20 ATaleofTwoMarkets
various series of actual stoc kmar ket data were indistinguishable
from various series of numbers generated by a random number table,
roulette wheel, lottery drawing, or another device of chance.
These findings had an important practical implication: Traders
could not systematically make above-normal gains from trading be-
cause a statistical lac kof correlation implies that the best estimate
of the future price of a stoc kis its present price. In other words, if
prices follow a random walk, the price change from one time to the
next will not affect the probability that a particular price change will
follow that one. Past prices cannot predict future prices.
Runs
A long known weakness of correlation tests is that the results can
be skewed by a small number of extraordinary data in the time series.
An alternative test that avoids this weakness is an analysis of runs
in the data—an investigation of whether there is any persistence to
the direction of successive changes.
A run is defined by an absence of directional change in a statistic
in the series. Thus, a new run begins any time the direction changes
(i.e., from negative to positive, from positive to negative, or from
unchanged to either negative or positive).
Instead of testing the correlation of numerical changes in the
data in the series, one investigates the relationship of the direction
of those changes. If price changes follow the random wal kmodel,
the number of sequences and reversals in time-series data of stock
prices will be roughly equal. If the same direction persists for a sig-
nificantly longer period, the random wal kmodel will be contradicted.
Among the numerous run studies conducted in the early 1960s,
the University of Chicago economist Eugene Fama’s is regarded as
the most careful.^3 Fama found that the direction of price changes
tended to persist but nevertheless concluded that no trading rule or
strategy could be derived that outperformed the market consistently.
Accordingly, almost everyone involved in the debate in the late 1960s
agreed that the observed departures from randomness were negligi-
ble and believed that this constituted strong support for the random
wal kmodel.
Trading Rules
Despite the widespread agreement, some participants in the debate
remained skeptical. Indeed, prescient commentators of that era oc-