Abstract
Economists usually assume that price and quantity are continuous variables, while most market designs, in reality, impose discrete tick and lot sizes. We study a firm’s trade-off between these two discretenesses in U.S. stock exchanges, which mandate a one-cent minimum tick size and a 100-share minimum lot size. A uniform tick size favors high prices because the bid–ask spread cannot be lower than one cent. A uniform lot size favors low prices because low prices reduce adverse selection costs for market makers when they have to display at least 100 shares. We predict that a firm achieves its optimal price when its bid–ask spread is two ticks wide, when the marginal contribution from discrete prices equals that from discrete lots. Empirically, we find that stock splits improve liquidity when they move the bid–ask spread towards two ticks; otherwise, they reduce liquidity. Liquidity improvements contribute 95 bps to the average total return on a split announcement of 272 bps. Optimal pricing can increase the median U.S. stock value by 69 bps and total U.S. market capitalization by $54.9 billion