投资组合分析：portfolio_analysis.Tangenvy_portfolio(切点组合)

实证资产定价（Empirical asset pricing）已经发布于Github和Pypi. 包的具体用法(Documentation)博主将会陆续在CSDN中详细介绍，也可以通过Pypi直接查看。

Pypi: pip install --upgrade EAP

Github: GitHub - whyecofiliter/EAP: empirical asset pricing

切点组合是有效前沿上最大夏普比率的组合，它与无风险利率的连线正切于风险资产的投资组合前沿。计算切点组合可以考察新加入的资产或投资组合是否显著影响切点组合，即新加入的资产是否有助于分散化风险和提高收益。如果新加入资产显著地影响切点组合，则说明它提供了已有资产无法提供的更有效的收益风险组合；如果新加入资产没有显著地影响切点组合，则说明它没有提供更有效的收益风险组合，这说明这项资产对提高投资效率或是夏普率没有实质的影响。

切点组合的计算方法为

上式中，t是切点组合的权重，u是资产的收益率，rf是无风险利率，sigma是资产收益率的协方差矩阵。

计算切点组合用的是portfolio_analysis.Tangency_portfolio。具体地说

def test_tangency_portfolio():
    '''
    This function is for testing rangency_portfolio
    '''
    import numpy as np
    from portfolio_analysis import Tangency_portfolio as tanport
    
    # construct the sample data 1
    mu = np.array([0.0427, 0.0015, 0.0285])
    cov_mat = np.mat([[0.01, 0.0018, 0.0011], [0.0018, 0.0109, 0.0026], [0.0011, 0.0026, 0.0199]])
    rf = 0.005
    
    # calculate the weight and the sharpe ratio
    portfolio = tanport(rf, mu, cov_mat)
    print(portfolio._portfolio_weight())
    print(portfolio.fit())
    portfolio.print()

    # construct the sample data 2
    mu = np.array([0.0427, 0.0015, 0.0285, 0.0028])
    cov_mat = np.mat([[0.01, 0.0018, 0.0011, 0], [0.0018, 0.0109, 0.0026, 0], [0.0011, 0.0026, 0.0199, 0], [0, 0, 0, 0.1]])
    rf = 0.005
    
    # calculate the weight and the sharpe ratio
    portfolio = tanport(rf, mu, cov_mat)
    print(portfolio._portfolio_weight())
    print(portfolio.fit())
    portfolio.print()

test_tangency_portfolio()

================================================================================================================================
[[ 1.02682298]
 [-0.32625112]
 [ 0.29942815]]
(matrix([[ 1.02682298],
        [-0.32625112],
        [ 0.29942815]]), 0.4202276695645767)
+--------+---------+----------+---------+
| Weight |  asset1 |  asset2  |  asset3 |
+--------+---------+----------+---------+
|        | 1.02682 | -0.32625 | 0.29943 |
+--------+---------+----------+---------+
[[ 1.03285649]
 [-0.32816815]
 [ 0.30118756]
 [-0.00587591]]
(matrix([[ 1.03285649],
        [-0.32816815],
        [ 0.30118756],
        [-0.00587591]]), 0.42028525345017165)
+--------+---------+----------+---------+----------+
| Weight |  asset1 |  asset2  |  asset3 |  asset4  |
+--------+---------+----------+---------+----------+
|        | 1.03286 | -0.32817 | 0.30119 | -0.00588 |
+--------+---------+----------+---------+----------+