ChaoticMarket 35understanding of public capital market phenomena with a broader
perspective on investor and market behavior.
There is no a priori reason to believe that public capital markets
are linear systems rather than nonlinear systems. Therefore, one of
the first questions that must be considered in understanding such
markets is whether they follow linear or nonlinear processes. More
sophisticated techniques than were available when the random walk
model was first developed are now used to investigate precisely that
question.
One reason such techniques were unavailable in the 1960s,
1970s, and even early 1980s was the need for powerful computer
systems that not only could process data more swiftly but also could
go beyond the simplified mathematical models of straight lines and
investigate the curvatures of multidimensional data streams. Armed
with such resources, researchers now start with the consensus view
that empirical research shows that a random wal kdescribes stoc k
prices fairly well, subject to some anomalies. Then they dig deeper.
One tool for the digging actually dates to the early part of the
twentieth century. It was developed by the hydrologist H. E. Hurst
when he was working on the Nile River Dam project.^2 Hurst had to
develop reservoir discharge policies to maintain reservoir water levels
in the light of rainfall patterns.
To understand how the reservoir system worked, Hurst would
record its water level each day at noon and calculate the range (es-
sentially differences between the high and low levels and the average
levels). If the range increased in proportion to the number of ob-
servations recorded, one could conclude that the reservoir system
was a random one. Otherwise, it was nonrandom and exhibited some
pattern, knowing either of which could enable the hydrologist to set
the reservoir’s discharge policies.
Hurst developed a simple tool called theHexponent to deter-
mine whether the range increased as would a random process or
whether it exhibited a more patterned behavior. Skipping the math-
ematical details, if a system’sHequals .50, then the system behaves
according to a random walk. The probability that any particular move
will follow any other move is 50-50 and thus completely up to
chance.
IfHis less than .50, the system is mean reverting. That means
that if the system has moved up for a number of observations, it is
more likely to move down over the next number of observations, and
vice versa. Conversely, ifHis greater than .50, the system is correl-