AI Portfolio Management with LSTM Networks & Hyperparameter Sweep

The Plus Side of Using AI in Portfolio Optimisation

The mean-variance approach, or for that matter any other traditional approach, can only be used to optimise a portfolio to a certain extent. We need something more intelligent. Something that can not only recognise patterns, but learn and change on the basis of these patterns. Hence, we choose to move beyond the traditional approaches and opt for AI. With AI you can expect to identify patterns and adapt to the time-series effect. Not just that, you can incorporate additional features rather than solely relying on historical returns. This can help to improve the decision making process.

Unlike traditional methods that often assume independence and constant distributions of returns, AI models excel at understanding and leveraging temporal aspects, such as trends, seasonality, and evolving market conditions.

We will take the Long Short-Term Memory (LSTM) model because it can handle time series data effectively.

Setting Up the Model

The objective is to calculate the optimal weights for a long-only portfolio consisting of 4 assets. The 4 assets are taken for illustration purposes only. AI model can be used to calculate the weights for more assets.

Input Layer
The input layer is 3-dimensional:

1. One of the dimensions is the number of input features passed to the LSTM model. Features could be historical returns, macroeconomic factors, or technical analysis indicators. For this scenario, let’s consider returns as the input features.
2. The other dimension is the timesteps. If you are using a lookback of 30 days to calculate the input features, then the number of timesteps would be 30.
3. The third dimension is the batch size. The batch size represents the number of different portfolios or scenarios you want to analyse simultaneously. If you set the batch size to 10, it means that during each training iteration, the model will analyse and update its weights based on the performance of 10 different portfolios (or scenarios) at the same time.

Output Layer:

1. Size of the output layer: The output layer size corresponds to the number of assets and since we are considering a portfolio of four assets, the size of the output layer will also be four.
2. Activation function: We are creating a long-only portfolio which means all the weights of this portfolio would be positive values ranging from 0 to 1 with the sum of all weights as 1, therefore, we will use the softmax activation function for the output layer.

In addition to input and output layers, you also have hidden layers added to the LSTM network. The input data from the input layer passes through hidden layers, and then to the output layer to calculate the weights of all four assets in the portfolio.

Training the Model

Now that you know what the structure of the LSTM model looks like, let’s try to understand the training process of the model. The model will calculate the weights but how will it know that these weights are optimal? This is where the loss function comes into play. The loss function helps to evaluate the weights calculated by the LSTM network.

Think about this, what should be the ideal portfolio? The one which gives you the best risk-reward ratio. In other words, the portfolio which yields the highest Sharpe ratio would be the one that has the optimal weight distribution. Therefore, we create a loss function based on the Sharpe ratio.

Ideally, while training the model we want to minimise the loss function. Does it mean we minimise the Sharpe ratio?

No, infact, it’s the opposite. We create a loss function that outputs negative Sharpe.

A Look at the Results

We used the LSTM model to create a long-only portfolio consisting of four assets, and these were the results:

We compare the performance of the optimised portfolio with that of the benchmark portfolio. The benchmark portfolio is nothing but the average returns of the four assets. As you can see, the optimised portfolio has performed far better than the benchmark portfolio.

It is important to note that backtesting results do not guarantee future performance. The presented strategy results are intended solely for educational purposes and should not be interpreted as investment advice. A comprehensive evaluation of the strategy across multiple parameters is necessary to assess its effectiveness.

In this classroom, you’ve learned the architecture of the LSTM model and how you can set up your own LSTM model to optimise a portfolio. But we’ve only scratched the surface here.

In this explanation, we skipped the whole train-test data split thing. We just wanted to focus on nailing down the concept of calculating weights for different assets. In this course, we break the data into training and test sets and analyse the performance in the test sets. Plus, we will also learn to create long-short portfolios. Want a sneak peek? Take a free preview of the course!

You can learn more about the implementation of LSTM for the optimisation of portfolio weights using Python. All you have to do is take a free preview of Section 10, Unit 1 of this course on Quantra.

What is walk-forward optimisation?

Walk-forward optimisation is a technique used in portfolio management to improve the robustness of a trading strategy by simulating its performance in real-time.

Instead of optimising a strategy using the entire historical dataset and then assessing its performance on a separate out-of-sample dataset, walk-forward optimisation continuously updates the strategy as new data becomes available.

How to perform walk-forward optimisation?

Here are the steps involved in a walk-forward optimisation process for portfolio management:

Initial optimisation:

• Begin by optimising your trading strategy using a historical dataset.
• Select parameters, indicators, and other elements of your strategy based on historical data to maximise performance.

In-Sample Period:

• Apply the optimised strategy to a specific in-sample period, typically a segment of historical data.
• Evaluate the performance metrics during this in-sample period.

Out-of-Sample Period:

• After the in-sample period, apply the strategy to a subsequent out-of-sample period that was not used during the initial optimisation.
• Evaluate the performance during this out-of-sample period to ensure the strategy generalizes well to new data.

Re-optimisation:

• After the out-of-sample period, re-optimise the strategy using an extended dataset that includes both the in-sample and out-of-sample periods.
• Adjust parameters or retrain models as needed to adapt to evolving market conditions.

Repeat:

• Repeat steps 2-4 iteratively as new data becomes available.
• Continuously update and re-optimise the strategy using the latest data.

The walk-forward optimisation approach helps to adapt the strategy to changing market conditions and ensures that it remains effective over time. It also reduces the risk of overfitting to specific historical patterns that may not persist in the future.

It's important to note that while walk-forward optimisation can enhance the robustness of a strategy, it doesn't guarantee future performance. Regular monitoring, evaluation, and adaptation are crucial to maintaining the effectiveness of the portfolio management strategy in dynamic market environments.

To summarise, walk-forward optimisation is used for the practical evaluation of trading or investment strategies. The walk-forward optimisation Iteratively trains and tests a model or strategy as new data becomes available

For WFO, a window size is defined to represent the size of the train/test set and a step size is defined to represent the size of the walk-forward step.

Walk-Forward Optimisation of LSTM Network

To perform WFO for an LSTM network created to calculate the optimum weights of assets in a portfolio, the LSTM network is initialised only once at the beginning. The weights of the LSTM network are updated in each WFO cycle.

Consider this example data of 20 days.

Initialise the WFO with:

No, infact, it’s the opposite. We create a loss function that outputs negative Sharpe.

• Window size = 5 days (Size of train/test data)
• Step size = 3 days forward (Size of walk forward step)

Also, initialise the LSTM model with random weights.

Iteration-1:

In the first iteration,

• In-sample training: Train the LSTM model on day 1 to 5 data. The weights are updated in the in-sample training step.
• Out-of-sample testing: Test the performance of the LSTM model on day 6-10 data and save the results.

Iteration-2:

In the second iteration,

• In-sample training: Train the LSTM model on days 4 to 8 data. The weights are updated in the in-sample training step.
• Out-of-sample testing: Test the performance of the LSTM model on days 9-13 data and save results.

Similarly, the in-sample training and out-of-sample testing are done in iterations 3 and 4.

Iteration-3:

• In-sample training: Train the LSTM model on days 7 to 11 data.
• Out-of-sample testing: Test the performance of the LSTM model on days 12-16 data and save results.

Iteration-4:

• In-sample training: Train the LSTM model on days 10 to 14 data.
• Out-of-sample testing: Test the performance of the LSTM model on days 15-19 data and save results.

It should be noted that the LSTM weights are updated in multiple training periods i.e. different market conditions. The performance of the test period gives backtest results of the portfolio created using the weights calculated by the LSTM model.

The following is the performance plot generated by applying the walk-forward optimisation on the LSTM network created on the assets AAPL, IBM, AMZN, and CSCO from December 31, 2009, to December 31, 2020, with a step size of 180 and a window size of 180.

It is important to note that backtesting results do not guarantee future performance. The presented strategy results are intended solely for educational purposes and should not be interpreted as investment advice. A comprehensive evaluation of the strategy across multiple parameters is necessary to assess its effectiveness.

For Python implementation of the walk-forward optimisation method for the LSTM network in the context of portfolio management, check out the section Walk Forward Optimisation With LSTM.