How do neural networks work at a high level, and what are the risks of using them in investment decisions?

Neural networks are powerful function approximators that can learn complex, non-linear relationships in data. For CFA Level II, you need to understand the architecture, training process, and key risks.

Architecture:

A neural network consists of layers of interconnected nodes (neurons):

1. Input layer: Receives the features (e.g., P/E ratio, momentum score, volatility)
2. Hidden layers: Transform inputs through weighted connections and activation functions. Each layer learns increasingly abstract representations.
3. Output layer: Produces the prediction (e.g., expected return, buy/sell signal)

Each connection has a weight (parameter). A simple network might have hundreds of parameters; deep networks can have millions.

Activation Functions:

These introduce non-linearity — without them, a neural network would just be a linear regression regardless of depth:

• ReLU (Rectified Linear Unit): max(0, x) — most popular, computationally efficient
• Sigmoid: Maps to (0,1) — useful for probability outputs
• Tanh: Maps to (-1,1) — centers output around zero

Training (Backpropagation):

1. Forward pass: input flows through the network to produce a prediction
2. Calculate error (loss function): compare prediction to actual
3. Backward pass: calculate how each weight contributed to the error
4. Update weights to reduce error (gradient descent)
5. Repeat thousands of times until convergence

Risks in Financial Applications:

Practical Example:

Atlas Capital builds a neural network to predict monthly stock returns using 50 fundamental and technical factors. The model achieves 65% accuracy on training data (2010-2022) but only 51% on test data (2023-2024). This gap signals severe overfitting — the model learned patterns specific to the training period that don't generalize.

Reducing the network from 3 hidden layers to 1, applying dropout (randomly disabling 20% of neurons during training), and adding L2 regularization brings test accuracy to 56% — modest but more reliable.

Exam Tip: The CFA exam focuses on conceptual understanding and risks, not mathematical details of backpropagation. Know the overfitting problem and mitigation techniques.

Explore ML in finance in our CFA Level II Quantitative Methods course.