I am writing this post in response to the CBS "60 Minutes" on 10/10/2010 on the subject of high frequency trading. If you think that achieving profit every single day for years and years is impossible, think again! In fact, the opposite is true: not making a profit EVERYDAY (or even every hour) is nearly impossible. I don't remember whether Thorp, Shannon, or Kelly proposed the problem of rebalancing on the stock that either goes up or down 50% each day. In reality, no stock goes up or down 50% everyday. In one of my previous posts, I have addressed the problem of this random jump vs random walk: http://www.elitetrader.com/vb/showthread.php?s=&postid=2796098#post2796098 Rigorous proof of how a trader who can enter bid and ask at sub-penny prices will have mathematically guaranteed upper hand over a trader who can only enter bid and ask at penny-level prices is simple. But here is a common sense way to think about it: For retail traders, they can only play at penny-level. For them, prices move up or down by multiples of one-penny each time. In other words, the smallest step of retail traders in their price random walk if one penny. Institutional traders, however, can play at 0.01 penny level (basis point), and will win nearly every time they trade against retail traders. Consider a random walk for retail traders. The price starts at 0 and goes up or down one penny with equal probability. The retail trader sets profit target at +2 pennies and stop loss at -1 penny. To trade against the retail trader, the institutional trader sets profit target at +1 penny and stop loss at -0.01 penny. Note that each step of the random walk of the retail trader is a random jump for the institutional trader whose steps are 100 times smaller. Now the walk begins. If the price goes to +1, the retail trader has not reaches his profit target, but the institutional trader has already made one penny; if the price goes to -1, the retail trader is stopped out, but the institutional trader loses only 0.01. Now at either +1 or -1, the institutional trader can again enter a profit target at one penny higher or a stop loss 0.01 lower, while the retail trader can only languish. One successful trade for institutional trader will cover 99 losing trades, and yet winning and losing trades occur with equal probability for institutional traders. If an institutional trader does a multitude of trades, how can he ever have a losing day, or a losing minute!?! Sub-pennying allows institutional traders or high-frequency traders unfair mathematical advantage. SEC must regulate to level the playing field to protect the public. To curb high frequency trading, financial transaction tax is unnecessary if sub-pennying is prohibited. We should write to our senetors and congressmen to outlaw sub-pennying. Dark pools, quote stuffing, front running are still conventional weapons, but sub-pennying is a nuclear weapon and must be stopped!!! Comments welcome! Please write to your senators and congressmen, write to Mary Schapiro, write to Sen. Ted Kaufman of Delaware.

This is all very convincing, but I do have one question. If retail investors can't 'play' at the sub penny level, then who's taking the other side of all of those sub penny stop loss trades?

The counter-party does not need to be another institution. Imagine 99 retail traders with no change in their net asset and one with a penny gain. The exchange or brokerage house computes the average of these 100 retail traders and fills the institutional trader's stop loss. Let A be a set of all retail traders whose fortunes go up and down with time, and B be a 100-element subset of A with the property that the average of B is k. Given k, you can almost always find B given A being large enough and time long enough. I use IB, and I frequently see my fill price beyond 2 decimal points in $USD, especially if an option quote is 0.01; factoring in commission, my fill price is not (0.01 - commission per share). I don't work at any exchanges or brokerage houses. Please correct me if I am wrong.

That guarantee falls apart when sub-penny trading becomes open to everyone. Trading is a zero-sum game. For someone to win, someone else has to lose.

IMHO, your analysis makes some sense but I think the probablility is not 50% win loss if the stop/target threshholds is .001 and .01. It is like saying in the pre decimalization days that the prob of hitting a win loss is 50% if your stop loss is 1/8 and a take profit target of 1/2.

What about fees and comissions ? or rebate ? Is it profitable for HFT and HFT institutional investors to aim for a 1 penny profit ? 100 losing trades at 0.01 penny should cost quite a bit in selling tax ?!?

Most of the sub penny prints that you see are in fact, a dealer buying from a customer - not traded openly on a exchange or ECN. The firm that gets the order fills the customer at a better then bid price (if a customer wants to sell), and the will inventory the stock. If the firm then chooses to either liquidate if the bid gets hit or not is entirely up to them. As soon as the firm takes the position, they have market risk due to the fact that they filled a customer order at a price better than the NBBO. Why would you want to make it illegal for a broker dealer to fill its customer at a better price? The main job of the regulators is to look after the customer, and as long as they are getting a better price from the dealer then the open market, I don't think they will change the rule.

Example given is very bad and impractical. It does not consider trading fees. The retail trader is there to profit as much as possible, to capture as many pennies as possible. Who cares if the institutions want to profit from subpennies. Furthermore, the two names mentioned are Democrat hacks. Democrats are proving they don't know how to run a country!