Month: May 2025

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.

The correlation between stocks and bonds plays a crucial role in portfolio allocation and diversification strategies. In this issue, I discuss stock-bond relationships, the factors that influence their correlation, and techniques for forecasting it.

What Influences Stock-Bond Correlation?

Correlation between stocks and bonds is crucial for portfolio allocation and diversification, but this correlation can vary over time due to factors like inflation and real returns on short-term bonds.

Reference [1] conducts a study on stock-bond correlation spanning an extended timeframe. Their findings indicate that contrary to conventional assumptions, stock-bond correlation generally tends to exhibit a positive or near-zero relationship. Exceptions, where the correlation drops below -0.2, were notably observed during the early 1930s, the late 1950s, and most of the 2000s.

Findings

-The correlation between stock and bond returns is a key component in asset allocation decisions. This correlation is not stable and can vary significantly over time, affecting how portfolios should be constructed.

– The recent market environment has shown that stock-bond correlation can turn positive, potentially impacting diversified portfolios negatively.

– The article suggests that contrary to conventional assumptions, stock-bond correlation generally tends to be positive or near-zero.

– Exceptions to positive correlation occurred during the early 1930s, late 1950s, and most of the 2000s.

– Factors such as inflation, real returns on short-term bonds, and uncertainty surrounding inflation play pivotal roles in determining the direction and strength of stock-bond correlation.

– Time variation in stock and bond volatility can also affect the impact of stock-bond correlation.

– Bond risk premia are positively correlated with estimates of the stock-bond correlation.

– The correlation between stocks and bonds can significantly fluctuate over time and across countries.

In short, the correlation between stocks and bonds can significantly fluctuate over time. Factors such as inflation and real returns on short-term bonds, along with the associated uncertainty regarding inflation, play pivotal roles in determining both the direction and strength of the stock-bond correlation.

Reference

[1] Molenaar, Roderick and Senechal, Edouard and Swinkels, Laurens and Wang, Zhenping, Empirical evidence on the stock-bond correlation (2023), SSRN 4514947

Forecasting Short-Term Stock-Bond Correlation

Reference [2] employs a country’s Correlation Outlook, Prospective Inflation Volatility, the Yield Curve Momentum Regime, and the Trailing 3-month stock-bond correlation to build a predictive model.

Findings

-This paper extends a macroeconomic framework that explains long-term changes in stock-bond correlation.

-Prior research explains around 70% of the variation in 10-year rolling stock-bond correlations using the relative volatility and correlation of growth and inflation.

-The authors shift focus to forecasting short-term (three-month) variations in stock-bond correlation.

-Their method uses indicators based on whether individual forecasters expect stock and bond markets to move in the same or opposite directions.

– This approach improves the ability to forecast stock-bond correlations over tactical, short-term horizons.

This paper complements previous work by focusing on short-term horizons, showing that detailed forecast data can help predict high-frequency changes in stock-bond correlation. It also highlights the value of granular forecast data, especially the correlation between responses, which may be missed in standard survey summaries.

Reference

[2] Flannery, Garth and Bergstresser, Daniel, A Changing Stock-Bond Correlation: Explaining Short-term Fluctuations (2023). SSRN 4672744

Closing Thoughts

As we have seen, stock-bond correlation plays a crucial role in portfolio management and asset allocation. We have discussed how this correlation shifts over time, influenced by macroeconomic factors such as inflation and growth volatility, and how it can be forecasted. Accurately anticipating these shifts enables more informed portfolio construction and risk management.