Quantifold

Finally on campus at King’s College London!

One of my absolute favourite books about quantitative trading: “The Man Who Solved the Market: How Jim Simons Launched the Quant Revolution” by Gregory Zuckerman is a biography detailing the meteoric rise of Jim Simons as a mathematician and pioneer in the field of quantitative finance. Simons was born in 1938 and graduated from MIT in 1958 with a bachelor’s degree in mathematics. He received his PhD from UC Berkeley in 1961 with his thesis “On the Transitivity of Holonomy Systems” under the supervision of Bertram Kostant. After working with Shing-Shen Chern he discovered the Chern-Simons secondary characteristic classes of 3-manifolds. Simons subsequently worked with the NSA as a codebreaker in 1964. Simons founded a currency trading firm called Monemetrics and a hedge fund called Limroy in 1978, quickly hiring Lenny Baum and James Ax who would go on to have an enormous impact on the success of the firm. Monemetrics was renamed Renaissance Technologies in 1982 and in 1988 they launched the Medallion fund which would become Simons’ flagship fund. Medallion has earned over $100 Billion in trading profits since its inception. This is roughly a 66.1% average gross annual return. For context, the S&P 500 typically has returned 9-10% average gross annual return. These numbers are absolutely staggering and they put into context just how dominant Renaissance’s strategies have been over the last 30 years. If you’re considering a career in the financial markets it is crucial you look at Jim Simons’ story and ask yourself how you might follow in his footsteps. It certainly doesn’t hurt to have a world-leading knowledge of mathematics, so maybe start there! We are always happy to point people in the right direction. Happy Sunday!

Here is a (pretty old and worn) monograph written by Gel’fand, Graev and Pyatetskii-Shapiro as part of the series “Generalized Functions”. This is a highly advanced text discussing topics such as adeles, Kloostermann sums and other special functions in number theory. Having studied quite a lot of representation theory during undergrad I decided to delve a bit deeper with this text and I am finding the material to be fascinating but enormously complex. The applications to algebraic number theory are quite intriguing as well so I might delve a bit deeper into this topic in particular.

Vying for the title of most dramatically named branch of mathematics, Catastrophe theory is the study of dynamical systems which exhibit radical difficult-to-reverse change in response to changes in some variable. Developed largely by mathematician René Thom, catastrophic geometries in codimension less than or equal to four can be broken down into seven distinct types: fold, cusp, swallowtail, butterfly, elliptic umbilic, hyperbolic umbilic and parabolic umbilic catastrophes. Applications of this field are manyfold, particularly in physics where it can be used to explain many thermodynamical systems. In cases such as phase transitions there are very clear cases of this “catastrophic” effect as the system exhibits path dependence while it changes phase (think of the process of boiling water vs distilling steam and and how the phase diagram will look). Other fun examples in this text include many topics in laser physics, the sizes and stabilities of bee societies, the dynamics of prison riots and how alcohol affects introverts! Modelling the financial markets as dynamical systems we could easily imagine crashes and states of extreme volatility as examples of catastrophic effects on this dynamical system. I highly recommend reading up on this topic, if nothing else it makes you sound like some kind of mad scientist!

Jack Schwager’s famous “Market Wizards” is a series of interviews carried out with exceptional traders. Throughout the book we get insight into the different mindsets and strategies employed by each interviewee as they navigate through the financial markets. What brings many of these market players together? An appetite for risk, an aggressive approach to taking profits, speed of ex*****on and veteran levels of experience. Before the advent and widespread adoption of electronic trading, many pit-traders were essentially embodiments of these characteristics. So called “merc-jerks” in the Chicago Mercantile Exchange (CME) were notorious for their killer instincts and extreme aggression to rival traders as they fought (often literally) for a trade. Nowadays we have a lot less pit-trading, with the vast majority of trades being processed electronically, however the principles that guided pit traders are still just as relevant. If you have an ability to gain a statistical edge in the financial markets then to maintain that edge you need speed, timing and risk management. I highly recommend reading this book for some insights!

Maths is such a powerful tool in almost every realm of human endeavour there is. Finding applications of mathematics to problems that we face over the course of our lives is an exercise in creativity and experimentation which often leaves us richer both in understanding of the underlying theory itself and the problem we’re looking to solve. Books like this one from Penguin are great inspiration for thinking up applications of your own while you solve everyday problems. Can you think of something in your life that could be improved by introducing a little mathematical thinking?

Risk management, equity, bet sizing, bankroll considerations, expected values of your holdings vs and opponent’s range: poker is a fantastic analogue for the thought processes that take place in the mind of a quantitative trader. That’s why “The Poker Face of Wall Street” by Aaron Brown has made its way into my reading list. Having played thousands of hands of poker both live and online I know that it has developed my ability to assess risk and make plays with a positive expected value when I am in a strong position, and it has also developed my ability to cut losses when playing with mediocre holdings. I highly recommend picking up a poker variant (hold ‘em, PLO, 7 card stud etc) and training yourself to intuitively manage your profit and loss based on inculcated game theory optimal strategy. Whether in trading, business or everyday life, this manner of thinking pays dividends as you make complex decisions under uncertainty. If we can get to 6000 followers on this account we will run a poker tournament sponsored by Quantifold, so make sure you follow and share around to grow this account!

This book is where I have been getting some inspiration from as I write the quantitative trader fundamentals course. Finding examples pertinent to the financial markets was important for the specificity of the materials and I think this book filled that niche nicely. I might put out some of the exercises from the game theory texts as challenges for you all (and I may also put out some problems I have come up with myself). One of the most interesting examples I might write about is the zero-sum games played by market makers when responding to changing price dynamics. When the price of a security shifts a market maker must dynamically update their bid and ask prices in order to collect the spread without subjecting themselves to too much risk. If another trader can anticipate the pricing engine of a market maker then they can scalp the price change for a profit. Thus the market maker must establish their pricing in such a way as to prevent these trades which take advantage of them. This can be represented as a game with certain expected values for different prices given a certain move in the security. Finding a strategy which has a positive expected value for the market maker will net them enormous profits in the long run, so they must be fast and accurate every single time, with systems uptime of 100% of market hours. This, as you can imagine, is a massively challenging undertaking! If you would like to learn more I can make another post on this topic, let me know!

Reading up a lot on game theory right now as I write teaching materials for Quantifold’s training program. This book by Mendelson is perfect as a reference, however I have another book I’m using as a set of interesting examples to flesh out the content (I will make a post about this one too). I plan on making a reading list for prospective quantitative traders and will include various books on a large set of relevant topics (including game theory). Which topics would you be interested in learning more about? Let us know!

Happy to be back in West Cork! It’s been a long time since I’ve been here and it definitely feels good to be home.

An absolute classic (and infamous) textbook is next in our book series: “Introduction to Quantum Mechanics” by David J. Griffiths. Born in Arlington, Virginia on the 5th of December 1942 to Winifred and Gordon Griffiths who were both faculty at the University of Washington (his father in the history department and his mother in the zoology department), David was educated at Harvard receiving his PhD in theoretical particle physics in 1970 with “Covariant Approach to Massless Field Theory in the Radiation Gauge” under the supervision of Sidney Coleman. Griffiths has published two other famous and highly regarded textbooks aside from the one mentioned in this post: “Introduction to Elementary Particles” and “Introduction to Electrodynamics”. He received the Robert A. Millikan award in 1997 for “outstanding scholarly contributions to physics education.” In 2009 he was named a fellow of the American Physical Society "For advancing the upper level physics curriculum through the writing of leading textbooks and through his contributions to the American Journal of Physics in many editorial roles and as an author."

On tour in London checking out the King’s College London campus and surrounding areas! Can’t wait to get started here in September, lots of fascinating places to see and things to do here. I’m particularly looking forward to meeting the various research groups in the King’s maths department as it is always really cool (and motivating) to talk to people who are fascinated by their work. If anyone in London wants to get in touch then reach out to us!