Matteo Bottacini, [email protected]
This project is to backtest different trading strategies applying different approaches from the Modern Portfolio Tehory (MPT) in Python 3.
The strategies backtested are:
- The Optimal Markowitz Portfolio;
- The Global Minimum Variance Portfolio;
- The Risk-Parity Portfolio;
- The Equally Weighted Portfolio
The ETFs considered are:
- EEM: iShares MSCI Emerging Markets ETF
- EMLC: VanEck Vectors J.P. Morgan EM Local Currency Bond ETF
- IAU: iShares Gold Trust
- IEF: iShares 7-10 Year Treasury Bond ETF
- IWM: iShares Russell 2000 ETF
- SPY: SPDR S&P 500 ETF Trust
- TIP: iShares TIPS Bond ETF
- TLT: iShares 20+ Year Treasury Bond ETF
- VGK: Vanguard FTSE Europe Index Fund ETF Shares
The scripts do the following:
- Download and analyse financial data;
- Find the optimal Markowtiz portfolio (mean-variance);
- Find the Global Minimum Variance (GMV) portfolio (minimum variance);
- Find the risk-parity portfolio (risk parity);
- Find the equally weighted portfolio (equally weighted);
- Backtest a trading strategy with monthly rebalance with out-of-the-sample results;
- Compare the results.
Folder structure:
trading-strategy-backtest/
deliverable/
run_backtest.py
src/
equally_weighted_portfolio.py
mean_variance_portfolio.py
minimum_variance_portfolio.py
risk_parity_portoflio.py
README.md
Each model is setup in its specific scripts.
def equally_weighted_portfolio(ret):
init_weights = [1 / len(ret.columns)] * len(ret.columns)
opt_weights = init_weights
return opt_weightsdef risk_parity_portfolio(ret):
init_guess = 1 / ret.std()
opt_weights = list(init_guess / init_guess.sum())
return opt_weightsimport numpy as np
from scipy.optimize import minimize
def minimum_variance_portfolio(ret):
# define objective function to minimize: variance
def get_portfolio_variance(weights):
weights = np.array(weights) # check
cov_mat = ret.cov()
port_variance = np.dot(weights.T, np.dot(cov_mat, weights))
return port_variance
# equality constraint: sum of the weights = 1
def weight_cons(weights):
return np.sum(weights) - 1
# model set-up
# - long only portfolio
# - initial guess
# - constraints
bounds_lim = ((0, 1),) * len(ret.columns)
init_weights = [1 / len(ret.columns)] * len(ret.columns)
constraint = {'type': 'eq', 'fun': weight_cons}
# find optimal portfolio
opt_port = minimize(fun=get_portfolio_variance,
x0=init_weights,
bounds=bounds_lim,
constraints=constraint,
method='SLSQP')
# find optimal weights
opt_weights = list(opt_port['x'])
return opt_weights# import modules
import numpy as np
from scipy.optimize import minimize
def mean_variance_portfolio(ret):
# define objective function to minimize: sharpe ratio
def get_portfolio_sr(weights):
weights = np.array(weights) # check
# expected returns
port_ret = np.dot(ret, weights)
mean_ret = port_ret.mean()
# volatility
cov_mat = ret.cov()
port_std = np.sqrt(np.dot(weights.T, np.dot(cov_mat, weights)))
# sharpe ratio
port_sr = mean_ret / port_std
return port_sr
def objective_fun(weights):
neg_sr = get_portfolio_sr(weights) * (-1)
return neg_sr
# equality constraint: sum of the weights = 1
def weight_cons(weights):
return np.sum(weights) - 1
# model set-up
# - long only portfolio
# - initial guess
# - constraints
bounds_lim = ((0, 1),) * len(ret.columns)
init_weights = [1 / len(ret.columns)] * len(ret.columns)
constraint = {'type': 'eq', 'fun': weight_cons}
# find optimal portfolio
opt_port = minimize(fun=objective_fun,
x0=init_weights,
bounds=bounds_lim,
constraints=constraint,
method='SLSQP')
# find optimal weights
opt_weights = list(opt_port['x'])
return opt_weightsIn the script ../deliverable/run_backtest.py you can change the main variables to spot your ideal asset allocation and strategy.
The parameters you can change are the following:
- Assets;
- Length of the training set
# feel free to change the following parameters:
tickers = []
months_training_set = 12 * 5
This configuration has been tested against Python 3.8