Pymarkowitz is an open source library for implementing portfolio optimisation. This library extends beyond the classical mean-variance optimization and takes into account a variety of risk and reward metrics, as well as the skew/kurtosis of assets.
Pymarkowitz can aid your decision-making in portfolio allocation in a risk-efficient manner. Pymarkowitz covers major objectives and constraints related with major types of risk and reward metrics, as well as simulation to examine the relationship between all these metrics. The flexibility in its implementation gives you the maximum discretion to customize and suit it to your own needs.
*Disclaimer: This library is for educational and entertainment purpose only. Please invest with due diligence at your own risk.
Head over to the directory demos to get an in-depth look at the project and its functionalities, or continue below to check out some brief examples.
install directly using pip
$ pip install pymarkowitzinstall from github
$ pip install git+https://github.com/johnsoong216/pymarkowitz.gitFor development purposes you can clone or fork the repo and hack right away!
$ git clone https://github.com/johnsoong216/pymarkowitz.gitFirst step is to import all availble modules
import numpy as np
import pandas as pd
from pymarkowitz import *Read data with pandas. The dataset is available in the datasets directory. I will select 15 random stocks with 1000 observations
sp500 = pd.read_csv("datasets/sp500_1990_2000.csv", index_col='DATE').drop(["Unnamed: 0"], axis=1)
selected = sp500.iloc[:1000, np.random.choice(np.arange(0, sp500.shape[1]), 15, replace=False)]Use a ReturnGenerator to compute historical mean return and daily return. Note that there are a variety of options to compute rolling/continuous/discrete returns. Please refer to the Return.ipynb jupyter notebook in demo directory
ret_generator = ReturnGenerator(selected)
mu_return = ret_generator.calc_mean_return(method='geometric')
daily_return = ret_generator.calc_return(method='daily')Use a MomentGenerator to compute covariance/coskewness/cokurtosis matrix and beta. Note that there are a variety of options to compute the comoment matrix and asset beta, such as with semivariance, exponential and customized weighting. Normalizing matrices are also supported. Please refer to the Moment(Covariance).ipynb jupyter notebook in demo directory
benchmark = sp500.iloc[:1000].pct_change().dropna(how='any').sum(axis=1)/sp500.shape[1]
cov_matrix = mom_generator.calc_cov_mat()
beta_vec = mom_generator.calc_beta(benchmark)Construct higher moment matrices by calling
coskew_matrix = mom_generator.calc_coskew_mat()
cokurt_matrix = mom_generator.calc_cokurt_mat()
coseventh_matrix = mom_generator.calc_comoment_mat(7)Construct an Optimizer
PortOpt = Optimizer(mu_return, cov_matrix, beta_vec)Please refer to the Optimization.ipynb jupyter notebook in demo directory for more detailed explanations.
Set your Objective.
### Call PortOpt.objective_options() to look at all available objectives
PortOpt.add_objective("min_volatility")Set your Constraints.
### Call PortOpt.constraint_options() to look at all available constraints.
PortOpt.add_constraint("weight", weight_bound=(-1,1), leverage=1) # Portfolio Long/Short
PortOpt.add_constraint("concentration", top_holdings=2, top_concentration=0.5) # Portfolio ConcentrationSolve and Check Summary
PortOpt.solve()
weight_dict, metric_dict = PortOpt.summary(risk_free=0.015, market_return=0.07, top_holdings=2)
# Metric Dict Sample Output
{'Expected Return': 0.085,
'Leverage': 1.0001,
'Number of Holdings': 5,
'Top 2 Holdings Concentrations': 0.5779,
'Volatility': 0.1253,
'Portfolio Beta': 0.7574,
'Sharpe Ratio': 0.5586,
'Treynor Ratio': 0.0924,
"Jenson's Alpha": 0.0283}
# Weight Dict Sample Output
{'GIS': 0.309, 'CINF': 0.0505, 'USB': 0.104, 'HES': 0.2676, 'AEP': 0.269}Simulate and Select the Return Format (Seaborn, Plotly, DataFrame). DataFrame Option will also have the random weights used in each iteration.
Please refer to the Simulation.ipynb jupyter notebook in demo directory for more detailed explanations.
### Call Portopt.metric_options to see all available options for x, y axis
PortOpt.simulate(x='expected_return', y='sharpe', y_var={"risk_free": 0.02}, iters=10000, weight_bound=(-1, 1), leverage=1, ret_format='sns')
Use pymarkowitz to construct optimized weights and backtest with real life portfolio. In this example, I am using SPDR sector ETFs to construct an optimized portfolio and compare against buy & hold SPY.
import bt
data = bt.get('spy, rwr, xlb, xli, xly, xlp, xle, xlf, xlu, xlv, xlk', start='2005-01-01')The configurations can be adjusted flexibly, please check backtesting.ipynb in demo directory for more detail. In this case we are minimizing volatility with a capped weight of 25% on each sector.
strategy = WeighMarkowitz(Config) #Imported from pymarkowitz.backtester.py
# Personal Strategy
s1 = bt.Strategy('s1', [bt.algos.RunWeekly(),
bt.algos.SelectAll(),
strategy,
bt.algos.Rebalance()])
test1 = bt.Backtest(s1, data)
# Buy & Hold
s2 = bt.Strategy('s2', [bt.algos.RunWeekly(),
bt.algos.SelectAll(),
bt.algos.WeighEqually(),
bt.algos.Rebalance()])
test2 = bt.Backtest(s2, data[['spy']].iloc[Config.lookback:])
res = bt.run(test1, test2)
res.plot()
Calculations of Correlation, Diversifcation & Risk Parity Factors:
https://investresolve.com/file/pdf/Portfolio-Optimization-Whitepaper.pdf
Calculations for Sharpe, Sortino, Beta, Treynor, Jenson's Alpha:
https://www.cfainstitute.org/-/media/documents/support/programs/investment-foundations/19-performance-evaluation.ashx?la=en&hash=F7FF3085AAFADE241B73403142AAE0BB1250B311
https://www.investopedia.com/terms/j/jensensmeasure.asp
https://www.investopedia.com/ask/answers/070615/what-formula-calculating-beta.asp
Calculations for Higher Moment Matrices:
https://cran.r-project.org/web/packages/PerformanceAnalytics/vignettes/EstimationComoments.pdf
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