The Dynamics of Dealer Markets Under Competition

The behavior of competing dealers in securities markets is analyzed. Securities are characterized by stochastic returns and stochastic transactions. Reservation bid and ask prices of dealers are derived under alternative assumptions about the degree to which transactions are correlated across stocks at a given time and over time in a given stock. The conditions for interdealer trading are specified, and the equilibrium distribution of dealer inventories and the equilibrium market spread are derived. Implications for the structure of securities markets are examined. IN THIS PAPER the behavior of competing dealers in security markets is examined. Much of the theoretical work on dealers (Demsetz [6], Tinic [18], Garman [8], Stoll [16], Amihud and Mendelson [1], Ho and Stoll [11], Copeland and Galai [3], Mildenstein and Schleef [13]) has recognized that dealers may face competition from other dealers or investors placing limit orders, but nonetheless has analyzed only a single (representative) dealer. This approach is quite reasonable for the New York Stock Exchange specialist who has a quasi-monopoly position, but it is less applicable when considering other markets such as the over-thecounter market where there are several dealers with equal access to the market. Similarly the empirical studies of dealer bid-ask spreads (Demsetz [6], Tinic [18], Tinic and West [19], Benston and Hagerman [2], Stoll [17], Smidt [15]) have either been based on models of a single dealer or have lacked a theoretical foundation based on the microeconomics of the dealer. This paper develops a theoretical model of equilibrium in a market with competing dealers and provides a basis for empirical work that would distinguish competing and monopolistic dealer markets. The paper is concerned with the behavior and interaction of individual competing dealers and with the determination of the market bid-ask spread. Markets with several dealers, several stocks and several periods are considered. Dealers bear risk arising not only from uncertainty about the returns on their inventories but also from uncertainty about the arrival of transactions. Each dealer also recognizes that his welfare depends on the actions of other dealers and each sets bid and ask prices to maximize his own expected utility of terminal wealth. A recent paper by Cohen, Maier, Schwartz and Whitcomb [5] examines similar issues in the context of an auction market in which the market spread is determined by limit orders. However, unlike the model of this paper, their analysis is not based as clearly on a model of individual traders' maximizing behaviors nor are the costs of placing * Financial support of the Dean's Fund for Faculty Research at the Owen Graduate School of