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The Right Math for Analysis of Financial Markets?

| | Posted in: Big Ideas

Where should investors look for methodological edges in 21st century financial markets? In his brief August 2016 paper entitled “Mathematics and Economics: A Reality Check”, Marcos Lopez de Prado advises finance students (and practitioners) what mathematical/analytical expertise to acquire for successful 21st century investing and trading. Based on his experience with what kinds of analysts and mathematics are most successful in financial markets, he concludes that:

  • Graph theory (applying mathematical structures used to model hierarchical pairwise relationships) is better suited to address the inherent complexity of financial systems than conventional econometrics (applying statistical methods based on linear relationships).
  • Information theory is a sensible way to understand the flow of information within and across markets.
  • Machine learning is a promising alternative to conventional portfolio optimization methods, which involve such large estimation errors that they fail out-of-sample.
  • Understanding how to tackle the complexity of financial markets with supercomputers, as in weather forecasting, is an important research perspective.
  • Understanding how to model complex systems and conduct experiments that avoid overfitting and selection bias is essential to investment strategy development and monitoring.
  • Independent implementation/monitoring of real investments based on academic research, with initial funding provided by the researcher, would (eventually) provide probative evidence of research findings comparable to that offered by actual funds.
  • The relative success of mathematicians in real investing may derive from their lack of interest in financial theory ideologies.

In summary, modeling and testing with mathematics suitable to the complexity of financial markets is important to successful investing and trading.

Cautions regarding findings include:

  • Research on what methods work best via live investing is limited, perhaps in substantial measure because those using such methods do not want to share.
  • Most investors can access the recommended kinds of expertise only via investment managers/funds. Many investors lack sufficient capital to access them at all (but must still compete with them).

“Mathematics & Economics: A Reality Check (Presentation Slides)” provides a presentation slide version of this paper.


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