Who Provides Liquidity and When: An Analysis of Price vs. Speed Competition on Liquidity and Welfare

Abstract

I model the interaction between buy-side algorithmic traders (BATs) and high-frequency traders (HFTs). When the minimum price variation (tick size) is small, BATs dominate liquidity provision by establishing price priority over HFTs in the limit order book (LOB), because providing liquidity is less costly than demanding liquidity from HFTs. A large tick size, however, constrains price competition and encourages HFTs to provide liquidity by establishing time priority. An increase in adverse selection risk raises the unconstrained bid-ask spread, reduces tick size constraints, and discourages HFTs’ liquidity provision. An increase in tick size increases transaction costs and harms liquidity demanders, but it does not benefit liquidity providers because the costs of speed investments dissipate the rents resulting from the tick size. I predict that mini-flash crashes are more likely to occur for stocks with a smaller tick size and higher adverse selection risk. I suggest that the literature should not use the message-to-trade ratio as a cross-sectional proxy for HFTs’ liquidity provision because stocks with more liquidity provided by HFTs have a lower message-to-trade ratio.