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To: Gary Korn who wrote (3520)	8/13/1999 10:53:00 AM
From: Joseph Silent	Read Replies (1) \| Respond to of 10027

Gary, I'm using a contrived example to show this. Assume only two traders on ISLD, you (selling) and I (buying). Assume increments are in units of 1/16 of a dollar. Assume that all trades are in $41 - $42 range (making it favorable to ECNs, just for the example), and assume uniformly random orders in the interval. Suppose I place a limit buy of XXX for $41-1/16. The probability that your limit sell order matches is 1/16 Suppose my limit buy is at $41-5/16 The probability that your limit sell order matches is 5/16 So there are 16 possibilities, using conditional probability, even if we make the assumption (favorable to ECNs) that both our orders are in the range $41 - $42. If we move to nickels, there will be 20 possibilities. If we move to pennies, there will be 100 possibilities. Fragmentation increases as the number of possibilities increases, and as fragmentation increases (fewer orders at each particular price) the probabilities of matches correspondingly decrease. [Contrast this to a system which, just as an example, restricts buying/selling only at the prices $41, $41.5 and $42 -- you will see the number of orders at each price and the probability of matches go up sharply here.] Its a question of distributing n orders in m bins. Keeping n fixed, as m goes up, n/m goes down, and the probability of selecting a bin with an order in it goes down. In reality, the probability of a match will depend on the number of buys and sells at different prices (the distribution), but as you move from $ 1/16, to $0.05 to $0.01 you get more and more fragmentation. This means "the probability of a match DECREASES" and quite rapidly. Perhaps the ECNs are saying that (new) volume will take care of this. Whether that is true or not (who knows? We'll need data -- probability distributions) I am wondering why this very obvious point is being hidden behind a lot of fluff. I can also see a lot more traffic as orders get put in and canceled in an attempt to make matches. This transalates into more delay (message processing) in overall execution. Anyone see anything wrong with my logic? I am open to correction. :) Joseph