Tushare Day7—— 第19章投資組合理論及拓展

投資組合的收益率與風險

不同相關系數下投資組合標準差隨投資比例變動的情況

設定calc_mean函式為采用的投資組合方式

以x/50為權重（其中x屬于0到50）進行投資組合（其實就是0到1中間等距抽權重）

計算不同相關系數的股票組合對應收益值

不同相關系數均值和標準差關系圖

Markowitz模型實作

獲取各只股票日線行情資料

計算每只股票的日收益率（個股回報率）并將其合并

了解各股票的日收益率及累計收益率時序圖

了解各股票之間的相關性

定義MeanVariance類，通過輸入收益率序列計算最優資產比例，繪制最小方差前緣曲線

定義MeanVariance類及類內函式

呼叫minvar函式計算最小方差

呼叫frontierCurve繪制效率前沿曲線

將資料拆分為訓練和測驗資料，輸出根據訓練資料計算的效率前沿曲線

給定收益率下，計算方差最小時對應的五種股票的比例權重

繪制收益率曲線

與隨機生成的組合進行比較

Black-Litterman模型

創建blacklitterman函式，計算后驗收益期望及協方差

創建blminVar函式，輸出最優資產配比

看不懂 就拆開看的：

帶例子計算結果去啦！

看不懂就拆開看的：