Quantifold

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.

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!