The Optimal Price of a Stock: A Tale of Two Discretenesses

63 Pages Posted: 8 Mar 2021 Last revised: 6 Nov 2021

See all articles by Sida Li

Sida Li

University of Illinois at Urbana-Champaign

Mao Ye

University of Illinois at Urbana-Champaign

Date Written: November 3, 3021

Abstract

Economists commonly assume that price and quantity are continuous variables, while in reality both are discrete variables. As U.S. regulation mandates a one-cent minimum tick size and a 100-share minimum lot size, we predict that less volatile stocks and more active stocks should choose higher prices to make pricing more continuous and quantity more discrete. Despite heterogeneous optimal prices, all firms achieve their optimal prices when their bid–ask spreads equal two ticks, when frictions from discrete pricing equal those from discrete lots. Empirically, our theoretical model explains 57% of cross-sectional variations in stock prices and 81% of cross-sectional variations in stock liquidity. We find that most stock splits move the bid–ask spread closer to two ticks and that correct splits contribute 94 bps to split announcement returns. Optimal pricing can increase median U.S. stock value by 106 bps and total U.S. market capitalization by $93.7 billion.

Keywords: Nominal price, liquidity, tick and lot sizes, stock split

JEL Classification: G14

Suggested Citation

Li, Sida and Ye, Mao, The Optimal Price of a Stock: A Tale of Two Discretenesses (November 3, 3021). Available at SSRN: https://ssrn.com/abstract=3763516 or http://dx.doi.org/10.2139/ssrn.3763516

Sida Li

University of Illinois at Urbana-Champaign ( email )

601 E John St
Champaign, IL 61820
United States

Mao Ye (Contact Author)

University of Illinois at Urbana-Champaign ( email )

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