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ORISKANY TCS™

Tactical Cycles Service

Executive Summary

Document pages: 14

Release: V1.f

Author: Laurent Zerbib, Didier Smadja

Validation: Hervé Kias, Cyril Alvarez-Pereyre

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Disclaimer This document is private and confidential; it is meant for the exclusive use of whomever it has been communicated to. It is indicative and does not carry any contractual value. It cannot be communicated, reproduced or published, whether partially or in full, to the benefit of a third party without the prior written agreement of Oriskany.

Oriskany cannot be held liable for the analyses it produces with respect to markets and/or instruments. This document has been created for information purposes only, and does not constitute an offer to subscribe to any product or service, the recipients being responsible for any operations they may undertake. Data, whether sourced internally or externally, are for information purposes only, and can be subject to errors and omissions.

Past simulations are no guarantee of future results and are not constant across time. Results can vary upwards as well as downwards.

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1. Introduction TCS Real Time™ is an industrialized and customizable research service allowing financial markets professionals to create innovative investment processes by targeting the key indicators that improve strategies efficiency and risk management.

TCS is broadly inspired by statistics created at Yale University by Benoit Mandelbrot and his team, and by the theories of chaos and non-linear dynamic systems.

TCS uses TCS Real Time Technologies™ which is fully owned by Laurent Zerbib, Telesystems Engineer, (75%) and Didier Smadja, UPMC Engineer, (25%). This software is being patented in Paris (APP Office).

The TCS Real Time™ approach is inspired by “Multifractal” and influenced by the theories of non-linear dynamic systems. In order to understand those systems, the best analogy is with weather forecasting, where the sensitivity to initial conditions is at the very centre of complexity.

The impossibility to generate reliable weather forecasts over the medium term (as opposed to the short term) originates in the second law of thermodynamics, characterised by entropy, about which statistical thermodynamics remind us that entropy can be interpreted as the measure of the degree of disorder of a system at a microscopic level. The higher the entropy of a system, the less its elements are organised, tied together, and able to produce mechanical effects.

Consequently, the time scale is crucial in the analysis. Indeed, the longer the horizon, the less precise the information will be, and the more entropy will increase. This is Shannon entropy (in his information theory): “entropy indicates the quantity of information needed so that the recipient can determine unambiguously what the sender has transmitted. If the recipient is weak in information about the message, the entropy (i.e. uncertainty) will be high about this message”, the variation in entropy being always positive.”

Furthermore, entropy is a discontinuous notion, meaning that it tends to produce jumps of undetermined origins. Indeed, even if the quantity of information was very large, the causes of the phase transitions are not determined. Therefore we should only aim at predicting the dynamic of a system up to a certain limit and with a given probability.

The analogy with prices predictions has been demonstrated by many academic studies. The efficiency of financial markets previsions is similar to weather forecasting: predicting is difficult, by nature probabilistic and the quality of the prediction worsens as the time horizon lengthens.

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Based on these findings, TCS Real Time™ approach aims at offering an actionable synthesis in a world where the overwhelming complexity is making predictions and the associated risk management more and more difficult.

The TCS Real Time™ approach is also a potential application of the “antifragile” thesis from Nassim Taleb, which essentially shows that the development of adaptability can be favoured by an uncertain environment.

Finally, sustainability is obviously a founding concept of the philosophy behind TCS Real Time™.

2. TCS Real Time™ philosophy

Long memory and deformation of time

The research of Benoit Mandelbrot suggests a new and more precise approach where jump-type Lévy processes are replaced by other processes where discontinuity fades over the long-run, and he introduces a memory effect of financial markets variations. Time is characterized as “multifractal” in order to describe the succession of calm and agitated periods: the amplitude of variation can remain independent from one day to the next while being correlated over the long-run. However as the speed of prices formation is not constant, the measuring process of variations needs to be auto-adaptive. This dynamic, well known in physics, calls upon the non-deterministic apparatus of the dynamic non-linear systems.

TCS Real Time™ includes the long memory, a founding notion of fractality, but also the discrete deformation aspect inherited from fundamental physics. The practical consequence is the non-linearity of the observation constants, which ensure that the analysis does not suffer from the classical risk optimisation, where patterns are identified and reproduced in extenso in the future.

Based on this principle, data will be deformed in order to adapt each cycle both to the initial and to the current conditions, the sensitivity to these elements being a crucial aspect of the dynamics of the system. Multifractal time is used regardless of the observation scale. The variation in volatilities is used to deform time: in analogy with the relativist relation between mass, energy and time, this indicator empirically produces the expected result on the auto-adaptability and the cycles detection.

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The chart below shows the effect of the deformation on the cycles of the EuroStoxx 50 future:

Chart: EuroStoxx50 Future Short Term Trend Market Cycles

Top part: the accumulated P&L from the cycles. Middle part: the succession of cycles detected (blue = long, orange = short). Bottom part: the rectangles around the price chart show how market time deforms the cycles (again, blue = long, orange = short)

Practically, each discrete cycle receives the long memory parameters that are then deformed by the conditions measured at inception of the cycle and by real-time data. For instance, a “fractalisation” done over 100 measurement points of historical data can be revised, according to initial and current conditions, by an exponential factor of, say, a variable ratio of 2.5, hence 250 points.

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Joseph and Noah effects

According to Mandelbrot, 2 phenomena are at play:

The Joseph effect: persistence of weak variations around a “norm” for a long time, corresponding by example, to market bubbles formation.

The Noah effect: sudden discontinuity can occur with dramatic change in variations, corresponding by example to overreactions observed on markets

Mandelbrot therefore defines two types of randomness:

Mild randomness, which is associated with Brownian random walk.

Wild randomness, which includes both Joseph and Noah effects.

Wild randomness, the most virulent form of randomness, is by nature unpredictable and disqualifies the use of averages.

Based on this empirical observation, TCS Real Time™ implements the following strategy:

Mild randomness is a source of efficiency by leaning on discrete transformations to follow the effect through a precise process. It is therefore crucial to look for promising configurations offering reasonable, measured and frequent results.

Wild randomness, by contrast, is unpredictable by nature. Therefore, one should only aim at minimizing exposure rather than frivolously attempting to predict it.

The TCS Real Time™ approach focuses its detections during mild randomness periods, leaving aside the chaotic moments. The “presence time on markets” and the exposure to risk become the overriding indicators, in accordance with the fact that the smaller the commitment (defined as presence time multiplied by exposure), the smaller the exposure to wild randomness. The linear approach to risk as defined by the Gaussian approach is totally discarded.

TCS Phases Forecasting Module (Low Volatility in Blue, High Volatility in red)

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3. Cycle detection in TCS Real Time™ Detection relies on two major families of indicators, the synthetic description of which is given below. Please note that the mathematical instruments used are reasonably simple. However the recursivity of the process justifies the use of algorithms. Nonetheless, this does not make TCS Real Time™ similar to algorithmic trading by any means, but we will explore this issue later.

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Indicators based on Volatility variations (i.e. Volatility Trend)

The empirical measures on volatility variations done by the teams of Mandelbrot concluded that the variations in short-term volatility offered a good predicting power. Volatility variations exhibiting stability of the standard deviations around a local mean deformed by multifractal time, point to a white noise or mild randomness configuration. The discrete transformations are distributed along a Gaussian law where the parameters are deformed exponentially. For the sake of simplicity, we call exponential standard deviations (or “exposigma”), the mathematical instrument measuring the distribution around the mean.

This “Volatility Trend” indicates the normal, “quiet” form or on the opposite the renormalization process. The normal form appears when the volatility variations are crossing down their local deformed mean, the denormalizing form appears when the opposite occurs.

Graph: Dynamic indicator Volatility Trend

Top part: EuroStoxx 50 Future. Middle part: the cycles detected (green = long, pink = short). Bottom part: the dynamic indicator “Volatility Trend” (green = normal forms, red = denormalizing forms)

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Indicators based on directional persistence in price (or Price Trend)

The natural complement to the Volatility Trend is the Price Trend. In TCS Real Time™ this direction requires the validation of the persistence, a usual notion in physical statistics. This approach serves to “denoising” the price trend. The result is a confident probability of an uptrend or downtrend cycle.

Graph: Dynamic Indicator Price Trend

Top part: EuroStoxx 50 future. Bottom part: the dynamic indicator of excess of persistence (red = downtrend, blue = uptrend)

Detection of the cycles

Two methods are applied. Naturally, these observation techniques require the confirmation of Volatility Trend to be actionable, and are also supplemented by an empirical probability, calculated on a moving historical basis.

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The Trend methodology

In the Trend methodology, persistence is observed when the Price Trend validates the crossing (upwards or downwards) of the variations surface. This surface determines dynamically the thresholds beyond which the trend exhibits persistence independently of the generating cause.

The Contrarian methodology

In the Contrarian approach, the cycle is identified when the price persistence validates the crossing (upwards or downwards) of the area of persistence variations. This surface determines dynamically the thresholds beyond which the trend exhibits reversal.

Mathematical expectation of return (Expected Return or Stop)

Once the normal form and the persistent direction of prices have been measured (in Trend or in Contrarian), the distribution of the variations is subjected to an exponential law, whatever the observation scale. It is this self-affine feature (long memory) that determines the fractal, which has the shape of the diagonal of a rectangle, whose length is a function of time and height a function of the exposigma amplitude of prices (cf. following page). The settings of the Expected Returns / Stops are determined by the empirical analysis of the success probabilities, and are underlying-specific. This statistical information needs to be dynamically accounted for.

Differences between Trend and Contrarian

Historical observation justifies different settings for the expected returns and stops depending whether Trend or Contrarian methodologies are used.

By definition, once the Trend is confirmed, part of the expected variation has already occurred. A reversal equal to one time the expected move would invalidate the cycle.

In the Contrarian approach, a cycle reversal does not necessarily indicate an extreme (high or low) of the variation. The distribution of returns around the point where a reversal is probable can represent, empirically, a factor of two times the expected variation.

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TCS Real Time™ is not algorithmic trading

Finance professionals sometimes consider fractal approaches as models readily implementable in trading systems. This confusion, though understandable, is often caused by the deterministic influences, inherited from “mean reversion” methods, for instance.

By contrast, a multifractal approach belongs to the generic domain of dynamic non-linear systems. Non-linearity invalidates the possibility of determinism and reinforces the core probabilistic philosophy. A fractal cycle is “just” a cycle and cannot constitute, without additional work, a trading signal. It must be considered a directional indication given a specific probability.

Example of results

Past estimated and/or simulated performance is not a guarantee or a reliable indicator for the future and cannot be considered as steady in time. The value of such investments can decrease as well as increase.

10/03/13 - 30/11/2013

Live PeriodPerf. Max loss Max win

Global Cumul* 63,10% -4,08% 4,48%

Nb E/S cycles 584

Govies -4,86% -2,01% 2,05%

Forex 35,93% -4,07% 4,40%

Equities HF3** 22,14% -2,59% 3,81%

Global Monthly Cumul perf.

Month Perf cum. Month var.

March (from 10/03) -1,88% -1,88%

April 3,17% 5,14%

May 17,93% 14,31%

June 19,99% 1,74%

July 35,37% 12,82%

August 40,68% 3,93%

September 36,69% -2,84%

October 46,03% 6,83%

November 63,10% 11,69%

Reporting Production Cycles

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Stressing process

The objective of the stress test is to observe deviations (focused on negative impact on performance) related to the "human" intervention in the process. This test assumes a maximum delay of 5 minutes for each time-stamped real time cycle. It takes into account first the most probable price in the 5 minutes delay, then the most unlikely. We then compute the average of all possible occurrences and establish a distribution of all observed deviations. The stress test displays a resilient performance, ie. if it is non sensitive to a 5 minutes delay, and has no extreme gaps. If it were not, the process would be considered fragile.

Proforma Reference (email based) Perf cum

From 10/03 to 31/10/2013 46,03%

Stress Process Deviation

From 15/05 to 31/10/2013 Perf cum delta

Proforma, 454 cycles timestamp data 36,17%

Deviations

1 min delayed deviation 27,14% -9,03%

5 min delayed deviation 26,65% -9,52%

Proforma -1 sigma (5 min delayed deviation) 23,92% -12,25%

Proforma +1 sigma (5 min delayed deviation) 49,62% +13,46%

Theorical ultra worst case deviation 5,91% -30,26%

Average Perf cum (All Cases) 28,24% -7,93%

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Distribution of deviations

-0,60%

-0,40%

-0,20%

0,00%

0,20%

0,40%

0,60%

0,80%

1,00%

15/05/2013 15/06/2013 15/07/2013 15/08/2013 15/09/2013 15/10/2013

-5

5

15

25

35

45

55

65

75

85

-0,60% -0,40% -0,20% 0,00% 0,20% 0,40% 0,60% 0,80% 1,00% 1,20%

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4. About Oriskany Oriskany is a financial markets advisory, research and strategic consulting firm.

Contrary to the tenets of modern financial theories (Efficient Markets Hypothesis, Modern Portfolio Theory, etc.), we believe that financial markets are intrinsically complex and

discontinuous.As dynamic and chaotic systems, they should be analysed using an

appropriate set of tools. In particular, statistical physics and fractal analysis provide much more robust results than the traditional Gaussian framework, when used to understand and describe financial markets behavior.

Oriskany offers a comprehensive range of services aimed at introducing and implementing such tools into our clients’ business process. We operate both at strategic level (investment philosophy, creation of discretionary mandates or new fund offerings) and at operational level (set-up of tactical allocation tools, improvement of investment and risk management processes, cost reduction and asset raising).

Our clients include Asset Managers, Fund Managers, Insurance Companies, Private Banks, Broker-Dealers, Family Offices, Corporate Treasuries and Hedge Funds.