When it comes to trading system design, there are two schools of thought: one advocates for simpler rules, while the other favors more complex ones. Which approach is better? This newsletter explores both perspectives through the lens of machine learning.
Use of Machine Learning in Pairs Trading
Machine learning has become an essential tool in modern finance, transforming the way financial institutions and investors approach data analysis and decision-making.
Reference [1] explored the use of machine learning in pairs trading. Specifically, the authors developed an algorithm to trade the classic Pepsi/Cola pair using three predictive methods: (i) fitting a linear model to real datasets of Pepsi and Coca-Cola stocks, (ii) employing a neural network approach to fit non-linear models, and (iii) utilizing an error correction model (ECM).
Findings
-The study investigates the relationship between two correlated stocks, Pepsi and Coca-Cola, using regression modeling and machine learning algorithms.
-The data is split into a training set (75%) and a testing set (25%) to evaluate model performance.
-A simple linear relationship between Pepsi prices (Y) and Coca-Cola prices (X) is modeled using both ordinary least squares (OLS) and a neural network (NN).
– A non-linear model between Y and X was fitted using the neural network (NN) method, and predictions were made for the X series.
-Two co-integrated stationary processes are used to analyze trading performance: the spread (Y − 𝑌^) and the ratio (𝑌^/X).
-The performance of each strategy is evaluated to determine the most effective approach for trading based on the co-movement of Pepsi and Coca-Cola.
– The total profit was computed and compared: the linear model generated a profit of $1.05102, while the neural network model produced $1.049395.
– The NN model’s performance was similar to that of the linear method.
– The NN model can outperform other methods if the optimal number of neurons is used in the hidden layers.
In short, the neural network performs similarly to the linear model method but can be improved by optimizing the number of neurons.
Reference
[1] R. Sivasamy, Dinesh K. Sharma, Sediakgotla, and B. Mokgweetsi, Machine Learning Algorithmic Model for Pairs Trading, in Machine Learning for Real World Applications, Springer 2024.
Can a Complex Trading System Be Profitable
The previous article shows that a more complex system does not lead to higher returns. Reference [2], however, demonstrates that such a complex system can provide better risk-adjusted performance. The authors achieved that by using Machine Learning techniques.
Findings
-Traditional financial literature often relies on simple models with few parameters to predict market returns.
-This study theoretically proves that such simple models significantly understate the potential for return predictability.
-The article provides new theoretical insights into the out-of-sample performance of machine learning portfolios.
-It demonstrates that high-complexity models in machine learning can improve investment strategies, contradicting conventional wisdom.
-Market timing strategies based on ridgeless least squares can generate positive Sharpe ratio improvements, even for highly complex models.
-The study shows that machine learning models can perform better with greater model parameterization, despite having fewer training observations and minimal regularization.
-The findings are supported by random matrix theory and explained through intuitive statistical mechanisms.
-The article argues that out-of-sample R² is a poor measure of a model’s economic value, as models with large negative R² can still generate large economic profits.
-It recommends that the finance profession shift focus from forecast accuracy to evaluating models based on economic metrics, such as Sharpe ratios.
Reference
[2] Kelly, Bryan T., and Malamud, Semyon and Zhou, Kangying, The Virtue of Complexity in Machine Learning Portfolios (2023). Swiss Finance Institute Research Paper No. 21-90
Closing Thoughts
So, should a trading system be simple and intuitive or complex and data-rich? In this edition, we featured research supporting both schools of thought. Perhaps both approaches have merit, depending on the context and objectives. What ultimately matters is not the simplicity or complexity of the model, but whether it has been thoroughly tested, proven robust across different market conditions, and shown to deliver consistent profitability before risking real capital.