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Tradagon's Behavioral Calculus™: Momentum Reimagined with One Universal Model of Crowd Behavior

December 1, 2017


Behavioral Calculus™, or BCalc™, is Tradagon's proprietary quantitative trading system and methodology that reimagines how momentum is analyzed and exploited by modeling crowd behavior in price action.


BCalc is a fully automated, algorithm-driven system that employs our all new proprietary spectral math and deep learning to predict price action and other "behavioral" non-stationary time series data, such as other economic and business data. BCalc is neither fundamental nor pure technical analysis, but rather a new kind of behavioral time series analysis that employs our bleeding edge spectral math to exploit momentum across equities, bonds, currencies and commodities.


Challenges of existing quant approaches to price analysis


Existing quant approaches to predicting “price from price” are less than optimal. Here are a few reasons why:


Time series analysis is too fuzzy: Most approaches attempt to provide a rolling forecast and don’t really distinguish between high & low probability forecasts. Since the emphasis is not on “signals”, such approaches lack the crisp actionability required in the markets.

Signal processing like Fourier is too narrow: The classic techniques only work when there is at least some periodicity in the data. In the general case, market data has no periodicity and these techniques are not useful.


Standard calculus is too analytic: It offers closed-form or numerical approaches to deal with change phenomena that can be represented analytically, that is, with equations. Market data is free form and is not governed by any equations. Force-fitting standard calculus to free form data does not have much predictive value.


Momentum strategies are a grab bag of esoterica without a firm foundation: All that physics has to say about momentum is that it equals Mass times Velocity. Price has no mass, and the velocity of price depends on how you measure it. The higher derivatives such as acceleration probably have some bearing too, and are generally thrown into the mix in any “momentum” analysis. Not surprisingly, momentum analysis of the markets is all over the place, and the results have been decidedly mixed.


The root of the problem is that there is a vast analytical gap between “momentum” as perceived in price action - or in any crowd behavior, for that matter - and “momentum” as defined in physics. With Behavioral Calculus, we have bridged that gap: BCalc - our bleeding edge spectral math - evaluates the entire hi-res velocity spectrum of price action, as well as all relevant lower and higher “spectral derivatives”. It further evaluates all relevant “spectral convolutions” of these derivatives. This enables it to consistently hone in on the “Confluence Events” or signals hidden in all that noise.


BCalc™: Momentum reimagined using one universal model of crowd behavior


Human beings are wired to recognize and react to crowd behavior. You see it in many aspects of life, ranging from socio-political movements to fads to actual, physical crowds. The same applies in the market - crowd behavior is a core driver of price action.

We have found that the key concept underlying crowd behavior is that of Confluence.


There are moments in time when everyone and everything seems to come together, and this Confluence triggers crowd behavior. As more and more individuals start taking notice of the behavior, it creates feedback loops, and the “confluential” event morphs into an ongoing confluential trend. Individuals keep jumping in or getting out of the way, so to speak, and the trend persists until the energy dissipates. Very often a trend will persist indefinitely until a new, more compelling trend takes its place. This is exactly what happens in price action, and very often there is no real explanation for even major price moves - even after the fact - which is a hallmark of crowd behavior.


How does BCalc™ work?


Our innovative spectral math system called Behavioral Calculus, or BCalc™, captures the essence of crowd behavior in price action. It detects the signals in the noise by deconstructing and examining all the crosscurrents in price action, across multiple spectral derivatives and convolutions. From there it hones in on the Confluence Events and Confluence Tails that correspond to major market moves – long or short and in any asset – in real time.


The input into the BCalc model is one or more real time or historical price data series (or economic data series). The system then performs a series of powerful decompositions, normalizations, and other transformations, and finally feature processing -- to automatically generate entry/exit/hold signals.


BCalc encompasses a host of our spectral math innovations, including:

  • Spectral Derivatives

  • Combinatorial Integrals

  • Spectral Coherence & Confluence

  • Confluence Events & Tails

  • More than 15 layered spectral features and convolutions

BCalc's elegant, layered approach provides a rich and extensible analytics methodology that can be adapted to support a wide variety of trading & investing use cases. It is also highly effective with business and economic time series.


Why is BCalc™ different?


Reimagines price analysis: Bridges the analytical gap between the physical science of momentum and the social science of crowd behavior.


Universal behavioral model: Offers fully automated trading strategies across all asset classes based on one universal, behavioral model of price action.


Robust and far-reaching: Uses deep learning approaches but with analytical feature engineering and processing (not black box) for a more robust and enduring foundation that is extensible to business and economic data series and beyond.

In sum, BCalc is an innovative, game-changing technology that captures the fundamental essence of price action like nothing else out there. Not only does the BCalc approach work in the markets but with its deep roots, it is likely to have staying power on a Darwinian scale.


BCalc™ products: Actionable trading signals across all asset classes

We have a product portfolio of fully automated strategies across all asset classes, including equities, bonds, currencies and commodities. These strategies produce actionable signals for institutional operations to consume for their particular use cases. All signals are generated from powerful price analysis to be used for directional trading.


Proof points


We have created a whole new way to analyze price action with one universal model. We have traded and religiously followed the markets for several decades, and our trading has been used primarily as a testing ground for our models. As such, we use our in-depth backtests to illustrate the power of BCalc.


About our backtests


All BCalc strategies are based on a binary, long-short model; each can be used in a long-short “always-in” mode with no stops or profit-targets (i.e. all trades are position reversal trades). For any given asset or asset class, the typical “Base” case uses the “always-in” mode with no leverage. For equities and bonds, we also include “longs-only” use cases using the same signals. For currencies and commodities, we include use cases with stops and profit targets as well as with leverage, again using the same signals as the Base case. None of the use cases involve scaling in or scaling out, or trailing stops.


All BCalc strategy backtests are conducted on daily price data. In each backtest, at least the final one-third of the data is out of sample. Each symbol backtest starts out with 1M in initial capital, which is fully invested/re-invested in each subsequent trade in that symbol (subject to any lot-size conditions). Any open position at the end of a run is marked to market. Not included - commission, slippage and position holding expenses (stock borrow expenses for equities/ETFs, daily rollover expenses for forex, etc).


You can view all backtests and learn more about what we are creating at


Thanks for reading,


The Tradagon Team.

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