The inventory models described in the previous sections dictate that inventory holding costs partially determine the bid-ask spread. The information-based models use the existence of asymmetric information in the market partially to explain the determinants of bid-ask spreads. These models are based on the fact that in the market there are two different types of traders: informed and uninformed. The existence of these two different kinds of traders creates information costs. This cost reflects the loss that the average investor will face when trading against an informed trader. An informed trader is expected to buy when he knows that the price of a particular stock is low and vice versa. In contrast, the market maker must always quote prices to buy and sell. Therefore,
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the market maker must offset his potential loss when trading against informed traders by gaining from uninformed traders from the existence of bid-ask spread.
Several papers focus primarily on the determinants of bid-ask spread based on the assumption that the dealer faces specially informed traders and liquidity- motivated traders.
The origin of the information models
The foundations of these theoretical approaches were set by Bagehot (1971). He explains the important role of the market maker in the stock market game. The role of the market maker is to provide liquidity by stepping in and transacting whenever equal and opposite orders fail to arrive in the market at the same time (Bagehot 1971). He describes those who are willing to participate in the market game and transact with the market maker. He identified three kinds of transactors: the Information-motivated transactors (those possessing special information), the liquidity-motivated transactors, and the transactors acting on information, which they believe, has not yet been fully discounted in the market price but which in fact has. The market maker will always lose when trading with informed market participants and always gain when trading with liquidity- motivated participants. Therefore, his gains from liquidity-motivated traders must exceed his losses from information-motivated traders. To achieve this, a market maker should set each time a bid-ask spread. A wide spread will deter information-motivated investors from trading and reduce money losses; however it will also reduce the volume of liquidity-motivated transactors, since there is an inverse relationship between liquidity of a market and the bid-ask spread (Demsetz 1968). According to Bagehot the bid-ask spread is determined by the average rate of flow of new information and the volume of liquidity-motivated transactions.
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Asymmetric Information and bid-ask spreads
Although market-makers are well-informed about their asset we should not undervalue the existence of individuals who possess special information about that asset. Trading against these specially informed individuals requires the identification of an additional cost that the market maker is facing. Jafee and Winkler (1976) state that previous analyses have ignored that cost. Their paper focuses on this potential cost and shows that a market-maker should expect to lose when trading with a rational individual, even if the market-maker is more knowledgeable and even if the bid-ask spread is included. They present a model and derive a decision rule that can be employed by any investor possessing special information in order to profit from that information. The model sheds light on the process by which special information is incorporated into the market prices.
Copeland and Galai (1983) study the determination of bid-ask spread in the theoretical context of information effects on the bid-ask spread and use a mathematical approach to model this relation. Their approach builds on Bagehot’s suggestion who mentioned that the main objective of the market maker is to determine a bid-ask spread that will maximize the gains from the liquidity traders and minimize the losses from the informed traders in order to maximize his profit.
Copeland and Galai (1983) derived a mathematical model (profit maximising spread model) that was based on Bagehot’s approach but was extended to predict that the bid-ask spread depends on: the percentage of traders who are informed, the elasticity of demand for liquidity trading, the degree of competition among dealers, the specific risk of the asset being traded, trading volume, and the size of the transaction. The authors developed two models based on the time point that the dealer offers his quote: the instantaneous quote model and the open quote model. The implications for the bid-ask spread are very similar in
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both cases. That is, if the percentage of informed trader’s increases, the bid-ask spread will increase. Moreover, the bid-ask spread decreases as the shift is made from monopoly to a competitive market situation. As the variance of the stock rate of return increases, ceteris paribus, the ask price is raised. There will be a negative correlation between the bid-ask spread and trading volume holding the size of the transaction per unit time constant and there will be a positive correlation between the size of the transaction and bid-ask spread, holding the number of transactions (per unit) constant.
The information of the trade outcome
Glosten and Milgrom (1985) extend the Copeland and Galai (1983) model by incorporating the information revealed by the trade itself. The assumptions of the model are similar to those of Copeland and Galai. The market maker and all market participants are assumed to be risk neutral and act competitively.
What was missing from the model of Copeland and Galai was the information that the market maker possesses following the trade that he has learned from the trade outcome. Therefore, the new price will include also his interpretation of the information of the trade outcome. In order to determine the bid-ask prices they use a standard Bayesian learning.
In particular, the market maker sets bid and ask prices such that _ _
a1 = E[V| B1] = V Pr{V = V|B1} + VPr{V = V|B1} Eq. 2.5 _ _
b1 = E[V| S1] = V Pr{V = V|S1} + VPr{V = V|S1} Eq. 2.6
where
V: when informed agents know that the true value of the stock will be low
_
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S1: when a trader wants to sell a stock to the market maker
B1: when a trader wants to buy a stock from the market maker
To determine the bid price and the ask price the market maker must calculate the following:
_ _
Pr{V = V|S1}, Pr{V = V|S1} and Pr{V = V|B1}, Pr{V = V|B1} Eq. 2.7
From the above we can understand that prices depend on the probability of a sale or a buy. Therefore, there may be more sell orders or more buy orders depending on the nature of the information. This contradicts the theoretical models discussed earlier since the assumption in these models was that buys and sells have the some probability. The model derived by Glosten and Milgrom predicts that the bid-ask spread depends on the nature of the underlying information, the number of informed traders, the trader’s elasticity and the trade size.
Finally, it is worth mentioning that according to the model, under some conditions, asymmetric information can result to lack of trades reflecting the unwillingness of the market maker to trade with a large number of informed traders and therefore setting a bid-ask spread that is so large that everyone is unwilling to trade. These can result in a breakdown of the market system. An important application of this is whether market structures are such as to prevent this undesirable likelihood.
In another study, Easly and O’Hara (1987) suggest a model where the traders have the ability to choose order sizes and therefore incorporate a strategic element in the process. Moreover, an additional uncertainty issue is considered, which relates with the fact that the existence of new information is not assumed. The market maker and all market participants are assumed to be risk neutral and act competitively. In addition, the fact that someone wishes to trade causes the
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market maker to revise his expectation of the asset’s value and inventory is not relevant. The most important conclusion in their paper is that trades could vary across trade sizes and that when a market maker revises his prices following a trade, he also takes into consideration the trade size.