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and only 1 year in 50 of losing 20 percent) Because LTCM was so confident of its positions, it was given obscene amounts of access to credit, which was used to leverage at a fantastic 100to-1 ratio One of the flaws, which the partners didn t realize until it was too late, was there was no independent party to review or oversee LTCM s trading operations Traders were given free rein to make any kind of trade they desired And although the partners thought they had limited risk, they had unexpectedly created a scenario where risk was incalculable Although it was theoretically possible for their trades to deviate from the norm, as the partners said, it was as likely as a hundred-year storm Perhaps their biggest mistake was not taking into account the twin emotions of fear and greed The end came rather quickly for LTCM In August 1998, Russia s stock, bond, and currency markets went bust after Russia devalued the ruble, causing LTCM insurmountable losses LTCM s computer models were not prepared to handle the level of fear and panic that spread across the world, as bond spreads widened to levels that no one at LTCM ever believed was possible LTCM lost millions in equity as its cleverly designed trading schemes unraveled With the markets around the world in turmoil, LTCM made a desperate attempt to raise money, turning to billionaire investors like George Soros and Warren Buffett Both men eventually declined to rescue the firm The spreads continued to widen, and more millions were lost In one month, LTCM had lost 44 percent of its capital, and 52 percent year-to-date, but that was just the beginning The firm was hemorrhaging money as all of its investments went south; in addition option volatility skyrocketed, destroying its derivatives portfolio By the end of the year, on the verge of bankruptcy, the firm was taken over by a consortium of 14 banks Several of the multimillionaire partners had already lost more than 90 percent of their wealth The Brightest and the Brokest, blared a headline from Time magazine Other papers came up with clever headlines nearly celebrating the fact that a group of arrogant wizards could self-destruct so dramatically.

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which results by eqn (573-574) in the state estimate x+ (k) = 101823 208216 with covariance P+ (k) = 06276 02139 02139 08136

For the set of m = 4 scalar updates, by eqn (576) the gain sequence is m Ki 1 09901 00000 2 00000 09901 3 04403 01887 4 02069 02999

This weekly sentiment survey, published by Chartcraft, polls independent newsletter writers for a view of what the market might do over the next six months: bullish, bearish, or neutral Chartcraft exchanges information with a variety of services, and it also analyzes newsletters received on the Internet, in the mail, and by fax

The sequence of state estimates from eqn (577) is m xi 1 0 0 2 101386 00000 3 101386 209901 4 103658 210874 5 101823 208216

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1 Type wwwschaefersresearchcom in your Web address line 2 Click once on the Quotes and Tools tab 3 Scroll down and to the left Under Market Tools, click on Investors Intelligence 4 The weekly survey results appear on the left 5 The Investors Intelligence survey will look something like Figure 12

By eqn (578) the second, fourth, and nal error covariance matrices are P2 = 09901 00000 00000 1000000 , P4 = 06850 01308 01308 09341 , and

06276 02139 02139 08136

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Note that the nal state estimate and covariance matrix from the sequence of scalar updates is identical to the result from the vector update; however, the Kalman gains are distinct for the two implementations

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The scalar measurement processing algorithm is only valid in situations where the measurement noise corrupting the set of scalar measurements is uncorrelated (ie, R is a diagonal matrix) In situations where this assumption is not satis ed, the actual measurements can be transformed into an equivalent set of measurements z(k) with uncorrelated measurement noise The transformed set of measurements can then be used in the scalar processing algorithm With y = Hx + , let E = R = UDU ,

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