34 ATaleofTwoMarkets
ing of stoc kmar ket behavior and how investors and managers should
think about markets and market prices.
Linearity means proportionality: A change in one variable pro-
duces a proportionate change in another specified variable. What
makes the CAPM linear, for example, is its assertion that the ex-
pected ris kpremium of a stoc kvaries in direct proportion toβ.
EMT is linear in two ways. First, the statistical models under-
lying the wea kform are simple linear regression analyses; correlation
coefficients are statements about how variables are related on a
straight-line basis over time. In other words, the time series of data
is tested for correlation by fitting a straight line to the data and then
calculating the correlation coefficient.
Second, the semistrong form of EMT is linear because it defines
a proportional relationship between information changes and price
changes. In particular, the semistrong form says that information is
swiftly incorporated into prices without bias. In other words, there
is a proportional relationship between information changes about
business values and resulting price changes in the financial asset
(stocks) representing those businesses.
In contrast and a bit simplistically, nonlinearity means the ab-
sence of proportionality: Changes in one variable will produce a
change in another variable, but exponentially rather than propor-
tionally. To take a prosaic example, the 1-gram straw that breaks the
1-ton camel’s bac kis nonlinear because the cause is utterly dispro-
portionate to the effect.
Volatile stoc kprices and roaring or crashing mar kets are often
attributable to an incremental bit of information piled on top of
cumulated bits of information. If one company announces that its
earnings aren’t going to be as strong as people had hoped, its stock
price may take a haircut, but the market overall may not blush. But
as the weeks go by and a few more companies in that sector say the
same thing, Wall Street gets rattled. The shares of all the stocks in
that sector can suddenly get punished, and the pounding can spread
across the market as a whole. At some point, the creepy Wall Street
saying that there is never only one cockroach starts to resonate.
The fact that the market may react slowly or may overreact to
bits of new information is of course what noise theory teaches and
explains. The distinction between nonlinear and linear systems goes
well beyond noise theory, however, because noise theory itself is con-
strained by the efficiency paradigm. Nonlinear dynamics and chaos
theory brea kfrom that context and imply a fundamentally different