2024马科维兹投资组合时间探索.py

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#               马科维兹投资组合实践探索
#
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import tushare as ts 
import pandas as pd 
import numpy as np 
import statsmodels.api as sm 
import scipy.stats as scs 
import matplotlib.pyplot as plt 

data = pd.DataFrame 
data1= ts.get_hist_data('600000.SH,'20240101','20250101')
data1= data1['close']
data1=data1[:,-1]
data['600000.SH']=data1 

data2= ts.get_hist_data('600000.SH,'20240101','20250101')
data2= data2['close']
data2=data2[:,-1]
data['600001.SH']=data2

data3= ts.get_hist_data('600000.SH,'20240101','20250101')
data3= data3['close']
data3=data3[:,-1]
data['600002.SH']=data3


data=data.dropna()
data.head()

##可视化后的时序数据为
data.plot(figsize=(8,4))


## 2 计算不同证券的均值，协方差和相关系数

returns = np.log(data/data.shift(1))
returns.mean() * 252 

returns.cov()

returns.corr()

## 3 给不同资产随机分配初始权重；
noa = 3 
weights = np.random.random(noa)
weights /= np.sum(weights)
weights
array([0.288,0.103,0.608])

## 4 计算组合预期收益率，组合方差，和组合标准差
np.sum(returns.mean()*weights)

np.dot(weights.T,np.dot(returns.cov(),weights))

np.sqrt(np.dot(weights.T,np.dot(returns.cov(),weights)))

## 5 用蒙特卡洛模拟产生大量随机组合；

port_returns=[ ]
port_variance=[ ]
for p in range(5000):
  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))))
  port_returns = np.array(port_returns)
  port_variance = np.array(port_variance)
  #无风险利率设定为1.5%
  risk_free=0.015
  plt.figure(figsize=(8,4))
  plt.scatter(port_variance,port_returns,c=(port_returns-risk_free)/port_variace,marker="o")
  plt.grid(True)
  plt.xlabel('volatility')
  plt.ylabel('expected return')
  plt.colorbar(label="Sharpe ratio")
  plt.legend()
  plt.show()
  
# 6 夏普比最大的最优资产组合；

 def statistics(weights):
   weights = np.array(weights)
   port_returns = np.sum(returns.mean()*weights)*252 
   port_variance=np.sqrt(np.dot(weights.T,np.dot(returns.cov()*252,weights)))
   return np.array([port_returns,port_variance,(port_return-risk_free)/port_variance])
   # 最优组合的推倒是一个约束条件下最优问题，引入optimize 函数；
   import scipy.optimize as sco 
   # 最小化夏普比的负值；
    def min_sharpe(weights):
      return-statistics(weights)[2]
   # 约束所有参数总和为1
   cons=({'type':'eq','fun';lambda x; np.sum(x) - 1})
   # 参数的权重限制在0~1之间；
   bnds = tuple((0,1) for x in range(noa))
   # 优化函数调用中忽略的唯一输入是起始参数列表
   opts = sco.minimize(min_sharpe,noa*[1./noa,],method='SLSQP',bounds=bnds,constraints=cons)
   opts 

opts['x'].round(3)
statistics(opts['x'].round(4))

# 7 方差最小的最优资产组合

def min_variance(weights):
  return statistics(weights)[1]
 optv= sco.minimize(min_variance,noa*[1./noa,],method='SLSQP',bounds=bnds,consttraints=cons)
 optv 
optv['x'].round(4)

statistics(optv['x']).round(4)


# 8 资产组合的有效边界

def min_variance(weights):
  return statistics(weights)[1]

# 在不同目标收益水平  target_returns循环时，最优化的一个约束条件会变化；
target_returns = np.linspace(0.0,0.5,50)
target_variance = [ ]

for tar in target_returns:
  cons = ({'type':'eq','fun':lambda x:statistics(x)[0] - tar},{'type':'eq','fun':lambda x:np.sum(x) - 1})
  res = sco.minizime(min_variance,noa*[1./noa,],method='SLSQP',bounds=bnds,constraints=cons)
  target_variance.append(res['fun'])
  target_variance= np.array(target_variace)
  
## 下面是最优化结果的战士。深色星：夏普比最大的投资组合; 浅色星：方差最小的投资组合；

plt.figure(figsize=(8,4))
plt.scatter(port_variance,port_returns,c=port_returns/port_variance,marker='o')
plt.scatter(target_variance,target_returns,c=target_returns/target_variance,marker='x')

plt.plot(statistics(opts['x'])[1],statistics(opts['x'])[0],'r*',markersize=15.0)
plt.plot(statistics(opts['x'])[1],statistics(opts['x'])[0],'y*',markersize=15.0)

plt.grid(True)
plt.xlabel('volatility')
plt.ylabel('expected return')
plt.colorbar(label='Sharpe ratio')
plt.legend()
plt.show()




















## 单项资产的期望收益和风险的估计量及Python应用；

from pandas import Series,DataFrame
import pandas as pd 
import numpy as np 

df = Series([])

np.mean(df)
np.var(df)
np.std(df)

# r均值与标准差差*2

## 单资产之间的协方差与相关系数及Python应用

df.var()
var(df)
df.cov()
df.corr()

## 多资产组合的期望与风险；
def portvar(x,y)
return x.T*v*x


## 资产组合均值方差模型；

import pandas as pd 
from numpy as *
import matplot.pyplot as plt 
r1 = 0.06
sigma1 = 0.12 
r2 = 0.11 
sigma2 = 0.22
rho = 0.19 
covar = rho*sigma1*sigma2 
x= pd.Series([0,.1,.2,.3,.4,.5,.6,.7,.8,1])

variance = x * 2 * sigma1 * *2 +(1-x)* * 2*sigma2* * 2 + 2 * x*(1-x)*covar 

sigma = sqrt(variance)

ret = x*r1 + (1-r)*r2 
print(x;sigma;ret)

plt.plot(sigma,ret,"k-o")