General Topics
Markets
Technical Topics
Brokerage Firms
Community Lounge
Site Support

# Sub-pennying MATHEMATICALLY GUARANTEES long term trading profit. SEC must regulate!

Discussion in 'Automated Trading' started by MathAndLogic, Oct 13, 2010.

1. ### MathAndLogic

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:

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

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
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
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
a multitude of trades, how can he ever have a losing day, or a losing
minute!?!

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!!!

write to Sen. Ted Kaufman of Delaware.

2. ### ASusilovic

Pffttt...legalized crime, so what ? Not the first time in the US of A...

3. ### Claudius

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?

4. ### MathAndLogic

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.

5. ### Kubinec

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.

6. ### mushinseeker

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.

7. ### luisHK

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 ?!?

8. ### Bigaeon

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.

9. ### luisHK

Sorry, I meant " for HFT and non HFT institutional investors "

10. ### Petsamo

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!

#10     Oct 13, 2010
ET IS FREE BECAUSE OF THE FINANCIAL SUPPORT FROM THESE COMPANIES: