HOW TO USE THIS SITE
As you can see in the innovations section, this website discusses a wide variety of investment subjects: From backtesting and strategy selection, to robust portfolio construction, to signal processing, ... all the way down to market microstructure. After many years searching for answers to critical questions in the academic literature, I began to collaborate with accomplished scientists and mathematicians, leaders in their fields. Our preferred approaches were inspired by Experimental math, modern Geometry and Topology. The outcome has been some of the most read publications in Finance. As Congresses and University programs invited me to present my methods, I developed materials for Seminars, including lectures, videos and software. Any earnings from these resources are donated in full to charities, like the John Hunter Memorial Fund. You can find my scheduled talks at the news section.
A few mathematical colleagues and I founded the first online community dedicated to Quantum Computational Finance, named Quantum4Quants.org. We also set up a blog and the MAFFIA think tank, where we debunk popular misconceptions in academic and practitioner's research. We have been particularly vocal about the need to correct for selection bias and multiple testing in empirical studies.
Despite of my general criticism of academic financial research, there are quite a few excellent publications that have made useful contributions. Some are listed in the favorites section.
TAKEAWAYS
If you take anything away from this website, I hope this is that:

The mathematical tools commonly used to solve financial problems are hopelessly rudimentary:

Regression analysis is a 200 years old technique. Yes, I know that every month comes out an expensive Econometrics textbook with new chapters, but any 19th century mathematician could read it and understand it promptly. It's mostly linear algebra with some basic calculus and inferential probability.

Economics is the only discipline that gives the Nobel prize to individuals that apply methods established in the 18th century. You won't strike gold at the same spot where everyone else has been digging for decades, and even if you do, you will have to share it with them. Search outside their reach.


Markets are complex networks that require tools and techniques adequate to capture such complexity. If you want to have a chance at outperforming your peers, you will have to:

Use/build datasets that nobody has, or nobody is able to model: Unstructured, asynchronous, hierarchical, Big data.

Apply more advanced methods than theirs: Graph theory, combinatorial mathematics, integer optimization, Bayesian networks, algorithm complexity, machine learning, etc. Embrace math by experiment. You may want to start by reading the books written by two of my coauthors, David H. Bailey and Jon M. Borwein.

Solve intractable (NPHard) problems: The harder to compute, the better. A problem that can be solved with a commercial computer or server is probably unworthy of your time. You need to build a customized HighPerformance Computing (HPC) cluster, supercomputer or, even better, gain access to a Quantum Computer.

Run your research department like a Physics laboratory:

If statistical analysis alone sufficed to identify investment strategies, most financial academics would be multimillionaires. That is not the case, hence there is no scientific evidence supporting their claims. Toy models and simulations do not constitute scientific evidence. No matter how ingenious, every theory must be tested and validated in the real markets. Apply rigorous Quantitative MetaStrategies to your investment process.

Avoid falling into the trap of backtest overfitting: Always control for the probability that your backtest is overfit. There is absolutely no merit in producing a backtest with a high Sharpe ratio. We have developed tools that, within a couple of minutes, find an investment strategy with a Sharpe ratio of 5.


Some of the most successful hedge funds in history are mathdriven. They are the product of the second quant revolution, which combines: Big Data + Machine Learning + HPC + Meta Strategies.