Letters by Technical Analysis
Clifford Sherry's article on the Gambler's Paradox (better known as the Gambler's Fallacy) in the October
issue contains a serious error. In using Chi square to test the independence of price changes, Dr. Sherry
gives the probability of obtaining a sequence of '+,+' or one of '-,-'as 0.1666 and the probability of
obtaining a sequence of '+,-' or of a ',+' as 0.3333. In any random and independent sequence of events,
each of which has any probability of 0.5, the probability of obtaining any one of the four possible
sequences is simply 0.25.
In the sample of 270 days of soybean-meal prices, using the correct probabilities yields a total Chi square
value of 3.88 rather than 51.73, which changes the conclusion of the study completely. Since 3.88 is not a
"significant" Chi square, there is no reason to conclude that these price changes were non-random. The
same correction also applies to the lagged-time Chi square value.
A finer point should also be made. In using Chi square to test for dependencies within sequences, the
overall trend of the date should be adjusted for. Using 0.5 as the probability of a price increase in the
soybean-meal data ignores the fact that there are more price increase days than price-decrease days in the
data and confounds the test for dependencies with a test for overall trend. In the soybean-meal data, the
total Chi square is only 0.61 when adjusted for trend.
Finally, traders should note that since Chi square only considers nominal changes in price and ignores the
magnitude of those changes, a sequential dependency uncovered by a Chi square analysis may or may not
be exploited as a profitable trade.
Gaylon L. Oswalt, Ph.D.