1. #1
    Dark Horse
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    game theory?

    Imagine a stock market somewhere. If it crashes, the economy crashes. By keeping it healthy the appearance of a healthy economy can be projected.

    At some point, to 'save the economy', it is decided to give financial institutions a huge amount of free money. The exact amount is not known, and can't be verified.

    The financial institutions, with this free money, buy up cheap stocks. The stock prices rise. Talk of economic recovery is in the air. For a while, everybody is happy.

    There is just one problem. Where the stock market, under normal circumstances, has a self-correcting mechanism, allowing for prices to drop, the unspecified amount of free money handed out to these financial institutions enables them to prevent drops. When a price of a key stock drops too far, they simply buy up more. (If they bought a stock at 20, and it is now at 40, why would they sell it when it drops to 38, when they can buy more and send the price to 45 and higher?)

    The eventual outcome of this bubble is inevitable. Yet, while it continues to grow, a profit can be made.

    What would you do?
    1) stay far away
    2) buy stocks
    3) short stocks
    Last edited by Dark Horse; 04-24-10 at 02:13 PM.

  2. #2
    trixtrix
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    this is typical layman garbage imo, the "free money" is not free, it is a loan that needs to be paid back w/ interest. using your theory, drops are inevitable when the money that the banks used to tank up the stock market must be repaid back to FED.

    this really need not be in think tank section

  3. #3
    Dark Horse
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    Imagine... (the very first word) <= consider the question hypothetical.

    The question is if there is a right strategy, using game theory, or not.

    The situation is borrowed from real life, but not intended to reflect real life perfectly. That should take care of your personal disagreement with the picture I painted.

  4. #4
    pats3peat
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    interesting stuff ill be keeping tabs on this thread

  5. #5
    mrmarket
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    "Markets can remain irrational longer than you can remain solvent."

    Interesting thread, and I will follow it.

  6. #6
    Flying Dutchman
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    Game Theory is NOT useful in the stock market.

    ...way too many decision makers to model and you really don't know just what each decision matrix is much less evaluate it.

  7. #7
    Dave Head
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    I would recommend option "1) stay far away". There are other places that you can put your money to get a decent return.

    Quote Originally Posted by Dark Horse View Post
    ...The question is if there is a right strategy, using game theory, or not...
    No, if you pick option "2) buy stocks", the "best" strategy is to monitor the market on a minute-to-minute basis. When the bottom begins to fall out, you'll know it, you won't need a mathematical model to tell you. If your job does not involve keeping your eye on the market, the next best strategy is the use of "stop-loss orders". For example, if the current price of an asset is $90, you can set up a stop-loss order at $85 or $80. If the price of that asset falls to your set price, "program trading" automatically sells your asset. WARNING: If you set the price at $80, that does not mean that you'll get $80. It means that if the price falls to $80, start looking for a buyer. If the market is in a free-fall, you might be lucky to get $75.

    Put yourself in the position of a broker. If the bubble pops, you can't call everyone and tell them to sell. That would cause a panic. (This is one case where game theory does apply.) You call your best client only and tell them to sell now. Then you let all your other clients (schmucks like us) prop up the market while your best client sells. Later, you tell all your other clients, who by now have lost a lot of money and are now calling you: "Remember that you are a long-term investor. Don't panic. Be patient."

    Quote Originally Posted by mrmarket View Post
    "Markets can remain irrational longer than you can remain solvent."...
    The source of this quote was "Hedge Hogging", p. 87, by Barton Biggs. If mrmarket is trying to say that option "3) short stocks" is a bad idea, then I agree. If you believe that bubbles are created by "even bigger idiots" that will pay more for an asset than you did, then expecting a bubble to pop when corporate profits are exceeding expectations is foolhardy.

    Quote Originally Posted by trixtrix View Post
    ...the "free money" is not free, it is a loan that needs to be paid back w/ interest. using your theory, drops are inevitable when the money that the banks used to tank up the stock market must be repaid back to FED.
    No, the Fed lends money at less than 1%. The borrower takes that money and buys US treasury notes at more than 3%. The difference is a gift, a hidden way of making the taxpayer repair the balance sheet of troubled financial corporations. This is one probable reason why the Fed is refusing an audit.

    Quote Originally Posted by trixtrix View Post
    this really need not be in think tank section...
    Agreed, it belongs in "Politics & Economics". As I recall, SBR had an "investments" forum, but I guess that withered and died.
    Last edited by Dave Head; 04-25-10 at 04:23 PM. Reason: typo

  8. #8
    suicidekings
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    Quote Originally Posted by Dave Head View Post
    Agreed, it belongs in "Politics & Economics". As I recall, SBR had an "investments" forum, but I guess that withered and died.
    Either way, interesting read, Dave. Nice post

  9. #9
    ljump12
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    If your interested in trading, go pick up a book "reminiscences of a stock operator" written 80 years ago, but still holds damn true.. Can also be applied to sports betting. I've said it before, wall st is a much bigger, smarter casino.

    Some interesting quotes

    Re what Dave was saying about stops "It happened just as I figured.* The traders hammered the stocks in which they figured would uncover the most stops, and sure enough, prices slid off."

    "What beat me was not having brains enough to stick to my own game – that is, to play the market only when I was satisfied that precedents favoured my play.* There is the plain fool, who does the wrong thing at all times everywhere, but there is also the Wall Street fool, who thinks he must trade all the time.* No man can have adequate reasons for buying or selling stocks daily – or sufficient knowledge to make his play an intelligent play."

  10. #10
    adlai
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    Quote Originally Posted by Flying Dutchman View Post
    Game Theory is NOT useful in the stock market.

    ...way too many decision makers to model and you really don't know just what each decision matrix is much less evaluate it.
    agreed. and i'm an economist by trade, it's what i do for a living. i'm not sure this is a relevant application of any game theory techniques.

  11. #11
    Flying Dutchman
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    ...on the other hand, I have found applications for game theory in sports

  12. #12
    Dark Horse
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    Nice post, Dave.

    To me, personally, the market's reliability can be measured by the presence of fluctuations. If there are virtually no fluctuations, and prices just go up without corrections, then a bubble is in the works. I can't trade without fluctuations, nor do I want to. But once they return, I will be shorting selected stocks for sure.

    It may still be preferable to invest with the positive momentum. Because if the bubble burst, and the economy truly tanks, then money is pretty much worthless anyway. An alternative would be to invest in something not affected by the dollar losing its value.

    My choice would be to wait out the wild growth period, until fluctuations return. Then I'll get back in by shorting, because many stocks will be overpriced (they already are). And if the bubble popped I'd be on the right side. I don't care about missing the growth phase of the bubble, because it is unreliable, by my definition, for lack of meaningful fluctuations.



    As to the politics and economics forum. You mention game theory there, and they'll turn it into a republicans versus democrates feud.

  13. #13
    adlai
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    Quote Originally Posted by Dark Horse View Post
    Nice post, Dave.

    To me, personally, the market's reliability can be measured by the presence of fluctuations. If there are virtually no fluctuations, and prices just go up without corrections, then a bubble is in the works. I can't trade without fluctuations, nor do I want to. But once they return, I will be shorting selected stocks for sure.

    It may still be preferable to invest with the positive momentum. Because if the bubble burst, and the economy truly tanks, then money is pretty much worthless anyway. An alternative would be to invest in something not affected by the dollar losing its value.

    My choice would be to wait out the wild growth period, until fluctuations return. Then I'll get back in by shorting, because many stocks will be overpriced (they already are). And if the bubble popped I'd be on the right side. I don't care about missing the growth phase of the bubble, because it is unreliable, by my definition, for lack of meaningful fluctuations.



    As to the politics and economics forum. You mention game theory there, and they'll turn it into a republicans versus democrates feud.
    read robert lichello's book "how to make $1,000,000 in the stock market automatically." it has an awful title, but the book is a great read and discusses this principle in great detail. some of the most profitable and successful money managers use his theory of investment. it is one of the most underrated investment management books. i highly recommend it if this type of stuff interests you.

  14. #14
    mrmarket
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    Quote Originally Posted by Dave Head View Post

    The source of this quote was "Hedge Hogging", p. 87, by Barton Biggs. If mrmarket is trying to say that option "3) short stocks" is a bad idea, then I agree. If you believe that bubbles are created by "even bigger idiots" that will pay more for an asset than you did, then expecting a bubble to pop when corporate profits are exceeding expectations is foolhardy.
    The quote is attributed to John Maynard Keynes.

    http://www.maynardkeynes.org/keynes-the-speculator.html

    What I meant is that you should probably not be participating in the market at all if the your profit depends on your timing the market it in this situation.

    Anyone guess where my screen name comes from?

  15. #15
    Dark Horse
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    On the topic of fluctuations. I believe volatility is back. lol The Dow dropped 700 points in 15 minutes, then bounced back 600 points in the next twenty minutes. Not the type of fluctuation I had in mind, though. Talk about gambling on steroids.

  16. #16
    roasthawg
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    Quote Originally Posted by Dave Head View Post
    No, the Fed lends money at less than 1%. The borrower takes that money and buys US treasury notes at more than 3%. The difference is a gift, a hidden way of making the taxpayer repair the balance sheet of troubled financial corporations. This is one probable reason why the Fed is refusing an audit.
    Interesting.

  17. #17
    FreeFall
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    Quote Originally Posted by Dark Horse View Post
    On the topic of fluctuations. I believe volatility is back. lol The Dow dropped 700 points in 15 minutes, then bounced back 600 points in the next twenty minutes. Not the type of fluctuation I had in mind, though. Talk about gambling on steroids.
    Now imagine if you had a bot doing high-freq trading and grabbed some of shares when it was down ~7-9%.

  18. #18
    Dark Horse
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    Quote Originally Posted by FreeFall View Post
    Now imagine if you had a bot doing high-freq trading and grabbed some of shares when it was down ~7-9%.

    Gambling on steroids. The market could have crashed today. A drop of 700 points in a matter or minutes, immediately followed by a rise of 600 points. lol If the second move was by the Plunge Protection Team, who was behind the first?

  19. #19
    trixtrix
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    Quote Originally Posted by Dave Head View Post

    No, the Fed lends money at less than 1%. The borrower takes that money and buys US treasury notes at more than 3%. The difference is a gift, a hidden way of making the taxpayer repair the balance sheet of troubled financial corporations. This is one probable reason why the Fed is refusing an audit.
    .
    pls provide evidence that FED loaned TARP money to firms at < 1%. additionally, part of the loan was to buy troubled assets at their current stressed market-values, pennies to the dollar on a notional basis.

  20. #20
    trixtrix
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    i assume by the lack of response that you did not know what you were talking about previously

  21. #21
    Dark Horse
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    As to the original dilemma. The market was finally correcting last week. And what happens? Another huge cash injection, this time from Europe. lol Consider me out for the next six months. Impossible trading conditions for contrarians.

  22. #22
    blix177
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    Buy stocks. Long term health of stock has always been upward. And if long term stock is going to be downward moving forward from this point on, the world will collapse and we got bigger things to worry about.

    World collapse because, of global recession. Countries don't have income to pay for outstanding debt. They will start printing money to lower the value of their money to reduce to absolute value of their debt. Some countries will be sent on hyper inflation with prolong global recession. Resource would be fought for, water, oil, metal, food. World War 3.

    So yea, all else equals, buy stocks. Because if that fails, your dead anyways.

  23. #23
    wrongturn
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    Investing is different from sports betting, in which bet's outcome is decided in short time, while investing outcome can have no time limit. You maybe correct about bubble, but you can't predict when it is going to pop and when it is the bottom for you to act.

  24. #24
    mathdotcom
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    Dark Horse this is why understanding macroeconomics requires micro foundations. It is all about game theory and expectations. Keep up the good work.

  25. #25
    Wrecktangle
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    Economics is about 95% Voodoo Mathematics; Game Theory is about the same, i.e. much more art than "science"

  26. #26
    Dark Horse
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    Quote Originally Posted by Wrecktangle View Post
    Economics is about 95% Voodoo Mathematics; Game Theory is about the same, i.e. much more art than "science"

    Game theory typically defines a problem, so that one choice is the best. Do this, do that, or do nothing. (It's the Joker's territory, if you've seen the last Batman movie). It often recognizes interlinked elements, that require one to see the whole picture, instead of just an isolated part. That may be out of the realm of specialized, blinders-on science, but it is certainly not unscientific.

    If economic experts weren't so busy with their rearview 20/20 vision, they might actually define a problem before it manifests. I've never come across a field where so many after the fact statements are given such importance. Game theory is about foresight. Economics, in the present day and age, seems to be about hindsight. If somebody has a rare original idea he's practically giving a f*cking Nobel prize. Printing and handing out virtually limitless amounts of money to 'financial experts' that f*cked up beyond belief. Yeah, I can see the logic in that. What do they think? That it's a game?

  27. #27
    CFA
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    Quote Originally Posted by Dark Horse View Post
    Game theory typically defines a problem, so that one choice is the best. Do this, do that, or do nothing. (It's the Joker's territory, if you've seen the last Batman movie). It often recognizes interlinked elements, that require one to see the whole picture, instead of just an isolated part. That may be out of the realm of specialized, blinders-on science, but it is certainly not unscientific.

    If economic experts weren't so busy with their rearview 20/20 vision, they might actually define a problem before it manifests. I've never come across a field where so many after the fact statements are given such importance. Game theory is about foresight. Economics, in the present day and age, seems to be about hindsight. If somebody has a rare original idea he's practically giving a f*cking Nobel prize. Printing and handing out virtually limitless amounts of money to 'financial experts' that f*cked up beyond belief. Yeah, I can see the logic in that. What do they think? That it's a game?
    Its out there. Its called Austrian Economics.

  28. #28
    mathdotcom
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    Dark Horse,

    Many have. Mankiw had been warning about Fannie Mae/Mac since 2005 (which was created and pushed by Clinton to [foolishly] promote home ownership). Politicians put politics/image before listening to their advisors. Don't blame the economists.

    And for someone like Bernanke who has more independence, he does not have many tools available to him.

    Look, suppose Bernanke was even able to predict bubbles perfectly and then comes out on TV and says "there is a bubble and it is going to burst in 2012". Then all he does is make the bubble burst today instead of tomorrow. There is no way to burst it in advance without pain.

    Economists are always pointing out huge problems and always get ignored. Economists have been warning about the unsustainability of social security. Economists have been warning especially fervently the past few years about U.S. debt. Is Obama listening? Obviously not. Are the voters concerned? Obviously not enough.

    So when the economy stagnates for the next 20 years, don't blame economists.

  29. #29
    Dark Horse
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    There are good economists. When I wrote the earlier post I was thinking of the parade of economists on MSNBC. The flawlessness of their analyses is matched only by their worry when the market drops 500 points. The most reliable 'economists' to me are successful traders and gamblers. They put their money where their mouth is, and can't afford not to own their mistakes.

    Bernanke is a different category. The Grand Wizard, who can print money out of thin air, and who's every word can impact the market. Don't get me started on the Fed. How does game theory include the ones that print the monopoly money? Quite frankly, I'd rather point to the original rules of the game and kick out a privately owned central bank that masquerades as 'Federal'. But I'm getting off base...
    Last edited by Dark Horse; 05-14-10 at 08:46 AM.

  30. #30
    marcoforte
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    I'm not a pro but I make money on the market. The key is to go against public opinion and have a longer term horizon ie 2-5 years. I bought gold at 250 and kept buying for many years. Haven't bought any now because everyone is doing it. At 250, no one was buying it. Bought stock at the bottom in dec 08 and early mar 09 when the market was its darkest. Listen to the media and go against it. Wait until they are at fever pitch, things like a newsweek or businessweek cover are good signs to go against. This past monday when the euro went haywire, I went long euros. We'll see how that one works out over the long term. You can't beat the market short term unless you're a pro. I prefer to go around them and let time work on my side.

  31. #31
    Wrecktangle
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    Quote Originally Posted by Dark Horse View Post
    Game theory typically defines a problem, so that one choice is the best. Do this, do that, or do nothing. (It's the Joker's territory, if you've seen the last Batman movie). It often recognizes interlinked elements, that require one to see the whole picture, instead of just an isolated part. That may be out of the realm of specialized, blinders-on science, but it is certainly not unscientific.

    If economic experts weren't so busy with their rearview 20/20 vision, they might actually define a problem before it manifests. I've never come across a field where so many after the fact statements are given such importance. Game theory is about foresight. Economics, in the present day and age, seems to be about hindsight. If somebody has a rare original idea he's practically giving a f*cking Nobel prize. Printing and handing out virtually limitless amounts of money to 'financial experts' that f*cked up beyond belief. Yeah, I can see the logic in that. What do they think? That it's a game?
    DH, my point about game theory is that it is all about how cleverly you can set up your categories, and then coming up with a good evaluation of each mostly done by gut feel. So, someone who is good at this can do it well whereas most folks working by formula, cannot. This very close to how well you can choose colors and shapes for a painting in my book. By the way, perhaps the best game theory book I've found is: Game Theory Evolving by Gintis. For you newbies there is a fair amount of math in it, so be forewarned. But a cool thing is: it has the answers worked out in the back of this text book.

  32. #32
    Snowball
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    the same way Henry Paulson threatened the Senate panel with MARTIAL LAW if TARP was not passed and the Dow dropped 700 points that day, (if you don't believe me, see comments of Senator Inhofe).
    They manufactured the 1000 point drop on the day they were stripping the Fed Audit bill of ALL it's power. They were also rewriting the financial overhaul bill to be favorable to the 6 largest banks.
    The media lied of course and said this insane drop was a human error. Yeah.

    Was Yesterday’s Stock Market “Glitch” Really Big Banking Blackmail?
    Posted on May 7, 2010 by willyloman
    by Scott Creighton

    The White House gets its way again. They get their way on two measures that would have given the people at least a little control of the “too big too fail” banking system. But how they got it, well that might just be the REAL story of the day.

    “I mean this really sounds like market manipulation to me. This is outrageous.”

    The “HOPE” of real getting real banking reform under this administration is dead. Dead on arrival. What is left is the “Chris Dodd Big Banking Giveaway Plan” which is to banking “reform” what Obamacare was to “healthcare reform”.

    Last night the Brown/Kaufman amendment was shot down by a vote of 61-33. The amendment would have broken up the largest 6 banks and then set limits on the size these institutions could become so their failure could not threaten the entire system. Thus… “too big too fail” would have been a thing of the past. 27 senate democrats voted with the large majority of republicans to kill the amendment and for the most part, the 30 who voted for the bill were either coming up on an election cycle this year, or they switched their votes after seeing the bill was going to fail. A clever little trick legislators use to end up on the “right side” of a voting issue.

    Though top Obama administration officials have not publicly opposed the amendment, its leading economists have opposed ending Too Big To Fail simply by breaking up the nation’s financial behemoths. Austan Goolsbee and Larry Summers have both fought back against this idea, as has Treasury Secretary Timothy Geithner.

    … Sen. Mark Warner (D-Va.) and Dodd of Connecticut spoke against the amendment.

    Sen. Judd Gregg (R-N.H.) was indignant. “I don’t understand this Brown-Kaufman amendment. Basically, what it says is if you’re successful…you’re going to break them up? I mean, where does this stop? Do we take McDonald’s on?” Huffpo

    This took place yesterday while another popular piece of legislation was being gutted by one of its authors.

    Ron Paul is livid and he has pulled his support from the “Audit the Fed” bill.

    I know that sounds crazy… Ron Paul has been pushing for this kind of accountability from the for-profit Federal Reserve Bank for decades. But yesterday, when the bill looked as if it were going to be passed, Ron Paul pulled his support and is actively campaigning against it.

    He has good reason.

    In a move frighteningly reminiscent of the now infamous Air Force One flight where single-payer advocate and “Obamacare” opposition leader Dennis Kucinich was brought before the anointed One, Barack Obama, for a little position changing “chat”, Bernie Sanders was brought in to the White House late yesterday to work out a “compromise” on the “Audit the Fed” bill. No one knows why the “compromise” was even needed with the Pro-Banking Industry Obama White House since by all accounts, the bill had the votes to pass in the Senate as it was.

    But, Bernie Sanders was brought before “the man” and had a little pow-wow in the White House. Since Sanders is one of the authors of the bill, he was authorized to change it, and “CHANGE” is what the White House got…

    Thursday afternoon, Deputy Treasury Secretary Neal Wolin voiced the administration’s opposition to the audit proposal. But hours later, following negotiations with Sanders, Wolin withdrew the opposition. Raw Story

    “Bernie Sanders has sold out and sided with Chris Dodd to gut Audit the Fed in the Senate. His “compromise” is what the Adminstration and banking interests want: they’ll allow the TARP and TALF to be audited, but no transparency of the FOMC, discount window operations or agreement with foreign central banks. We need to take aciton and stop this!” Ron Paul

    The audit is only allowed back to December 2007, which leaves most of the work of the Fed’s Open Markets Committee in the dark — they were the ones who were supposed to be watching over Wall Street when they were laying the groundwork for the collapse. And according to Jay Newton-Small of Time Magazine, there will only be one audit — it will not be ongoing.

    Ron Paul and Alan Grayson worked like dogs to get this through the House. And the White House would not have gone to Sanders if they’d been able to peel off the votes to tank the amendment. But with 68 Senators having voted for it or cosponsored it in the past year, that was a heavy lift. Bernie was the weak link. Firedoglake

    How did all this happen late yesterday afternoon? What was the threat that forced all of these legislators to vote against the will of the people and to suddenly side with the corrupt banks? How on earth did all this happen LATE YESTERDAY AFTERNOON?

    Hmmmm…. what else happened yesterday, PRIOR to the vote in the senate and Bernie Sander’s meeting in the White House? Hmmm…

    Could it be the “glitch” in the supercomputer that crashed the stock market by nearly a 1000 points in a few minutes? Could that have had something to do with it?

    Could it have been Goldman Sachs and the big 6 mega banks sending a message to congress that if they think they are going to break up their hold on this nation, they will bring it all down with their stock market manipulating supercomputer?

    Nesto calling these trades “bogus” drew backlash from the host and CNBC veteran Maria Bartiromo, who said those trades sounded like “market manipulation” to her.

    “ That is ridiculous,” Bartiromo replied. “I mean this really sounds like market manipulation to me. This is outrageous.” Business and Media Institute

    Hmmm… I think we might be onto something.

    Think about it… all that money poured into the CEOs and banking bigwigs bank accounts in the form of record-setting bonuses. Why is that important? Because if they chose to gut the economy, if they chose to trash the markets by 10,000 points in one day, they will be in their private jets by noon and super wealthy in another country sipping single-malts on the sea-shore by dinner.

    And we will be left to fight for the scraps while the dollar becomes virtually worthless.

    That was the threat yesterday. While the MSM was busy blaming the working class Greeks who are being robbed right in front of everyone’s eyes, our congress was busy quietly handing over control of the nation to a bunch of criminal bankers who caused all of this in the first place.

    The market didn’t crash by a “glitch” and it wasn’t the European Union or Greek riots either… it was terrorism. It was a message: Don’t **** With Us. Congress got the message and acted accordingly.

    The banking oligarchs sent a clear and unmistakable message that they could drop this nation’s economy into the toilet at any time they wished and if congress thought for a minute that they really ran America, they had better rethink that position.

    That’s what happened yesterday.

    It isn’t a “coincidence” that the super-computer “glitch” happened a few hours before that senate vote and just a while before the White House had a chat with Sanders about his Audit the Fed bill. It was financial terrorism, pure and simple.
    http://willyloman.wordpress.com/2010...#comment-16447

  33. #33
    Dark Horse
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    Quote Originally Posted by Snowball View Post
    the same way Henry Paulson threatened the Senate panel with MARTIAL LAW if TARP was not passed and the Dow dropped 700 points that day, (if you don't believe me, see comments of Senator Inhofe).
    They manufactured the 1000 point drop on the day they were stripping the Fed Audit bill of ALL it's power. They were also rewriting the financial overhaul bill to be favorable to the 6 largest banks.
    The media lied of course and said this insane drop was a human error. Yeah.
    Thanks for the article. I have the same dark view of the market. It is - by far - the most corrupt game in town. Nothing comes close.

    This power, to pull the rug from underneath it whenever it serves their purpose, is what prompted me to call this game theory. Back in that crisis time you can also throw in the oil price that mysteriously rose to 150. That was actually a much more potent blackmailing tool than the 700 pt drop, which was more of a 'reminder'.

  34. #34
    Flying Dutchman
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    Quote Originally Posted by Dark Horse View Post
    This power, to pull the rug from underneath it whenever it serves their purpose, is what prompted me to call this game theory.
    Maybe you should have called it playing games, that way we wouldn't have Wrecktangle going off on an airbender on real game theory.

  35. #35
    Dark Horse
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    Maybe. Then again, maybe not.

    This thread was started before volatility was back. "Everybody was happy", so to speak. How quickly things have changed. Not quite the type of volatility I was looking for, however.

    http://www.marketwatch.com/story/cra...5?pagenumber=1
    Last edited by Dark Horse; 05-25-10 at 06:01 AM.

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