Python--投资组合

import sys
sys.path.append("E:/Python/tushare-0.6.8/")import tushare as ts
import pandas as pd
import pandas as pd
import numpy as np
import statsmodels.api as sm #统计运算
import scipy.stats as scs #科学计算
import matplotlib.pyplot as plt #绘图a=ts.get_hist_data('600848',start='2016-11-01',end='2017-01-02')
a=a['close']
a.name = '600848'b=ts.get_hist_data('000002',start='2016-11-01',end='2017-01-02')
b=b['close']
b.name='000002'c=ts.get_hist_data('002285',start='2016-11-01',end='2017-01-02')
c=c['close']
c.name='002285'd=pd.DataFrame([a,b,c])
##转置
data=d.T
##回报率
returns = np.log(data / data.shift(1))
##年化收益率
returns.mean()*252
##计算协方差矩阵
returns.cov()*252##计算股票个数
noa=len(data.T)##随机生成初始化权重
weights = np.random.random(noa)
##计算百分比
weights /= np.sum(weights)
weights##下面通过一次蒙特卡洛模拟，产生大量随机的权重向量，并记录随机组合的预期收益和方差。
port_returns = []port_variance = []for p in range(4000):weights = np.random.random(noa)weights /=np.sum(weights)port_returns.append(np.sum(returns.mean()*252*weights))port_variance.append(np.sqrt(np.dot(weights.T, np.dot(returns.cov()*252, weights))))
##因为要开更号，所以乘两次weight
##dot就是点乘 
port_returns = np.array(port_returns)
port_variance = np.array(port_variance)#无风险利率设定为4%
risk_free = 0.04
plt.figure(figsize = (8,4))
plt.scatter(port_variance, port_returns, c=(port_returns-risk_free)/port_variance, marker = 'o')
plt.grid(True)
plt.xlabel('excepted volatility')
plt.ylabel('expected return')
plt.colorbar(label = 'Sharpe ratio')##投资组合优化1——sharpe最大def statistics(weights):weights = np.array(weights)port_returns = np.sum(returns.mean()*weights)*252port_variance = np.sqrt(np.dot(weights.T, np.dot(returns.cov()*252,weights)))return np.array([port_returns, port_variance, port_returns/port_variance])#最优化投资组合的推导是一个约束最优化问题
import scipy.optimize as sco#最小化夏普指数的负值
def min_sharpe(weights):return -statistics(weights)[2]#约束是所有参数(权重)的总和为1。这可以用minimize函数的约定表达如下
cons = ({'type':'eq', 'fun':lambda x: np.sum(x)-1})#我们还将参数值(权重)限制在0和1之间。这些值以多个元组组成的一个元组形式提供给最小化函数
bnds = tuple((0,1) for x in range(noa))opts = sco.minimize(min_sharpe, noa*[1./noa,], method = 'SLSQP', bounds = bnds, constraints = cons)opts##sharpe最大的组合3个统计数据分别为：#预期收益率、预期波动率、最优夏普指数statistics(opts['x']).round(3)##通过方差最小来选出最优投资组合。def min_variance(weights):return statistics(weights)[1]
optv = sco.minimize(min_variance, noa*[1./noa,],method = 'SLSQP', bounds = bnds, constraints = cons)optv##方差最小的最优组合权重向量及组合的统计数据分别为：
optv['x'].round(3)#得到的预期收益率、波动率和夏普指数
statistics(optv['x']).round(3)