Complexity, Risk, and
Financial Markets. By Edgar E. Peters.
New York
Complexity,
Risk, and Financial Markets completes
a trilogy of books on chaos and fractal analysis. Fractal analysis examines self-similarity or
scale invariance, a structure that is often present in seemingly random and
otherwise complex processes. Time
series, for example, exhibit self-similarity if subsamples
resemble compressed versions of longer samples.
Pioneered by engineers, mathematicians, and natural scientists, fractal
analysis is now routinely applied to financial markets. Author Edgar E. Peters is a leading
practitioner and also chief investment officer at PanAgora
Asset Management, a distinguished quant firm managing over $13 billion. Peters published Chaos and Order in the
Capital Markets in 1991 (expanded and corrected second edition 1996), a
conceptual application of fractals and chaos theory in economics and finance,
followed by the more technical Fractal Market Analysis in 1994, which
remains an excellent introduction to fractal methodology, though recent
advances have rendered it technically obsolete in some respects. Chaos and
Order in the Capital Markets includes a sophisticated and devastating
critique of the efficient market hypothesis.
Complexity,
Risk, and Financial Markets
completes Peters' trilogy by presenting the underlying philosophical case for
chaos theory, which turns out to be grounded on distinctively Austrian views of
information and market process. This
book should be read by Austrians interested in, or already familiar with,
fractal analysis or chaos theory, a statistical methodology developed
extensively by Benoit Mandelbrot. (See particularly Mandelbrot 1963a, 1963b,
1972, Mandelbrot and van Ness 1968, and Mandelbrot and Wallis 1969 for the
original applications to income distributions and the distribution of financial
returns. Fractal analysis of asset
returns is of special interest because it can provide conclusions about the
market processes which generate asset prices).
It addition, this book should also be read by practitioners of fractal
analysis and related statistical techniques, in order to receive an
introduction to the Austrian school and deepen their understanding of their
methodological paradigm's justification, implications, and limitations.
Although it can
be read profitably on it own, Complexity, Risk, and Financial Markets
calls for some discussion of the context it occupies in the larger
trilogy. In particular, this book serves
as a philosophical background and introduction to Peters' two earlier books, to
which readers should go for more detailed critiques of market efficiency and
conventional quantitative economics, as well as a range of empirical
applications of fractal analysis.
Peters' applications use financial or macroeconomic data, and give
readers a good feel for how these statistical methods can be used in
research. Though many applications are
common to both earlier books, some of the techniques described in Fractal
Market Analysis have been superseded.
Anyone interested in conducting a fractal
research program should refer in addition to more advanced techniques,
(particularly those described by Calvet, Fisher, and
Mandelbrot (1997), Cheung (1993), Lo (1991), and Mandelbrot, Fisher, and Calvet (1997)). In
addition, fractal analysis can be applied in many situations where conventional
econometrics and statistical inference are invalid. Chaos and Order in the Capital Markets
and Fractal Market Analysis remain outstanding guides to interpreting
fractal analysis as applied to finance, and constitute the best introduction to
the literature.
Complexity,
Risk, and Financial Markets
is an engaging book, abounding in the kind of memorable and succinct examples
that can inject more life and relevance into anybody's classroom teaching. Simultaneously, it offers a broad,
philosophical look at how market economies self-organize into complex and
sometimes chaotic systems. Peters
introduces uncertainty as a necessary precondition for the market order, which
arises spontaneously through the interaction of self-interested
individuals. Very specific conditions
are required for such an order to be stable, and Peters notes economic markets
are unstable in societies like Sudan and Bosnia, where uncertainty may be high
but where little complexity is present (p. 191).
Central planning
aims at removing this uncertainty, but makes it impossible for markets to
function. Planned economies attempt to
insulate their citizens from risk, but can succeed only to a limited
extent. A free market operates beyond
the control of any one individual.
Investment in a planned economy should offer a guaranteed return, but
clearly things do not always go according to plan. Often, planned economies suffer greater
impact from uncertainty precisely because they lack the flexibility and freedom
of a market economy. Peters notes that
uncertainty goes along with freedom of choice, forming a necessary precondition
for competition and innovation, two things a planned economy attempts to do
without.
Although he sees
many problems with government intervention, he is frequently critical of
monopoly pricing (contrast particularly with Mises
1997 pp. 357-362), and concludes government regulation is the best hope for
solutions to market failure and the business cycle. Deterministic markets, the ideal of central
planning, cannot survive, as the first person to solve the riddle of
deterministically chaotic market structure would eventually accumulate all
wealth. In addition, however, Peters
feels markets must be regulated to ensure competition and equal access. Peters criticizes the Austrian school for its
rejection of antitrust regulation (pp. 181-183), and develops a rationale for
the Microsoft antitrust case (p. 113).
He makes the argument that antitrust regulation is necessary to ensure
competitive markets. In his view,
spontaneously evolved market order may be suboptimal, and then must be improved
by government intervention.
Peters' critique
of the Austrian positions on antitrust, though well-reasoned and
thought-provoking, would likely be better received if he made more explicit
what kinds of intervention he felt could be justified. Like all complex systems, free markets must
be stable but must also be free to grow and adapt. The structure must be decentralized to be
capable of incorporating many individuals' subjective goals. Free markets need rules that do not constrain
uncertainty, but also encourage cooperation and trust, promote coordination,
protect property rights, and ensure competition. Implicitly, Peters seems to require very
strict limitations on the kinds of market regulations he would accept, and it
is a weakness of his argument that these limitations are not made more explicit. It is not entirely clear that Peters'
position on antitrust regulation is really different from Mises'.
Self-organizing
systems like the market order, patterns which emerge spontaneously from the
actions of independent and (externally) uncoordinated individuals, result when
individuals respond to one another, a broad class of behavioral responses
conventionally categorized as feedback.
Adam Smith recognized this principle when he described the coordination
of productive activity in a free market as the working of an invisible hand.
Peters contrasts
the approaches to uncertainty taken by mainstream or Keynesian economics and
subjectivist or Austrian economics.
Mainstream economics assumes uncertainty can always be modeled
mathematically, and that everyone should arrive at the same assessment of an
uncertain event's probability, at least given the same information. The Austrian school notes every individual
always perceives a unique information set, and that each individual values
every item of information in a unique manner.
Even if participants had identical information, their assessment of its
importance would be subjective. One
person's behavior may be quite different from another's, even facing identical
choices.
Peters invokes
the Austrian theory of subjectivism to criticize mainstream theoreticians'
frequent recourse to representative agents.
Peters motivates his presentation by providing examples of how market
participants attempt to project a spurious order on their understanding of the
world (pp. 11-14). Chaotic behavior,
which can display seemingly non-random structure, but is generated by random,
uncoordinated influences, can thus inspire conspiracy theories, convenient
assumptions which explain observed regularities.
Peters praises
the Austrian school for its recognition of the diversity and uniqueness of
market participants, supporting a more realistic economics. Investors, for example, are not all alike –
each has a unique and subjective combination of time horizon and risk tolerance. In contrast, mainstream and Keynesian
economics ignore differences among individual agents by assuming, for
simplicity and analytical convenience, that everyone is identical, or that differences among market participants do not matter and
can be ignored. The diversity of
individual goals and actions enables entrepreneurs to create profit
opportunities by better satisfying individual wants. The Austrian school views
knowledge as subjective, and unique to the individual
who acts on that knowledge. Far from
consisting of identical agents, the real economy consists of perfectly unique
agents who react differently in response to the same information.
A market process
is a complex process because it works toward individuals' goals of moving goods
and services to those who value them the most, and because the market works for
its own survival. The market is not a
living being, but in some ways acts as if it were. In Peters' view, mathematics
has finally caught up with the Austrian school's intuitive models (p. 63), and
he believes that quantitative, though possibly non-deterministic, models will
emerge based on Austrian insights.
Though developed
extensively in Chaos and Order in the Capital Markets, Peters extends
his critique of the Efficient Market Hypothesis, which he views as being fallaciously
based on homogeneous expectations and valuation. In the Austrian view, these are subjective
factors, and thus heterogeneous. It
would be impossible for one price to reflect everyone's information even if
everyone has the same information, because our evaluation of the facts is
subjective and unique (p. 91). Peters
emphasizes differences in investment horizons as the principal source of
heterogeneity in the investment market, rather than differences in risk
tolerance. He suggests the stability of
financial markets is directly proportional to the diversity of participants'
knowledge bases and investment horizons.
When long-term investment funds dry up, short-term assets experience
bubbles, and volatility increases. When no particular criterion dominates the
market, valuation is less likely to be distorted, and volatility declines.
Peters suggests
the business cycle results from the complexity necessary for financial markets
to provide liquidity without systematically favoring one investor over another. His treatment of business cycles is
particularly weak from an Austrian perspective; his discussion owes more to Schumpeter than Hayek or Mises. Peters' view of business cycles is that they
are a natural and inevitable part of the market process, rather than externally
imposed by credit manipulation. Adoption
of the Schumpeterian business cycle seems more due to the author's admiration
for Schumpeter's theory of the entrepreneur than conscious rejection of
Austrian capital theory.
In financial
markets, investors compete to employ capital in the most productive manner, and
to provide liquidity to whoever is willing and able to pay the most. The market has no mind of its own, but
rewards investors who succeed in this competition, and
this steady process of creative destruction drives the business cycle. In Peters' view, the Great Depression and the
Asian financial crisis led to market reforms which laid the foundation for
future prosperity. It is somewhat
disappointing that there is little reference to Mises'
and Hayek's theories of the business cycle.
Austrian capital theory's emphasis on the discoordination
caused by credit inflation as the driver of the business cycle may have been
more relevant to Peters' thesis. The
Austrian conception of the government and/or the central bank's attempt to
manipulate and control investment spending leading to malinvestment
seems highly complementary with Peters' critique of central planning.
Complexity,
Risk, and Financial Markets presents
a coherent overview of how local randomness, existing at the level of diverse
and independent individuals, interacts to form the global structure of a market
economy, which is stable and yet continuously in flux. It can be read profitably on its own, or as
the philosophical introduction to the trilogy it forms in conjunction with
Peters' (1994, 1996) two other books on fractal analysis. Although Austrians will occasionally take
exception to minor conclusions, Peters' trilogy remains the best introduction
to fractal market analysis, and the final volume demonstrates the largely
Austrian foundation on which the economic interpretation of fractal analysis is
based.
Robert F. Mulligan
References
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