36 ATaleofTwoMarkets
ative or persistent: if the system has moved up for a number of
observations, it is more likely to continue to move up over the next
number of observations, and vice versa. IfHis .60, for example, the
probability that a positive move will follow a positive move is 60%.
Hmay change over time. For example,Hmay be in the .70s over
some period and then drop to near .50 and subsequently increase
again. The number of observations (or time periods) over whichH
is sustained at other than .50 (before returning to near .50) is a
measure of the average cycle length of the system.
In the case whereHexceeds .50 for a sustained period, the
length of that period is a measure of the system’s memory—the ex-
tent to which past events influence present and future events. In
the context of investment analysis, it measures the period over which
an investor can use information to his or her advantage.
During the 1990s, some market analysts figured out that theH
exponent can also be applied to markets to determine whether they
are random too. One of them even published his results. Edgar Pe-
ters, a money manager in Boston, applied it to the Standard and
Poor’s 500 Index (the S&P 500) for monthly data over a 38-year
period from January 1950 through July 1988.^3
Peters found thatHwas .78 for average periods of approximately
four years, indicating a strong persistent element in the S&P 500
rather than a random process. Beyond average periods of four years,
however,Hwas not significantly different from .50 (it was .52/-.02).
So Peters concluded that the S&P 500 begins to lose memory of
events after four years. The S&P 500 thus is not random, and events
today continue to affect price changes for up to an average of four
years.
NEX TWAVE
This dashing of the economist’s dream of a perfect market has been
amplified by studies of the chaotic behavior of markets. Just as
Hurst’sHsuggests that markets are not linear as EMT assumes,
EMT’s assumption of market rationality is put into scientific doubt
by principles first developed by physicists in the field of chaos theory.
Chaos theory was popularized by the publication of James
Gleick’s 1987 best-selling book Chaos, primarily an exposition of
chaos in natural science. The potential role of chaos theory in eco-
nomics and finance was made prominent by the Santa Fe Institute’s