Portfolio Optimization and Performance Evaluation

Alpha factors generate signals that an algorithmic strategy translates into trades, which, in turn, produce long and short positions. The returns and risk of the resulting portfolio determine the success of the strategy.

To test a strategy prior to implementation under market conditions, we need to simulate the trades that the algorithm would make and verify their performance. Strategy evaluation includes backtesting against historical data to optimize the strategy's parameters and forward-testing to validate the in-sample performance against new, out-of-sample data. The goal is to avoid false discoveries from tailoring a strategy to specific past circumstances.

In a portfolio context, positive asset returns can offset negative price movements. Positive price changes for one asset are more likely to offset losses on another, the lower the correlation between the two positions is. Based on how portfolio risk depends...

How to measure portfolio performance

To evaluate and compare different strategies or to improve an existing strategy, we need metrics that reflect their performance with respect to our objectives. In investment and trading, the most common objectives are the return and the risk of the investment portfolio.

Typically, these metrics are compared to a benchmark that represents alternative investment opportunities, such as a summary of the investment universe like the S&P 500 for US equities or the risk-free interest rate for fixed income assets.

There are several metrics to evaluate these objectives. In this section, we will review the most common measures for comparing portfolio results. These measures will be useful when we look at different approaches to optimize portfolio performance, simulate the interaction of a strategy with the market using Zipline, and compute relevant performance metrics using the pyfolio library in later sections.

We'll use some simple...

How to manage portfolio risk and return

Portfolio management aims to pick and size positions in financial instruments that achieve the desired risk-return trade-off regarding a benchmark. As a portfolio manager, in each period, you select positions that optimize diversification to reduce risks while achieving a target return. Across periods, these positions may require rebalancing to account for changes in weights resulting from price movements to achieve or maintain a target risk profile.

The evolution of modern portfolio management

Diversification permits us to reduce risks for a given expected return by exploiting how imperfect correlation allows for one asset's gains to make up for another asset's losses. Harry Markowitz invented modern portfolio theory (MPT) in 1952 and provided the mathematical tools to optimize diversification by choosing appropriate portfolio weights.

Markowitz showed how portfolio risk, measured as the standard deviation of portfolio...

Trading and managing portfolios with Zipline

In the previous chapter, we introduced Zipline to simulate the computation of alpha factors from trailing market, fundamental, and alternative data for a cross-section of stocks. In this section, we will start acting on the signals emitted by alpha factors. We'll do this by submitting buy and sell orders so we can enter long and short positions or rebalance the portfolio to adjust our holdings to the most recent trade signals.

We will postpone optimizing the portfolio weights until later in this chapter and, for now, just assign positions of equal value to each holding. As mentioned in the previous chapter, an in-depth introduction to the testing and evaluation of strategies that include ML models will follow in Chapter 6, The Machine Learning Process.

Scheduling signal generation and trade execution

We will use the custom MeanReversion factor developed in the previous chapter (see the implementation in...

Measuring backtest performance with pyfolio

Pyfolio facilitates the analysis of portfolio performance, both in and out of sample using a rich set of metrics and visualizations. It produces tear sheets that cover the analysis of returns, positions, and transactions, as well as event risk during periods of market stress using several built-in scenarios. It also includes Bayesian out-of-sample performance analysis.

Pyfolio relies on portfolio returns and position data and can also take into account the transaction costs and slippage losses of trading activity. It uses the empyrical library, which can also be used on a standalone basis to compute performance metrics.

Creating the returns and benchmark inputs

The library is part of the Quantopian ecosystem and is compatible with Zipline and Alphalens. We will first demonstrate how to generate the requisite inputs from Alphalens and then show how to extract them from a Zipline backtest performance DataFrame. The code...

Summary

In this chapter, we covered the important topic of portfolio management, which involves the combination of investment positions with the objective of managing risk-return trade-offs. We introduced pyfolio to compute and visualize key risk and return metrics, as well as to compare the performance of various algorithms.

We saw how important accurate predictions are for optimizing portfolio weights and maximizing diversification benefits. We also explored how machine learning can facilitate more effective portfolio construction by learning hierarchical relationships from the asset-returns covariance matrix.

We will now move on to the second part of this book, which focuses on the use of machine learning models. These models will produce more accurate predictions by making more effective use of more diverse information. They do this to capture more complex patterns than the simpler alpha factors that were most prominent so far.

We will begin by training, testing, and...