Exhibit 31.1



CERTIFICATION



I, Kenneth A. Shewer, certify that:



| | 1. | I have reviewed this quarterly report on Form 10-Q of World Monitor TrustSeries B (Series B);
| | -- | ------------------------------------------------------------------------------------------------



| | 2. | Based on my knowledge, this quarterly report does not contain any untrue statement of a material fact or omit to state a material fact necessary to make the statements made, in light of the
circumstances under which such statements were made, not misleading with respect to the period covered by this quarterly report;
| | -- | ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------



| | 3. | Based on my knowledge, the financial statements, and other financial information included in this quarterly report, fairly present in all material respects the financial condition, results of
operations and cash flows of Series B as of, and for, the periods presented in this quarterly report;
| | -- | -----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------



| | 4. | Series Bs other certifying officers and I are responsible for establishing and maintaining disclosure controls and procedures (as defined in Exchange Act Rules 13a-15(e) and 15d-15(e))
for Series B and we have:
| | -- | -------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------



| | a) | designed such disclosure controls and procedures, or caused such disclosure controls and procedures to be designed under our supervision, to ensure that material information relating to
Series B, including its consolidated subsidiaries, is made known to us by others within those entities, particularly during the period in which this quarterly report is being prepared; | 
| | -- | ---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- | 



| | b) | evaluated the effectiveness of Series Bs disclosure controls and procedures and presented in this report our conclusions about the effectiveness of the disclosure controls and
procedures, as of the end of the period covered by this report based on such evaluation; and | 
| | -- | ----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- | 



| | c) | disclosed in this report any change in Series Bs internal control over financial reporting that occurred during Series Bs most recent fiscal quarter that has materially affected,
or is reasonably likely to materially affect, Series Bs internal control over financial reporting; and | 
| | -- | -------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- | 



| | 5. | Series Bs other certifying officers and I have disclosed, based on our most recent evaluation of internal control over financial reporting, to Series Bs auditors and the board of
directors of the managing owner of Series B:
| | -- | ---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------



| | a) | all significant deficiencies and material weaknesses in the design or operation of internal control over financial reporting which are reasonably likely to adversely affect Series Bs
ability to record, process, summarize and report financial information; and | 
| | -- | ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- | 



| | b) | any fraud, whether or not material, that involves management or other employees who have a significant role in Series Bs internal control over financial reporting. | 
| | -- | -------------------------------------------------------------------------------------------------------------------------------------------------------------------- | 



|                          |  |                       |  |                                                                                                                                     
|------------------------- |  | --------------------- |  | ------------------------------------------------------------------------------------------------------------------------------------
|Date:    November 8, 2004 |  | /s/ Kenneth A. Shewer
|                          |  |                       |  | Kenneth A. Shewer Chief Executive Officerof Preferred Investment Solutions Corp.,the managing owner of Series Bas of October 1,
2004