Linear regression models, often marketed as 'factor-based investing,' dominate traditional quant strategies. Yet, they fail to capture the non-linear dynamics inherent in how markets and investors operate.
Consider a simple value-investing process inspired by Ben Graham: Buy stocks with a Price:Book ratio below 1, ignoring all else. This creates a step function—buy or don’t buy—based on a single threshold. Now imagine approximating this step function with a linear model using Price:Book as the sole factor. The fit would be poor. For investors using multi-attribute stock screeners (a common starting point for professionals), the complexity grows exponentially with each additional criterion. Linear models struggle to reflect these non-linear decision boundaries.
Non-linear effects are pervasive in finance. For example, many bank loans include covenants requiring companies to keep leverage ratios (e.g., net debt:EBITDA) below a threshold, such as 3. Stock traders often ignore this covenant when the ratio is below 1.5, resulting in a negligible impact on price. However, as the ratio approaches 2, the effect on stock price becomes noticeable, growing non-linearly and turning exponential near 3, pushing the stock into distressed territory.
Such dynamics cannot be adequately captured by linear factor models, highlighting the need for more sophisticated approaches.
Neural networks, with their ability to model non-linear relationships, offer a promising alternative to linear models. They can capture complex patterns in financial data that traditional methods miss. However, their non-convex nature introduces significant challenges.
Training neural networks involves optimizing a non-convex objective function, often using gradient descent. This process can get trapped in local minima, leading to sub-optimal models—without any indication of failure. The problem scales exponentially with more variables and parameters, a risk often overlooked by practitioners who prioritize large datasets over mathematical rigor.
Financial markets, unlike static domains such as language or image recognition, are dynamic and constantly evolving. Addressing these challenges requires a deep understanding of mathematics, hands-on market experience, and innovative problem-solving. At M³, we combine these elements to push the boundaries of human+AI trading systems.
Our technology is built from the ground up, diverging from established quant paradigms. We aim to collaborate with the best minds and serve leading institutions to redefine the future of finance.