Size Discovery

Updated on

Size Discovery

Darrell Duffie

Stanford University – Graduate School of Business; National Bureau of Economic Research (NBER)

Haoxiang Zhu

Massachusetts Institute of Technology (MIT) – Sloan School of Management; National Bureau of Economic Research (NBER)

November 1, 2015


Size discovery is the use of trade mechanisms by which large quantities of an asset can be exchanged at a price that does not respond to price pressure. Primary examples of size discovery include “workup” in Treasury markets and block-trading “dark pools” in equity markets. By freezing the execution price and giving up market-clearing, a size-discovery mechanism overcomes large investors’ concerns over price impacts. Price-discovery mechanisms clear the market, but cause investors to internalize their price impacts, inducing costly delays in the reduction of position imbalances. We show that augmenting a price-discovery mechanism with a size-discovery mechanism improves allocative efficiency.

Size Discovery – Introduction

This paper shows that size-discovery mechanisms, by which large transactions can be quickly arranged at fixed prices, improve allocative efficiency in markets with imperfect competition and private information over latent supply or demand imbalances. An important aspect of market liquidity is the ability to quickly buy or sell large quantities of an asset with a small price impact. Price impact is primarily a concern of large strategic investors, and not of small or “price-taking” investors. Those particularly worried about price impact therefore include large institutional investors such as mutual funds, pension funds, and insurance companies. Price impact also concerns major financial intermediaries such as broker-dealers, who often absorb substantial inventory positions in primary issuance markets or from their client investors, and then seek to offload these positions in inter-dealer markets. For example, Duffie (2010) surveys widespread evidence of substantial price impact around large purchases and sales, even in settings with relatively symmetric and transparent information.

Under imperfect competition, the strategic avoidance of price impact is a major cause for allocative inefficiency in markets that offer price discovery, such as sequential double auctions or central limit order books. As we will explain, in order to reduce price impacts in price-discovery markets, investors “shade” their order sizes, meaning that they only partially express their true trading interest at any moment and at any given price. This is manifested, for example, by splitting large orders and executing them piecemeal over time, which can involve costly execution delays.

We argue that size discovery is an effective way to mitigate the allocative inefficiency caused by strategic avoidance of price impact. Examples of size-discovery mechanisms used in practice include:

  • Workup, a trading protocol by which buyers and sellers successively increase, or “work up,” the quantities of an asset that are exchanged at a fixed price. Each participant in a workup has the option to drop out at any time. In the market for U.S. Treasuries, Fleming and Nguyen (2013) find that workup accounts for 43% to 56% of total trading volume on a typical day. Workup has been increasingly adopted for trading standardized over-the-counter derivatives.1 Workup is the primary example of size discovery modeled in this paper.
  • Block-crossing “dark pools,” which are predominantly used in equity markets. In a typical “midpoint” dark pool, buyers and sellers match orders at the midpoint of the best bid price and best offer price shown on transparent exchanges. Dark-pool allocations are either by time priority or by pro-rata rationing on the heavy side of the market. Dark pools account for about 15% of trading volume in the U.S. equity markets. Certain dark pools offer limited price discovery. Others do not use price discovery at all. For an overview, see Zhu (2014). Dark pools are our secondary example of size discovery.

Despite some institutional differences discussed later in the paper, workups and mid-point dark pools share the key feature of size discovery: crossing orders at fixed prices without price impact. Although aware of the trade price, the participants in a workup or dark pool are uncertain of how much of the asset they will be able to trade at that price, which is not sensitive to their demands. One side of the market is eventually rationed, being willing to trade more at the given price. Thus, a size-discovery mechanism cannot clear the market, and is therefore inefficient on its own. Nevertheless, precisely by giving up on market clearing, a size-discovery mechanism reduces the adverse effect of investors’ strategic incentives to dampen their immediate demands. We show, as a consequence, that a market design combining size discovery and price discovery offers substantial efficiency improvement over a market that relies only on price discovery. In particular, we demonstrate that in a market with imperfect competition and private information concerning order imbalances, allocative efficiency is improved by adding a size-discovery mechanism, modeled as a workup, before a price discovery mechanism, modeled as a sequential-double-auction market.

Our modeling approach and the intuition for our results can be roughly summarized as follows. An asset pays a liquidating dividend at a random, exponentially-distributed future time. Before this time, double auctions for the asset are held among n strategic traders at evenly spaced time intervals of some length Thus, the auctions are held at times Screenshot_2 and so on. Before the first of these auctions, the inventory of the asset held by each trader has an undesired component, positive or negative, that is not observable to other traders. Each trader suffers a continuing cost that is increasing in his undesired inventory imbalance. In each of the successive double auctions, traders submit demand schedules. The market operator aggregates these demand schedules and calculates the market-clearing price, at which total demand and supply are matched.

Size Discovery

See full PDF below.

Leave a Comment