The Theory of Quantitative Relativity indicates cone-shaped plotting of domains representing order size execution of issuances trading on electronic exchange markets. Circular base of order size cones generate upon convergence of velocity bound sums; inclusive of mass aligned with directional vectors of closed, subspace sums bound to a linear mapping of transaction exchange energy patterns.

Published September 2008…

As market fragmentation grows, fueled by ECN competition as well as individual bank platforms, market aggregation becomes more important. In fact, it has become one of the most important developments in recent years. Independent trading platform vendors have emerged to meet this growing market demand from clients. In addition, large dealing banks have increasingly turned to internalization to reduce costs and improve profit margins. More specifically, internalization enables banks to capture the spread internally and avoid paying the spread to an ECN, leaving virtually no footprint in the marketplace and eliminating ECN brokerage fees and associated interbank settlement fees, such as CLS costs.

Published December 2008…

Retail and institutional investors have been stunned at recent stock market volatility. The general thinking is that everything is related to the global financial crisis, starting, for the most part, in August 2007, when the Volatility Index, or VIX, started to climb. We believe, however, that there are more fundamental reasons behind the explosion in trading volume and the speed at which stock prices and indexes are changing. It has to do with the way electronic trading, the new for-profit exchanges and ECNs, the NYSE Hybrid and the SEC's Regulation NMS have all come together in unexpected ways, starting, coincidently, in late summer of 2007.

This has resulted in the proliferation of a new generation of very profitable, high-speed, computerized trading firms and methods that are causing retail and institutional investors to chase artificial prices. These high frequency traders make tiny amounts of money per share, on a huge volume of small trades, taking advantage of the fact that all listed stocks are now available for electronic trading, thanks to Reg NMS and the NYSE Hybrid. Now that it has become so profitable, according to Traders Magazine, more such firms are starting up, funded by hedge funds and private equity (only $10 million to $100 million is needed), and the exchanges and ECNs are courting their business.

Geometrically, an order-relative domain forms upon a circular base. The diameter of that base of the corresponding cone parallels an assimilated plotting (or linear progression) of issue transactional velocity. This line ends at the point of divergence among indicators constituting that directional function of the issuance transaction (or series of order executions).

Diameter of circular base of domain represents averaging of order size. Linear sequencing of orders therewith generate plotting of closed, convex sets less extreme points (e.g., apex connecting legs of cone).

This rules-based construct of geometric portioning offers a method to reconstruct electronic exchange market footprinting. The purpose (or value) of such plotting is being able to quantify patterns of market relativity otherwise eliminated or nontransparent within increasingly fragmented markets. That inability to correlate is also caused by low latency, high frequency systematics as well as during (artificial) pricing gyrations of market aggregation and periods of high levels of volatility.


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