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Old 08-04-2008, 08:02 PM   #1

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Arrow Price Distribution and Probability of a Winning Bet

Hey all, havn't been here in a bit, thought i'd contribute.


In a straight-forward trade, your probability of winning is dependent on the risk/reward ratio(i'll call bet ratio) available to you. The bet ratio available is dependent on the number of participents in your market(who use up these ratios). The more participents, the more betting ratios, the more evenly price is distributed.









What i mean by price distribution can be easily seen by comparing QQQQ and EBAY. Because the Q's market is more elaborate, the probable outcomes of a bet are more accuratly realized by price in the given time-frame. For example: one plays a bet with a reward of 3 points and a risk of 1 point. In an elaborate market, he loses 3 times more than he wins and breaks even. Distances for price to travel are matched with a probable frequency (i.e.: price can move 4 points once, 2 points twice, 1 point four times)

In EBAY, it's not the case. The lack of participents creates a lack of bet ratios... and the distribution of price does not reflect an elaborate market. The reason the Q's price distribution appears more volatile in the short-term is because it is realising the probabilities of every bet more accuratly. Also, in EBAY, the ratio of day traders to long-term traders is less, pushing price trends.

So...the odds of a traders success is much more likely in an unelaborate market, where the chances of his bet ratio being matched by an opposing bet with the same ratio at any given point in time are less likely.

If liquidity is not an issue, there's no reason imo to be playing in a more elaborate market than the trader needs to. to find the bet ratios that aren't being used just make a judgement call with the chart or run enough data in excel and find distance/frequency pairs that are inefficient.

ps: I put the post in this section because although it's not MP, it's alot about observing the distribution of price and can be analyzed with MP.

Last edited by Northern boy; 08-04-2008 at 08:08 PM.
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Old 08-09-2008, 09:28 PM   #2

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Re: Price Distribution and Probability of a Winning Bet

eg, markets differ in degree of difficulty.

lol can i get a witness?
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Old 08-09-2008, 10:01 PM   #3

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Re: Price Distribution and Probability of a Winning Bet

Actually, I'm going to make a list of markets in order of difficulty to trade. It will allow new and experienced traders to find just enough liquidity without being in a more elaborate market than necessary. If you weren't already familiar with this concept it will make you that much more money and it will save new traders boat loads.

if any of all this doesn't make sense let me know.
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Old 08-11-2008, 04:06 AM   #4

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Re: Price Distribution and Probability of a Winning Bet

Are you implying 'elaborate' markets have less inefficiencies and so are harder to find a statistical edge in? Are elabroacy and liquidity always correlated?
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Old 08-11-2008, 07:35 AM   #5

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Re: Price Distribution and Probability of a Winning Bet

Yes, that's it. All else aside, I think if one traded blind they would be significantly more ahead in the latter market than the former.

the distances for price to travel aren't paired with their corresponding frequency as efficiently. The trader's r/r wouldn't break him even in the latter market, as it instinctively should. If one picks the appropriate r/r I think there's an advantage in these distance/frequency inefficiencies.

I wouldn't assume that the correlation is perfect between liquidity and elaboracy(not a word?), but at a certain point there's enough room for funds to run programs. Not only does the r/r break even, but the odds are worse because they watch the books and open orders.
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Old 08-11-2008, 09:43 AM   #6

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Re: Price Distribution and Probability of a Winning Bet

I'm not sure I totally agree with this. First, by "elaborate" aren't you simply refering to volatility if your only looking at price?
I guess there is another factor in there that I do agree with as far as the participants motivations for trading the instrument. Q's have more volatility because of the arbitrage players, ect...I'm not sure I agree though that this correlates much with liquidity. I think you have to take into consideration that the purpose of a market is to price an instrument forward and the real reason that Q's have more volatility than ebay is because its fundamentally harder to price Q's forward than ebay.
The real problem though is if you compare this idea between corn futures, eur/usd in forex and a small cap equity X on the AMEX.

eur/usd is far more deeply liquid but you don't see crazy volatility since the variables trying to be priced are so huge and the rate of information that effects the participants trading is slower. Are corn futures harder to trade than equity X? How would you order these 3?
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Old 08-11-2008, 02:05 PM   #7

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Re: Price Distribution and Probability of a Winning Bet

As an aside there are a couple of things that have a big impact on volatility 'thickness' (volume) is one of them as is 'granularity' (tick size). Good old Harris goes into great detail why.
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Old 08-12-2008, 01:10 AM   #8

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Re: Price Distribution and Probability of a Winning Bet

Quote:
Originally Posted by BlowFish »
Good old Harris goes into great detail why.
Blowfish, any chance you can do a review of this book? Maybe point to parts that you found interesting? I'm not sure what it is about this book that it defeats me without mercy.
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