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Penny Wise, Dollar Foolish: Buy-Sell Imbalances On and Around Round Numbers*

Utpal Bhattacharya Indiana University

Craig W. Holden** Indiana University

Stacey Jacobsen

Indiana University

March 2011

Abstract This paper provides evidence that stock traders focus on round numbers as cognitive reference points for value. Using a random sample of more than 100 million stock transactions, we find excess buying (selling) by liquidity demanders at all price points one penny below (above) round numbers. Further, the size of the buy-sell imbalance is monotonic in the roundness of the adjacent round number (i.e., largest adjacent to integers, second-largest adjacent to half-dollars, etc.). Conditioning on the price path, we find much stronger excess buying (selling) by liquidity demanders when the ask falls (bid rises) to reach the integer than when it crosses the integer. We discuss and test three explanations for these results. Finally, we find that buy-sell imbalances are a major determinant of the variation by price point of average 24- hour returns. Thus, round number effects lead to unconditional (conditional) transfers of an aggregate -$813 ($40) million per year. JEL classification: C15, G12, G20. Keywords: Cognitive reference points, round numbers, left-digit effect, nine-ending prices, trading

strategies. * We thank Brad Barber (Editor), Charles Lee (Associate Editor), and two anonymous referees for excellent comments that have significantly improved the paper. We thank Darwin Choi, Bob Jennings, Sreeni Kamma, Shanker Krishnan, Denis Sosyura, Brian Wolfe, and seminar participants at the 2011 American Finance Association Conference, 2010 European Finance Association Conference, Indiana University, the Investment Industry Regulatory Organization of Canada, and McMaster University. ** Corresponding author. Address: Kelley School of Business, Indiana University, 1309 E. Tenth St., Bloomington, IN 47405-1701; tel.: 812-855-3383; fax: 812-855-5855; email: cholden@indiana.edu

Penny Wise, Dollar Foolish: Buy-Sell Imbalances On and Around Round Numbers

Abstract

This paper provides evidence that stock traders focus on round numbers as cognitive reference points for

value. Using a random sample of more than 100 million stock transactions, we find excess buying

(selling) by liquidity demanders at all price points one penny below (above) round numbers. Further, the

size of the buy-sell imbalance is monotonic in the roundness of the adjacent round number (i.e., largest

adjacent to integers, second-largest adjacent to half-dollars, etc.). Conditioning on the price path, we find

much stronger excess buying (selling) by liquidity demanders when the ask falls (bid rises) to reach the

integer than when it crosses the integer. We discuss and test three explanations for these results. Finally,

we find that buy-sell imbalances are a major determinant of the variation by price point of average 24-

hour returns. Thus, round number effects lead to unconditional (conditional) transfers of an aggregate

-$813 ($40) million per year.

1

1. Introduction

In an ideal world, liquidity demanders would be equally likely to buy or sell at any given price

point. In the real world, they often focus on round number thresholds as cognitive reference points for

value. If security traders do focus on round numbers as reference points for value, a security price path

that reaches or crosses a round number threshold may generate waves of buying or selling.

This paper examines three different kinds of round number effects. First, we consider the “left-

digit effect,” which claims that a change in the left-most digit of a price dramatically affects the

perception of the magnitude. To illustrate, a price drop from $7.00 to $6.99 is only a one cent decline, but

a quick approximation based only on the left-most digit suggests a one dollar drop. In other words, when

assessing the drop from $7.00 to $6.99, people anchor on the left-most digit changing from 7 to 6, and

believe it is a $1 drop. They do not round $6.99 up to $7.00, because this is mentally costly. The second

round number effect we analyze is based on round number thresholds for action, which we call the

“threshold trigger effect.” The idea is that investors have a preference for round numbers, where the

hierarchy of “roundness” from the most round to the least round is: whole dollars, half-dollars, quarters,

dimes, nickels and pennies. So, in the example above, when the price reaches the round number $7.00 or

crosses below it to $6.99, this drop triggers trades.

Both the left-digit effect and the threshold trigger effect depend on the actions of value traders,

who are traders that buy underpriced stocks and sell overpriced stocks relative to their valuations. The

trader’s valuation is derived from earnings, dividends, book assets, or other measures of fundamental

value. For example, suppose that a value trader engages in fundamental analysis and determines that a

particular stock is worth $7.52. If the stock price drops below that level and no new information causes

the investor to change his valuation, then the stock will be considered underpriced and this will generate a

buy trade at some point. Theoretically, a buy trade could be triggered by any price below $7.52. However,

the left-digit effect causes a great discontinuity in the perceived market price as it crosses a round number

threshold, and so a change from $7.00 to $6.99 triggers more buys than a change from, say, $7.08 to

$7.07. Similarly, under the threshold trigger effect, some value traders may have selected $7.00 as a target

for buying. Thus if the price falls to $7.00 or goes below it, there is excess buying by value traders.

Conversely, with respect to overpriced stocks, both effects predict that if the price rises to $8.00 or above

it, there is excess selling by value traders. Note that the left-digit effect, unlike the threshold trigger effect,

does not predict excess buying when prices fall exactly to a round number.

The third round number effect we examine is based on a combination of limit order clustering

and undercutting. Limit order clustering occurs when limit order prices are more frequently on round

numbers. For example, Chiao and Wang (2009) find that limit order prices are clustered on integers,

dimes, nickels, and multiples of two of the tick size on the Taiwan Stock Exchange. Bourghelle and

2

Cellier (2009) document the same phenomenon in Euronext. Undercutting occurs when a new limit sell

(buy) is submitted at a penny lower (higher) than the existing ask (bid). The “cluster undercutting effect”

is a combination of both limit order clustering and undercutting. Due to limit order clustering, it is

relatively common that existing limit sell orders set the current ask at a round number, say, $7.00. Then a

new limit sell undercuts at $6.99 and sets a new ask price. Then a market buy hits the new ask price. Thus

a buy trade is frequently recorded below a round number. Conversely, due to limit order clustering, it is

relatively common that existing limit buy orders set the current bid at a round number, say, $5.00. Then a

new limit buy undercuts at $5.01 and sets the new bid price. Then, a market sell hits the new bid price.

Thus a sell trade is frequently recorded above a round number. Hence, the “cluster undercutting effect”

predicts excess buying below round numbers and excess selling above round numbers. Note that unlike

the left-digit and threshold trigger effects, this cluster undercutting effect does not predict excess selling

(buying) when prices rise (fall) to an exact round number.

To provide evidence for or against the three effects, which are all based on the unifying

hypothesis that stock traders focus on round numbers as cognitive reference points for value, we choose

all trades of 100 randomly selected firms each year from 2001 to 2006. This is the decimal pricing era,

where the tick size is $.01. We obtain a sample of 137 million trades. Following Huang and Stoll (1997),

trades above the bid-ask midpoint are classified as liquidity demander buys, trades below the midpoint are

classified as liquidity demander sells, and trades equal to the midpoint are discarded.1

We first perform an unconditional analysis. For each .XX price point, we aggregate all buys and

all sells for each firm in each year (e.g., trades at $1.99, $2.99, $3.99, etc. are aggregated at the .99 price

point). The buy-sell ratio is then computed for each firm-year. This ratio is computed in three different

ways: number of buys / number of sells, shares bought / shares sold, and dollars bought / dollars sold. The

median of these three ratios over all firm-years is then computed for each price point from .00 to .99. We

find that, irrespective of how we compute the buy-sell ratio, there is excess buying by liquidity demanders

at all price points one penny below integers, half-dollars, quarters, dimes, and nickels (i.e., .04, .09, .14,

.19, etc.) and excess selling by liquidity demanders at all price points one penny above integers, half-

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