The Mathematical Investor: A personal perspective by QJZ

[Editorial note: During the next few weeks, each of the editors of the Mathematical Investor will provide, in an essay format, some personal background explaining the origins of their interest and work in this area. This is a perspective essay by Qiji J. Zhu.]

Education and research

I entered college and started my academic career in 1978 after spending the last several years of the `cultural revolution’ in a farm. My graduate and post graduate research first started in control theory dealing with control systems modeled by ordinary, partial and stochastic differential equations in Zhejiang University, Hangzhou, Fudan University, Shanghai, Northeastern University, Boston and University of Montreal.

My focus has always been on  practical yet complex nonsmooth phenomena. This naturally led me to the area of nonsmooth and variational analysis. I conducted research in this area at the Centre for Experimental and Computational Mathematics (CECM) at Simon Fraser University, University of Victoria, and at Western Michigan University, my academic home for the past 20 years. Much of my research was centered on symmetry, nonsmooth phenomena on smooth manifolds, and  intrinsic relationships among fundamental results within variational analysis.  Much of this work is summarized in the book “Techniques of Variational Analysis” jointly written with Laureate Prof. Jon Borwein, co-editor of this blog, and related papers can be found on my webpage. The tools and methods developed in my academic research have found significant use in my work in financial mathematics.

Introduction to the financial world

In 1997,  I opened a trading account out of curiosity as online trading became increasingly widespread. The road was initially bumpy, but  over time I learned lessons through trial and error and by utilizing  the theories and experiences of other successful traders. Thorpe’s theory on risk control via proper capital allocation had a profound influence on me – I recently further developed this theory with Marcos Lopez de Prado, co-editor of this blog, and Ralph Vince, an experienced practitioner. My systematical trading techniques benefited tremendously from Jack Schwager’s book “Market Wizards’’.

By 2000, with the help of my wife and computer programmer Lilly, I tested and established a stable computer  trading system. The computer code developed in this process enabled us to more easily test various investment `rules’  described  by financial commentators and columnists. While one would not expect to find a hugely profitable trading strategy in open publications,  it did surprise us that some of these claims were simply baseless, yet still appeared in quite reputable sources.

Trading-related research also led to collaboration with practitioners, in which I see further financial applications. It also led me into joint research with my longtime friend Qing Zhang, a fellow mathematician and trader. We continue to collaborate on theoretical justifications of trend following strategies and other practices that are known to practitioners but lack a quantitative framework. This research and collaboration eventually led us to co-found Zeta Asset Management.

The research gap

In the process of disseminating our research, I realized that mainstream financial theories focus, understandably, on serving  the big financial institutions. The main business of these big financial institutions is concentrated on creating and selling financial products,  from mutual funds and ETFs to exotic financial derivatives, increasing their trading volume, and justifying less regulation — in such fashion, so goes the focus of mainstream financial mathematical research.

The consequence is a huge void in rigorous research that provides concrete guidance to individual investors.  Unfortunately, this gap was filled by many commercially motivated advice and opinions, often proclaiming to be based on science.  On the other hand, many practitioners have valid insights through their experience, yet lack the time or training to summarize and communicate these observations theoretically.

The result is a somewhat chaotic information market in which insightful observations are mixed with bogus investment tips channeled through all kinds of media from newspapers, and private newsletters  to online blogs.

I find myself drawn more and more to this area. I enjoy finding theoretical justifications of time tested observations from experienced practitioners. On the other hand, I also believe it is important to expose the pseudo-science in a large part of self-proclaimed financial research.

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