The recent success of crossing networks is often attributed to reduced transaction costs. There are three distinctive characteristics of a crossing network which make the cost situation for crossed orders different from the cost situation for orders traded in the regular market. First, passive matching of orders makes traditional broker/dealer services unnecessary. Second, the price discovery is taking place elsewhere, i.e. there is some primary market from which prices are derived. Third, the network do not guarantee execution.
Passive order matching without the presence of brokers yields low explicit costs. Keim and Madhavan (1998) report that crossing commissions are usually below 2 cents a share. This is substantially lower than commissions charged by brokers on exchanges. The crossing partici- pants are not using dealers to provide liquidity. Hence there are no spread costs. Furthermore, because the crossing price is set independently of the characteristics or the crossed orders, there are no direct price impact costs. There may however be an “implicit” price impact if the exis- tence of a large crossing order is known to participants in the primary market. On the other hand, the risk of non-execution suggests that both timing costs and other forms of opportunity costs from failure to execute may be significant for crossed orders. Moreover, the anonymity provided by most networks makes crossing attractive to informed traders. Uninformed liquidity traders who use crossing networks to reduce explicit and implicit trading costs might therefore incur costs related to adverse selection. Note that, while adverse selection costs for exchange traded orders will be included in the implicit cost component of the implementation shortfall cost, this is not so for crossed orders. As will be discussed further below, the lack of a price mechanism in the network imply that the presence of informed traders can only affect the probability of getting an order executed.
The total cost for an order sent to a crossing network is conditional on whether the crossing attempt is successful or not. Assuming that the investor goes to the regular market if he or she is not able to cross, the ex ante cost situation for a crossed order can be summarized as follows,
E[Crossing cost] = p(cross)E [Total cost|cross] + ( − p(cross))E [Total cost|market]. (2.3) With a given probability, p(cross), the order is executed on the crossing network. If crossed, it will have a cost,
Total cost|cross = Crossing commission | {z }
Explicit cost
+ Implicit price impact| {z } Implicit cost
(2.4)
If the order is not crossed, it is sent to the market and will have a cost as determined by equa- tion 2.1.
Let us now turn to the problem of detecting adverse selection costs in the crossing network. We argue that the presence of informed trading in the network, will affect the subsequent per- formance of the stocks offered in the crossing network. To see this, suppose first that there are only liquidity traders in the network. The probability of getting an order crossed should then be a result of the random idiosyncratic preferences of these liquidity traders, and therefore com- pletely unrelated to the subsequent performance of the desired stocks. Next, suppose that there are also informed traders in the crossing network. Consider the submission of a buy order and look at the situation where an order is not crossed. Non-execution may have one of two reasons: 1. There did not happen to be any liquidity traders who wanted to sell these stocks on these particular dates, nor did anyone have private information on these stocks indicating that they should be sold.
2. The trader was “crowded out” by other traders who wanted to buy the stocks. The other traders could have been either liquidity traders or informed traders.
Let us also assume that informed traders with (relatively) long lived information will use an opportunistic strategy of trying crossing first and then trading in the main market if the crossing attempt fails.9Our trader then knows that the informed traders are most likely on the same side of the market: they are also buying. If the informed traders are selling, case 1 is ruled out, and the only reason that the trader did not get a cross is that he was “crowded out” by other liquidity traders also wanting to buy. The presence of informed traders on his side will make case 1 less likely and tend to “crowd out” his trades from any liquidity traders wanting to sell in case 2. The opposite argument applies to stocks where our liquidity trader did manage to buy in the cross. Then it is more likely that any informed traders were on the opposite side of the trade. More specifically, suppose that the trader is facing informed traders who know that the current price is “too high,” the stock is overvalued. These traders will try to sell, increasing the probability of a cross. On the other hand, suppose he is facing informed traders who know the price is “too low.” These traders will try to buy, decreasing the probability of a cross. In symbols, let subscript “l” denote pure liquidity trading and subscript “l, i” denote the presence of both liquidity traders and informed traders, and let superscripts “+” indicate positive information (undervalued stock) and superscript “−” indicate negative information (overvalued stock). Thus, for an uninformed investor, we will have that
p(cross)−l,i> p(cross)l> p(cross)+l,i (2.5)
The above discussion is rather informal, but gives the gist of the argument.10 Applying these arguments about execution probability, if we look at the difference in ex post performance be- tween the stocks a liquidity trader managed to buy in a crossing network and those that did not get crossed, the non-crossed stocks are likely to perform better than the crossed stocks.
9This is shown to be a feature of the informed’s strategy in Hendershott and Mendelson (2000). 10The same result is shown more formally on page 2085 of Hendershott and Mendelson (2000).
If there are traders present who have information about whether a stock is overvalued (un- dervalued), the expected conditional costs are higher (lower) than they would otherwise be, both in the cross and the market. However, since informed traders also affect execution probability (p(cross) in equation (2.3)), there is no unambiguous prediction about how the presence of in- formed traders will affect expected total execution costs (E[Crossing cost] in equation (2.3)). Thus, in the case of informed trading in the crossing network, the optimal choice of order sub- mission strategy for an uninformed trader will depend on the cost advantage of the crossing network relative to the main market, and the magnitude of adverse selection costs in the cross- ing network relative to the main market.