JQData | 基于JQData的有效前沿及投资组合优化

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基于JQData的有效前沿组合及投资组合优化

转自 https://www.joinquant.com/community/post/detailMobile?postId=15331&page=&limit=20&replyId=&tag=

（1）现代资产组合理论（MTP）是关于在特定风险水平下投资者（风险厌恶）如何构建组合来最大化期望收益的理论，这一理论最基本的原则是投资者可以构建投资组合的有效集合，即有效前沿，有效前沿可以在特定风险水平下使期望收益最大化；
（2）资产的风险一般使用资产回报的波动方差来表示，在回报和风险相权衡的时候，根据资本资产定价模型(CAPM)一般使用夏普率来评估风险回报比，来衡量特定风险下投资收益的表现，希望在尽可能小的风险下获得最大的回报；
（3）下面介绍通过JQData及Monte Carlo模拟来建立有效前沿组合，然后找出最优组合和有着最低波动率的组合。

1 通过JQData获取数据

# 导入所需的python库
import jqdatasdk as jq
import pandas as pd
import numpy as np
import matplotlib.pyplot as plt# JQData认证
jq.auth('注册手机号', '密码')# 设置起止时间及股票池
start_date = '2018-01-01'
end_date = '2018-11-16'
security_list = ['513100.XSHG', '518800.XSHG', '163407.XSHE', '159926.XSHE']# 获取数据
stocks_price = jq.get_price(security_list, start_date=start_date, end_date=end_date, fields=['close'])['close']
stocks_price.head()

auth success

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	513100.XSHG	518800.XSHG	163407.XSHE	159926.XSHE
2018-01-02	2.218	2.730	1.889	105.0
2018-01-03	2.248	2.735	1.915	105.0
2018-01-04	2.256	2.729	1.904	105.0
2018-01-05	2.250	2.740	1.892	105.0
2018-01-08	2.268	2.740	1.881	105.0

2 通过Monte Carlo模拟产生有效前沿组合，并找出最优组合和有着最低波动率的组合

通过Monte Carlo模拟50000个不同权重的投资组合产生的不同期望收益和期望波动率并绘图。有效前沿上的每个点代表了股票的一个最优组合，最优组合在特定的风险水平下最大化了期望收益率。

# 通过Monte Carlo模拟产生有效前沿组合returns_daily = stocks_price.pct_change()
returns_annual = returns_daily.mean() * 250cov_daily = returns_daily.cov()
cov_annual = cov_daily * 250port_returns = []
port_volatility = []
sharpe_ratio = []
stock_weights = []num_assets = len(security_list)
num_portfolios = 50000np.random.seed(101)for single_portfolio in range(num_portfolios):weights = np.random.random(num_assets)weights /= np.sum(weights)returns = np.dot(weights, returns_annual)volatility = np.sqrt(np.dot(weights.T, np.dot(cov_annual, weights)))sharpe = returns / volatilitysharpe_ratio.append(sharpe)port_returns.append(returns)port_volatility.append(volatility)stock_weights.append(weights)portfolio = {'Returns': port_returns,'Volatility': port_volatility,'Sharpe Ratio': sharpe_ratio}for counter,symbol in enumerate(security_list):portfolio[symbol+' Weight'] = [Weight[counter] for Weight in stock_weights]df = pd.DataFrame(portfolio)
column_order = ['Returns', 'Volatility', 'Sharpe Ratio'] + [stock+' Weight' for stock in security_list]
df = df[column_order]
df.head()

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	Returns	Volatility	Sharpe Ratio	513100.XSHG Weight	518800.XSHG Weight	163407.XSHE Weight	159926.XSHE Weight
0	0.059716	0.092775	0.643661	0.401223	0.443388	0.022123	0.133266
1	0.038346	0.088553	0.433024	0.251963	0.306608	0.112865	0.328564
2	0.024950	0.121362	0.205584	0.396923	0.104486	0.304882	0.193709
3	-0.055661	0.092769	-0.600004	0.084002	0.362809	0.445883	0.107306
4	-0.054688	0.089040	-0.614192	0.049376	0.356635	0.430760	0.163229

# 将投资组合绘制出来plt.style.use('ggplot')
df.plot.scatter(x='Volatility', y='Returns', c='Sharpe Ratio',cmap='autumn', edgecolors='black', figsize=(15, 9), grid=True)
plt.xlabel('Volatility (Std. Deviation)')
plt.ylabel('Expected Returns')
plt.title('Efficient Frontier')
plt.show()

# 找出最优组合和有着最低波动率的组合min_volatility = df['Volatility'].min()
max_sharpe = df['Sharpe Ratio'].max()sharpe_portfolio = df.loc[df['Sharpe Ratio'] == max_sharpe]
min_variance_port = df.loc[df['Volatility'] == min_volatility]plt.style.use('ggplot')
df.plot.scatter(x='Volatility', y='Returns', c='Sharpe Ratio',cmap='autumn', edgecolors='black', figsize=(15, 9), grid=True)
plt.scatter(x=sharpe_portfolio['Volatility'], y=sharpe_portfolio['Returns'], c='yellow', marker='D', s=200)
plt.scatter(x=min_variance_port['Volatility'], y=min_variance_port['Returns'], c='red', marker='D', s=200 )
plt.xlabel('Volatility (Std. Deviation)')
plt.ylabel('Expected Returns')
plt.title('Efficient Frontier')
plt.show()

# 接下来输出这两个特殊组合的具体信息：pd.concat([min_variance_port.T, sharpe_portfolio.T], axis=1)

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	1195	17048
Returns	-0.009542	0.119439
Volatility	0.056354	0.148343
Sharpe Ratio	-0.169316	0.805155
513100.XSHG Weight	0.082041	0.616620
518800.XSHG Weight	0.763013	0.014128
163407.XSHE Weight	0.086762	0.002443
159926.XSHE Weight	0.068184	0.366809