How can you optimize a neural network portfolio with transaction costs?

To put into example, you have a neural network-based portfolio with three assets: A, B, and C. The neural network predicts their future returns. You decide to rebalance the portfolio based on these predictions. However, each transaction incurs a transaction cost, such as a 1% fee. If the neural network suggests increasing the allocation to asset A, you need to account for the transaction cost when buying more of A. Conversely, if it suggests reducing exposure to asset B, you consider the cost of selling. Optimizing involves finding a balance between the predicted returns and the transaction costs. You might adjust the portfolio based on the net expected return after accounting for transaction costs.

In the neural network galaxy, optimizing with transaction costs is a financial ballet. Picture this: a transaction cost model, not just a calculator but a choreographer orchestrating each neural move. It's a portfolio waltz where minimizing costs isn't a routine; it's the artistry of aligning algorithms with the rhythm of market dynamics. In this data-driven ballroom, the transaction cost model isn't a backstage player; it's the director crafting a symphony of neural elegance, where every computational step dances to the tune of strategic financial finesse.

To optimise a portfolio of neural networks with transaction costs, the model must incorporate cost-aware methods. Techniques such as modifying the weights of the portfolio to account for trading costs or directly integrating transaction fees into the optimisation function are helpful. The best portfolio weights can be chosen by combining strategies like mean-variance optimisation with models for transaction cost estimation (like proportional or fixed costs per trade). Additionally, more practical and economical neural network portfolio optimisation is made possible by utilising regularisation techniques to stop excessive trading and taking transaction fees into account when evaluating risk-adjusted returns.

Defining a transaction cost model is pivotal for optimizing a neural network portfolio. Personally, I find the linear proportional model effective, especially for liquid assets. Its simplicity aids implementation, capturing trading costs proportional to the asset price and trade size. However, in my experience, for more intricate scenarios, exploring models that consider market impact, liquidity, or taxes can be beneficial. The chosen model shapes how the neural network adapts to real-world trading conditions, striking a balance between accuracy and complexity.

Each neuron in the input layer represents feature relevant to the portfolio decision. These layers contain neurons that learn complex relationships between input features and the expected portfolio returns. The neural network learns patterns, trends from historical data. Neurons in the output layer represent the predicted future returns for each asset in the portfolio. ReLU/ Sigmoid functions can be used in hidden layers to introduce non-linearity. Linear activation might be used in the output layer if predicting continuous values. The loss function measures the difference between the predicted returns and the actual returns. After obtaining predictions from the neural network, you simulate portfolio adjustments based on these predictions.

The output layer uses softmax activation to produce a probability distribution over different assets in the portfolio. Ground truth labels represent the desired portfolio allocation. For example, if there are three assets (A, B, C), the ground truth might be [0.3, 0.5, 0.2] indicating the desired proportions. Define a customized loss function that incorporates both the prediction accuracy and transaction costs. For example, a loss function could be a combination of the cross-entropy loss and a penalty term based on transaction costs. During training, the neural network aims to minimize this combined loss function, striking a balance between making profitable portfolio adjustments and keeping transaction costs low.

incorporating a transaction cost penalty into the loss function is a crucial step for practical neural network portfolio optimization. This modification encourages the network to trade more judiciously, considering the impact on transaction costs. The turnover rate factor is a practical addition, measuring how much the portfolio weights change over time. Striking the right balance here is essential, as too much trading can erode returns. This adjustment aligns the neural network's learning objectives with real-world trading dynamics, fostering a more robust and cost-effective portfolio strategy.

training and testing phase is pivotal for validating the neural network portfolio's effectiveness. Backtesting, utilizing historical data, provides valuable insights into its performance and robustness. I recommend employing techniques like rolling windows or cross-validation for data splitting, ensuring a comprehensive evaluation. Metrics such as the Sharpe ratio or drawdown can offer a quantitative measure of portfolio performance. It's essential to iterate and fine-tune the neural network based on backtesting results, aligning the model with real-world dynamics for more reliable and actionable insights.

Integrating cost-awareness into the objective function is crucial. Implement algorithms such as Mean-Variance Optimization with transaction cost constraints. Regularly rebalance the portfolio, considering cost-efficient trading strategies.