In this article, I showed how to combine zipline with pypfopt in order to backtest trading strategies based on mean-variance optimization. We might want to rebalance back to 50–50 by selling some of X and buying more Y. As a result, asset X constitutes 65% of our portfolio’s worth, while Y has only 35%. Over a month, the price of X increased sharply while the price of Y decreased. Why? We can imagine that we hold a portfolio of two assets X and Y and at the beginning of the investment horizon the allocation is 50–50. What often happens in practice is that the portfolio is rebalanced every X days to bring the allocation back to 1/n. To keep it simple, we do not do any rebalancing. The idea is very simple - on the first day of the test, we allocate 1/n% of our total capital to each of the considered n assets. We start by creating a simple benchmark strategy - the **1/n portfolio**. the first trading decision is made on the last day of December, but the orders are executed on the first trading day of January 2016.when performing optimization, the investor considers 252 past trading days to calculate the historical returns and covariance matrix.there is no short selling (the investor can only sell what he/she currently owns).the investor can only invest in the following stocks: Tesla, Microsoft, Facebook, Twitter.the investment horizon covers years 2016–2017.In this article we use the following problem setting: Which results in the following weights: įor convenience, we use the clean_weights() method, as it truncates very small weights to zero and rounds the rest.
We obtain the weights maximizing the Sharpe ratio by running the following lines of code: # get weights maximizing the Sharpe ratio ef = EfficientFrontier(avg_returns, cov_mat) weights = ef.max_sharpe() cleaned_weights = ef.clean_weights() cleaned_weights # calculate expected returns and sample covariance amtrix avg_returns = expected_an_historical_return(prices_df) cov_mat = risk_models.sample_cov(prices_df) Pypfopt allows us to easily calculate the expected returns and the covariance matrix directly from the prices, with no need for converting to returns beforehand.
A key concept connected to the mean-variance analysis is the Efficient Frontier - a set of optimal portfolios providing the highest expected portfolio return for a given level of risk - or framing it differently - providing the minimum level of risk for the expected portfolio return. We will not go deeply into the assumptions of MPT, but the main ones are that all investors share the goal of maximizing the returns on investment while avoiding as much risk as possible, they can borrow and lend money at the risk-free rate (without limits) and the transaction costs are not taken into account.īased on all of the above, the mean-variance analysis is the process of finding optimal asset allocation that provides the best trade-off between the expected return and risk (measured as the variance of returns).
#Vector magic 1.14 key series
This is the fifth part of a series of articles on backtesting trading strategies in Python. Learn how to create and implement trading strategies using Markowitz’s optimization!
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