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QUANTUM ECONOMICS
Or
“How To Get Inside Knowledge On FX Market Dynamics”
1/ Some Background – Is there any certainty in FX Markets?
There is no certainty in financial forecasting, in particular the large and liquid FX capital markets, other than
prognosticators will continue to make extreme comments that reflect the fear, uncertainty and doubt inherent in FX
markets. Let’s consider first of all market commentary on the uncertainty of market directions.
1.1 As general comments on the chaotic and complex movements of markets, consider…
• J.P. Morgan, the turn-of-the-century financier whose name still echoes through American finance in J.P.
Morgan and Morgan Stanley, had a stock answer when asked him what the market would do: "It will
fluctuate." [Ref 1]
• Lloyd Bentsen, former U.S. Treasury Secretary, also has a stock answer when asked what financial
markets will do: "If I knew, I wouldn't be standing here. I'd be calling from my yacht." [Ref 1]
Nevertheless in long (secular)bull markets as they approach their peak there usually is a vocal and vociferous group
of market authorities assuring investors and the public that the old rules of thumb are no longer valid, that rising
“trends” will continue or at least hold their investors value…
• The most famous of these predictions came just before the market crash of 1929, when Yale professor Irving
Fisher reassured investors that prices had attained a "permanently high plateau." [Ref 1]
1.2 But when market sentiment turns bearish, or enters periods of uncertain cyclical movement, many simply
give up their previous claims for their predictive capability, several such comments came out of market authorities
and commentators after the recent end of the U.S. dollar secular bear market currency strength, in its major decline
from October 2004 to Feb 2005…
• Alan Greenspan, the Federal Reserve chairman, said in 2002: "There may be more forecasting of
exchange rates with less success than almost any other variable." … and in 2004 "Forecasting exchange rates
has a success rate no better than that of forecasting the outcome of a coin toss” [Ref 2]
• Mervyn King, Governor of the Bank of England, said in 2004: "I have no idea where exchange rates will
go in the future and I have no intention of ever starting to forecast exchange rates. That's a mug's game."
[Ref 3]
• Chris Giles, FT’s Economics Editor said in December 2004 “ So here are two early new year resolutions for
currency analysts. … When the dollar goes down, they should say: "At the old price there were more sellers
than buyers." When asked where it will go next, they should say: "I haven't the foggiest." … Forecasting daily,
weekly or monthly exchange rate movements is a known unknown. Studies have shown that the best
forecast of today's exchange rate is yesterday's level” [Ref 3]
From 1.1 and 1.2 we can make a hypothesis:-
Being 100% Certain about a Future Market Value = False [Rule No 1]
It seems that we can be fairly confident that being certain about any long term market prediction is unsafe. In point
of fact many traders might build a contrarian trading strategy that factors a certain amount of hedge trading in the
opposite direction when advice begins to manifest itself that Secular Bull or Bear runs are likely to continue despite
some emerging evidence to the contrary.
1.3 Though once financial markets become more settled again these same market authorities and
commentators do make their opinion on market direction known and frequently they do move markets accordingly,
as trader’s factor the “explanations” these statements make into their market “risk” positions…
• Alan Greenspan, the Federal Reserve Chairman said in Feb 2005: “Arguably, however, it has been
economic characteristics special to the United States that have permitted our current account deficit to be

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driven ever higher, in an environment of greater international capital mobility. In particular, the dramatic
increase in underlying growth of U.S. productivity over the past decade lifted real rates of return on dollar
investments. These higher rates, in turn, appeared to be the principal cause of the notable rise in the
exchange rate of the U.S. dollar in the late 1990s.” [Ref 4]
The implication in the statement above is that FX rates are at least partly explained (i.e., are predictable), if you
have the “right” macro-economic model. In this case U.S. productivity was the “principal” explanatory variable, and
if this variable was not seriously undermined in 2004, then neither should be the value of the U.S. dollar. In the late
part of 2004 Economists had been “over-concerned” over the “serviceability” of U.S. trade deficits apparently. As FX
Economists thus re-considered their “fundamentals” and turned their sentiment around through the first two
quarters of 2005. At that time several market commentators, e.g., from Reuters to independent “Bloggers”,
reflected that this specific statement did in fact “move the dollar” [see Ref 5]. See figure 1 to see EURUSD price
movements around this time.
Figure 1 EURUSD – I Year Actual Chart by eFXSysTM
It is not my point that market authorities and commentators are inconsistent or misleading, e.g., Alan Greenspan in
his earlier quoted remarks [Ref 2] qualified his comments in detail and are broadly consistent with his later
comments mentioned above [Ref 4]. The key point is rather that Financial markets are very influenced by human
sentiment, which is capricious, since the choice of the “right” explanatory variable (e.g., Deficit or Productivity
figures), and the failure to place comments in the full context of a market situation or commentary leads to simplistic
understandings. It is understandable though in that Traders want simple directions and advice, since explaining the
“detail” of complex & chaotic phenomenon can lead to no practical market insight as to whether to place a “buy or
sell” trades.
If we are to get more direction we need to look at mathematical models that offer us more reliable predictive
power. We need to develop models that address these issues of human sentiment if we have hope of understanding
FX market dynamics, they will need to model the reality of complex and chaotic phenomena.
2/ Modeling the Chaos & Complexity of Financial Markets
2.1 Statistics is at the core of much of financial modeling. It is used to circumvent the unfortunate fact that we
are challenged in capturing the complexity of the markets. Financial markets involve thousands of agents
(“Traders”) whose rules and reasons (“heuristics”) for doing things are partly hidden from us or based on dynamic
circumstances that are difficult to track.

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Furthermore the businesses implicit in the instruments traded in the markets are themselves at another level of
complexity and chaos that we can’t hope to fully capture. Thus conventional wisdom based mathematical analysis
has contented itself with gross characterizations of market forces and attributed a large part of the events we see to
non-deterministic random noise.
In general many quantitative financial models involve characterizing market forces as random variables with certain
statistical distributions and many of the interactions between these variables are often assumed to be non existent or
of a certain rigid form so that the analysis is tractable.
A commonly held belief about financial markets is that they are “efficient” which is often taken to mean that
predictability cannot be profitably exploited in a trading heuristic on the basis of publicly available information once
the proper discounting for risk is done. A narrower statement of this basic belief is the Random Walk Hypothesis
which proposes that the best prediction for future values of a series is the last observed value.
If these hypotheses are true it is easy to see that statistical modeling will not easily yield useful predictive results.
However the premise of the efficient market simplifying hypotheses is suspect to say the least. Traders are,
ultimately, intelligent (and emotional) agents whose specific motivations on individual trades, whilst may be obscure,
are nevertheless seen occasionally to manifest in predictable manners to certain external influence, e.g., consensus
actions taken on basis of fear, uncertainty and greed - the so called “Herd instinct” or Avalanche effect. Individual
Traders in financial markets are also subject to learning processes and intelligent action that is purposefully directed,
e.g., Risk Management/Profit Taking. Financial markets thus may indeed have deep non-linear information layers
or patterns that can be filtered from the “noise”, though these “signals” may be intermittent and difficult to detect.
The fact that markets are not always 100% efficient is now well established, but is there enough “signal”, and do we
have enough “intelligence” to detect it and exploit it? This is the key issue. For some big investors this is not in
question.
• Warren Buffet: Has made several comments in this area, such as; [Ref 6]
o “I'd be a bum in the street with a tin cup if the markets were always efficient”
o “Investing in a market where people believe in efficiency is like playing bridge with someone who
has been told it doesn't do any good to look at the cards.”
o “The professors who taught Efficient Market Theory said that someone throwing darts at the stock
tables could select stock portfolio having prospects just as good as one selected by the brightest,
most hard-working securities analyst. Observing correctly that the market was frequently efficient,
they went on to conclude incorrectly that it was always efficient”
2.2 Thus our hypothesis is that the dynamical systems comprising the financial markets require more complex
and dynamic models than have been tried previously. For instance much statistical modeling and hypothesis testing
in the financial markets has traditionally been done with linear models. Partly this has been done for practicality,
linear models have the best developed and understood techniques for specification, estimation and testing, and
given processing/memory capability of computers in recent past realistic in algorithmic implementation performance
constraints.
Another possibility for capturing complexity may lie in estimating larger models. The problem with larger models,
however, is that the potential for capturing extra complexity does not come for free. Larger models mean more
parameters which means either that we need more data to estimate the parameters (an issue of both data
availability and computational effectiveness) or we are less certain in our estimates and thus in the overall usefulness
of the model. However we have argued that it is possible or even likely that many important relationships in
finance are nonlinear, and that no simple transformation can be made to make them practically linear.
Furthermore patterns of the past may not persist into the future, in other words Market characteristics or Modality
may “evolve”. A more dynamic “learning” non-linear model is required that can handle this inherent complexity
and chaotic behavior. Fortunately in recent years there has been an explosion in research and interest in this area.
3/ Complexity & Chaos Theory – Some new insights and emerging economic models
3.1 What have Mathematicians and Financial Theorists, taking into account latest insights into complexity &
chaos theory, recently been saying about Predictability and Trends in Financial Markets?…
• John Allen Paulos in his landmark book “A Mathematician Plays the Market” in 2003 argued that whilst
most financial theorists doubt that traditional technical analysis will make more money than investing into

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an index linked fund, there is nevertheless “tantalizing evidence for the effectiveness of momentum
strategies or short-term trend-following…result in moderate excess returns, having done so over the years,
their success is not the result of data mining”. And furthermore… “…they do seem to point to behavioral
models and psychological factors are relevant”. [Ref 7]
• Benoit Mandelbrot in his 2004 revolutionary re-evaluation of the standard tools and models of financial
theory “The (mis)Behavior of Markets”, wrote “Conventional financial theory assumes that variation of
prices can be modeled by random processes that, in effect, follow the simplest “mild” pattern, as if each
uptick or downtick were determined by the toss of a coin…by that standard, real prices misbehave very
badly.” Furthermore he writes … “What is an investor to do? Brokers often advise their clients to buy &
hold. Focus on the average increases in stock prices they say. Do not try to “time the market”, seeking the
golden moment to buy & sell. BUT THIS IS WISHFUL THINKING. What matters is the particular not the
average. Some of the most successful investors are those who did, in fact, get the timing right. [Ref 8]
• Stephen R Waite in his 2004 book “Quantum Investing” makes several good points…[Ref 9]
o “Conventional financial theory bears a strong resemblance to Newtonian or Classical Physics. It
describes a hypothetical state where the future is known rather than uncertain. Just as it is in the
Quantum world of atoms and subatomic particles, uncertainty is pervasive in the investment
world”
o “The essence of investment is “the hidden future”…If the road ahead was always clear, we would
readily adjust to what we see and tomorrows stock prices would always equal today’s. In their
calmer moments, investors recognize their inability to know what the future holds. In moments of
extreme panic or enthusiasm, however, they become remarkably bold in their predictions. During
such times, they act as though uncertainty has vanished and the outcome beyond doubt….A switch
from doubt to certainty defines major tops and bottoms in the stock market”
o “Complexity theorists have discovered that wild fluctuations and extreme volatility in financial
markets – things that cannot be explained by mainstream models – can be easily produced in non-
conventional economic models by assuming that heterogeneous (multi-direction) expectations and
beliefs suddenly become homogeneous (single-directional), the result is extreme volatility”
o “In the future, computer-based agent models are likely to help researchers better understand how
complex, real-world financial markets behave. These models simulate the real world and can
generate patterns of stock market booms and busts.”
From 1.2, 2.1, 2.2 and above we can make another hypothesis:-
Being 100% Uncertain about a Future Market Value = False [Rule No 2]
It seems that we can be fairly confident that being entirely uncertain, a piori, about any short term market
prediction is ignoring opportunity – particularly if we can see risk clearly not being managed efficiently in a market.
The timing then of trades can become safer. Trading in these situations when profitable will make the market more
efficient.
E.g., quite recently in April 2005 the Board of Governors of the Federal Reserve System produced an “International
Financial Discussion Paper” that modeled the predictive ability of Order Flow (buyer initiated orders net of seller
initiated orders) on Exchange Rate Dynamics [Ref 10]. This paper found that not only is their indeed a statistically
significant correlation in the very short term (so called very high frequency trading) but also this evidence is
inconsistent with the simple efficient markets view. From such a “guarded and conservative source” this is a very
interesting finding, particularly given Mr Greenspan’s earlier remarks in 2002 on the predictability of FX [Ref 2].
Getting insight into Order Flow is a tough issue though. Large trading houses do have this “inside” information, to a
limited extent through knowledge of the trades they are managing. The issue becomes one of “can we build a
model of Order Flow, disentangling it from very high frequency market data?” To do so we will have to contend
with building a view of the financial markets in very short time scales and with a market model that seeks to build a
representation of “price” based on discrete and probabilistic views of Order Flow.
4/ Quantum Economic models - eFXSysTM
4. 1 Given the above and from our Hypothesized Rules No 1 & 2, can we find a mathematical model that
handles this uncertainty in the small scale structure of the market? In Quantum Physics we have such a
mathematical paradigm.

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As a commentator on “Quantum Economics” recently said …[Ref 11]
• François-René Rideau” “In elementary physics, scientists know they cannot pretend they have certainty
anymore; actually, uncertainty about which events happen to a particle is deeply rooted in the laws of
quantum physics. The best way to express knowledge about a particle is through “wave functions” that
describe the probability of its possible states, depending on the infinitely many sequences of interactions in
which it may or may not participate. Of course, when it appears that a particle effectively interacted with
other particles in an observable way, then this new knowledge corresponds to an update in the wave
function that describes the particle (or set of particles); the technical term is that the wave packet collapses.
In quantum physics, information has a cost, because you may only extract useful information through
interaction, which not only costs you energy, but also modifies the system in ways that void other
information.”, …and “If economics has to have any future as a science, it will probably be as Quantum
Economics: a science describing human interrelations in terms of uncertain discrete transactions, where
information matters, where it has a value and a cost; where it is acquired by interaction, and used by
interaction; where it is unknown until the interaction happens, and where it is uncertain when the
interaction will happen and what it will be, but where it is certain that the interaction will eventually
happen, leading to an inevitable according reduction of the wave packet”
This “transactional view” can be expressed simply in trading terms. We can say we know the value of an asset only
at the time it is quoted, and the quote itself is a function of expected future valuations, which is dependent, in part, if
the transaction is executed (or not) at that price. Consider the following commentary in this respect…
• George Soros: “The prevailing wisdom holds that markets tend toward equilibrium--i.e., a price at which
willing buyers and sellers balance each other out. That may be true of the market in widgets, but it is
emphatically not true of financial markets. In financial markets a balance is difficult to reach because
financial markets do not deal with known quantities; they try to discount a future that is contingent on how
they discount it at present.” [Ref 12]
• John Walker: Founder of Autodesk Inc said: “Saying “The market was up 15 points today'' is
meaninglessness layered on meaninglessness. The market is neither up nor down. The market is a place
where discrete transactions occur--a surging organic sea of buyers and sellers with different goals, opinions,
and strategies, who momentarily and unpredictably agree to exchange specific assets. We aggregate these
transactions into the abstraction of a continuum of price. We aggregate a selection of these abstracted
continua into an average price. We then assign meanings to the action of this average, and impute its
behavior as being representative of the market.” [Ref 13]
In Quantum Physics we have one interpretation of how to understand the value of a wave function that is based on
what is known as the “Many Worlds” view, where the wave function at time t is a probabilistic “composite” of all of
the possible wave function values at time t. However how can we get a view of this composite? If we are able to
do so we would have genuine “inside” knowledge as to the movement of markets.
Sigma Delphi has built eFXSysTM
, using the advanced techniques of Artificial Intelligence (“AI”), such techniques are
becoming increasingly popular in this domain [see Ref 14, 15]. This eFXSysTM
application service is based on the
integration of AI techniques with a “Quantum Economics” model, a non-conventional model that simulates market
agents as individual “worldviews”. Each worldview is an independent trading simulation that comprises 4 factors;
1. Currency pairs - Tracking pairs comprising key crosses of: USD, EUR, JPY, GBP, CHF, NZD, CAD and AUD
2. Market modality – Modeling a variety of market characteristics/sentiments including; Secular Bear/Bull,
Cyclical Bear/Bull, Range, Trend, etc.
3. Forecast horizon - Forecasting in 1,2,4,8,16 hour “horizons”, each of 15 intervals (e.g., 1 hour horizon Forecast
is comprised of fifteen (15) 4 minute intervals)
4. Forecast method. – We use a combination of Neural Network, Technical Analysis and
Fundamental/News/Judgment Bias algorithms to make biasing judgment on market future direction
Further information can be found on this technology in Sigma Delphi’s white paper “Financial Market Modeling
using Hybrid Learning Networks & Expert Systems” available on its website www.sigmadelphi.com [Ref 16]
The current eFXSysTM
application service models 2,520 such worldviews updating every 4 minutes using very high
frequency market data input in sub-minute intervals. The results of each worldview can be individually monitored
(as shown in Figure 2 below) or the many worldviews can be monitored simultaneously.
Examining the current active recommendations of many worldview helps Traders to get insight into circumstances
where heterogeneous (multi-direction) expectations and beliefs suddenly become homogeneous (single-directional),

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resulting is extreme volatility in a particular direction. Such circumstances are exploitable by Traders who wish to
anticipate market movement profitably.
Take a look at the following screenshot from eFXSysTM
Alert Composite page (following page). This page display
many “worldviews” or simulating many individual trading agents buy, hold, sell transactions. When these actions are
taken together as a composite of many trades that comprise a real market, we can make a judgment if the overall
movement is heterogeneous or homogeneous. In this example we see many worldviews of the USDJPY currency pair
all declaring their interaction “advice” as a homogeneous “sell”. Some four hours later the subsequent screenshot was
taken (on following page). A significant movement is noted.
Martin Ciupa
Managing Director & Founder
Sigma Delphi Ltd
15th
Sept 2005
References
Ref 1: http://www.j-bradford-delong.net/OpEd/slategreenspan3.html
Ref 2: http://www.federalreserve.gov/boarddocs/hh/2002/july/testimony.html
Ref 3: http://news.ft.com/cms/s/779564ce-39a1-11d9-b822-00000e2511c8.html
Ref 4: http://usinfo.state.gov/usinfo/Archive/2005/Feb/04-916926.html
Ref 5: http://www.williampolley.com/blog/archives/2005/02/carrying_the_do.html
Ref 6: http://www.global-investor.com/quote/2710/Warren-Buffett
Ref 7: John Allen Paulos, “A Mathematician Plays the Market”, Penguin Books 2003
Ref 8: Benoit Mandelbrot & R L Hudson, “The (mis)Behaviour of Markets”, Basic Books 2004
Ref 9: Stephen R Waite “Quantum Investing”, Texere, 2004
Ref 10: http://www.federalreserve.gov/pubs/ifdp/2005/830/default.htm
Ref 11: http://www.livejournal.com/users/fare/34676.html
Ref 12: http://www.geocities.com/ecocorner/intelarea/gs21.html
Ref 13: http://www.fourmilab.ch/autofile/www/subsectionstar2_73_4_2.html
Ref 14: http://www-psych.stanford.edu/~andreas/Misc/DavidsonNewScience.html
Ref 15: http://www-psych.stanford.edu/~andreas/Misc/DavidsonNewTools.html
Ref 16: http://www.sigmadelphi.com/article_en.aspx

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Figure 2 eFXSysTM
Audit Trail of Past 10 Trades (Trade Worldview EURUSD/Range/SDEFNJTA)

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