Yes, given sufficient resources and the incentive to deploy them.
As well as risks from information and passwords stored on the disk or in the browser, especially if any of these could be unencrypted, there are also risks associated with keylogging software and other malware introduced, for example, from visited web sites, not just by people with access to the physical machine.
Keylogging hardware can be used, as well as more esoteric hardware-based interception mechanisms if these are worthwhile.
Social engineering and associated weaknesses (e.g. leaving a piece of paper with the account details and even passwords on your desk) are outside the scope of the question, as are issues around network interception (even with robust SSL protecting the data in transit subversion may be possible when one has control of the PC and its network infrastructure and enough interest and knowledge to put in the effort to do it).
If these are transactions for your employer and they are of sufficient value and the risks thought to be high enough then perhaps a secure, dedicated machine could be considered. If they are your personal transactions then, even when the use of work resources is allowed for this, perhaps you would feel safer using a personal machine that you control and that you could use in privacy, away from work.