and Stock Price Clustering: evidence from the Peoples' Republic
of China, Brown and Mitchell, 2004
Price clustering is the tendency of prices to be observed more frequently
at some numbers than others. It results from human bias and from
haziness or imprecise beliefs about underlying value. Some numbers,
such as those ending in zero or 5, are traditionally more salient.
Market agents tend to settle on more salient numbers when submitting
an order or quoting a price. To many Chinese, the number "8"
is salient because it is considered "lucky", while "4"
is "unlucky" and to be avoided. We conduct a tightly controlled
experiment to determine whether a culturally heuristic number preference
exists, by studying trading on the Shanghai and Shenzhen stock exchanges,
which have been relatively segmented along cultural lines. Our results
are extremely clear. For much of our sample period (1994-2001),
the prices of A-shares (mostly held by Chinese organisations or
individuals) traded on the Shanghai stock exchange were more than
twice as likely to end in 8 as 4.
clustering and natural resistance points in the Dutch stock market:
a natural experiment, Sonnemans, 2003
"The next explanation is from the marketing literature and
cognitive psychology. Odd pricing (also called odd-ending pricing
or just-below pricing) is very common in marketing of consumer goods
(e.g. Holdershaw, Gendall and Garland 1997, Stiving and Winer 1997,
Schindler and Kirby 1997). It means that the price is just below
some round number (for example $9.99 instead of $10.00). Consumers
(or at least some of them) tend to consider the odd price as significantly
lower than the round numbered price. Humans may process and store
numerical information in a way that the first digits, which contain
more significant information than later digits, are treated as more
valuable information (Brenner and Brenner 1982). To compare two
numbers a left-to-right comparison (first compare the hundreds,
if these are the same the tens, etc) is a very efficient procedure.
The human tendency to overemphasize the first digits can also be
observed in time measurement. Passing from an age of 39 to 40 is
considered by many as a bigger step than for example from 38 to
39 or from 40 to 41. In a financial market it would mean that a
stock price of 30 would be considered (much) higher than a price
of 29.9. A seller will be relatively happy to sell at 30 (and more
limit sell orders will be placed at 30) while a buyer would be reluctant
to pay a price that is not in the 20s but in the 30s. Note that
the odd pricing hypothesis predicts that round number effects in
guilders would immediately cease to exist in January 1999 and round
number effects in euros would immediately show up".
Model for Ordered Data with Clustering of Observations, Harris
and Fry, 2001
"Such a multimodal distribution may be the result of individuals
being captive to particular choices. Such a case arises when there
is digit preferencing (particular numbers, such as 0, 5 and 101
are often favored in many survey-based data sets). This paper introduces
a new discrete choice model, the Dogit Ordered Extreme Value (DOGEV),
that does account for both ordering and digit preferencing in the
data, and applies it to an Australian Inflationary Expectations
New Look at Clustering of Stock Prices, NIEDERHOFFER, 1966
"Let us consider the case of a small investor who recently
bought a stock at 72 and would like to sell somewhere about 80.
He would be well advised to place his sell-limit order at 79.9 rather
than at 80. On the average, there will be a greater concentration
of sell orders at 80 than at any other nearby prices. The sell orders
create a bearish effect, but the investor must decide whether the
benefits from a quick sale at 79.9 are worth the possible sacrifice
of 0.1 point. On the other hand, if a mutual fund contemplated the
purchase of this stock after it broke through 80 and rose to 99.9,
it might be wiser for them to postpone the purchase until the issue
traded at 100, just long enough to cover all the sell limits at
100 except for an amount sufficient to match their purchase order.
The reason for this is that so many sell-limit orders are placed
at the fascinating figure of 100 that the great volume of these
orders would act as a resistance to an advance beyond 100".
in the Futures Market: Evidence from S&P 500 Futures Contracts,
Schwartz, and Van-Ness, 2003
"While trade price clustering is evident throughout time to
maturity of these contracts, there is a dramatic change when the
S&P 500 futures contract is designated a front-month contract
(decrease in clustering) and a back-month contract (increase in
clustering). We find that trade price clustering is a positive function
of volatility and a negative function of volume or open interest.
In addition, we find a high degree of clustering in the daily opening
and closing prices, but a lower degree of clustering in the settlement
Price Clustering and Discreteness, Harris, 1991
"Stock prices cluster on round fractions. Clustering increases
with price level and volatility, and decreases with capitalization
and transaction frequency. Clustering is pervasive".