Backtesting trading strategies

Last Update February 25, 2021

Matteo Bottacini, matteo.bottacini@usi.ch

Project description

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

Trading strategy configuration

Each model is setup in its specific scripts.

Equally weighted portfolio

def equally_weighted_portfolio(ret):
    init_weights = [1 / len(ret.columns)] * len(ret.columns)
    opt_weights = init_weights

    return opt_weights

Risk parity portfolio

def risk_parity_portfolio(ret):
    init_guess = 1 / ret.std()
    opt_weights = list(init_guess / init_guess.sum())

    return opt_weights

Minimum variance portfolio

import 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

Mean-variance portfolio

# 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_weights

Backtest configuration

In 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

Results

Supported versions

This configuration has been tested against Python 3.8