Penny Wise, Dollar Foolish: The Left-Digit Effect in Security Trading

Abstract

The left-digit effect is defined as when a change in the left-most digit of a price (e.g., 7 to 6 when $7.00 drops to $6.99) dramatically affects the perception of the magnitude. Using a random sample of more than 100 million stock transactions, we find excess buying by liquidity demanders when the price starts above an integer and then drops below the integer. Conversely, we find excess selling by liquidity demanders when the price starts below an integer and then rises to the integer or above it. This is true under three buy-sell ratio measures, in multivariate regressions with various controls, and in multiple robustness checks. We consider the left-digit effect and two other possible explanations that are not mutually exclusive. We test which of the three explanations predominates. We find that liquidity demanders who buy when the price falls below an integer or who sell when the price rises to an integer earn lower 24-hour returns than other benchmark liquidity demanders and, in aggregate, lose $350 million per year. This finding plus two other findings suggest that the left-digit effect predominates over the two other explanations.