okama.EfficientFrontier.mdp_points

property EfficientFrontier.mdp_points

Generate Most diversified portfolios frontier.

Each point on the Most diversified portfolios frontier is a portfolio with optimized Diversification ratio for a given return.

The points are obtained through the constrained optimization process (optimization with bounds). Bounds are defined with ‘bounds’ property.

Returns:

DataFrame

Table of weights and risk/return values for the Efficient Frontier. The columns:

• assets weights

• CAGR (geometric mean)

• Mean return (arithmetic mean)

• Risk (standard deviation)

• Diversification ratio

All the values are annualized.

Examples

>>> ls4 = ['SP500TR.INDX', 'MCFTR.INDX', 'RGBITR.INDX', 'GC.COMM']
>>> y = ok.EfficientFrontier(assets=ls4, ccy='RUB', last_date='2021-12', n_points=100)
>>> y.mdp_points  # print mdp weights, risk, mean return, CAGR and Diversification ratio
        Risk  Mean return      CAGR  ...    MCFTR.INDX   RGBITR.INDX  SP500TR.INDX
0   0.066040     0.094216  0.092220  ...  2.081668e-16  1.000000e+00  0.000000e+00
1   0.064299     0.095342  0.093451  ...  0.000000e+00  9.844942e-01  5.828671e-16
2   0.062761     0.096468  0.094670  ...  0.000000e+00  9.689885e-01  1.110223e-16
3   0.061445     0.097595  0.095874  ...  5.828671e-16  9.534827e-01  0.000000e+00
4   0.060364     0.098724  0.097065  ...  3.191891e-16  9.379769e-01  0.000000e+00
..       ...          ...       ...  ...           ...           ...           ...
95  0.258857     0.205984  0.178346  ...  8.840844e-01  1.387779e-17  0.000000e+00
96  0.266583     0.207214  0.177941  ...  9.130633e-01  3.469447e-18  0.000000e+00
97  0.274594     0.208446  0.177432  ...  9.420422e-01  0.000000e+00  1.075529e-16
98  0.282873     0.209678  0.176820  ...  9.710211e-01  2.428613e-17  6.938894e-18
99  0.291402     0.210912  0.176103  ...  1.000000e+00  2.775558e-16  3.951094e-09
[100 rows x 8 columns]

To plot the Most diversification portfolios line use the DataFrame with the points data. Additionaly ‘Plot.plot_assets()’ can be used to show the assets in the chart.

>>> import matplotlib.pyplot as plt
>>> fig = plt.figure()
>>> # Plot the assets points
>>> y.plot_assets(kind='cagr')  # kind should be set to "cagr" as we take "CAGR" column from the ef_points.
>>> ax = plt.gca()
>>> # Plot the Most diversified portfolios line
>>> df = y.mdp_points
>>> ax.plot(df['Risk'], df['CAGR'])  # we chose to plot CAGR which is geometric mean of return series
>>> # Set the axis labels and the title
>>> ax.set_title('Most diversified portfolios line')
>>> ax.set_xlabel('Risk (Standard Deviation)')
>>> ax.set_ylabel('Return (CAGR)')
>>> plt.show()