Discrete Prices, Discrete Quantities, and the Optimal Price of a Stock
60 Pages Posted: 8 Mar 2021 Last revised: 7 Jul 2023
Date Written: July 4, 2023
U.S. regulations mandate a one-cent minimum tick size and a 100-share minimum lot size, so a firm that chooses a low (high) price for its stock will see a more discrete (continuous) price and a more continuous (discrete) quantity per share. We show that this trade-off generates a U-shaped relationship between a stock’s price and its liquidity, and our model explains 81% of cross-sectional variations in bid–ask spreads. We then solve the liquidity-maximizing price, which explains 57% of cross-sectional variation in stock prices. Adjustments toward optimal prices rationalize 91% of stock splits and contribute 94 bps to split-announcement returns.
Keywords: Nominal price, liquidity, tick and lot sizes, stock split
JEL Classification: G10, G14, G18, D47
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