Due to my job, I know inside information on dozens of publicly traded companies. It doesn't mean that I can't own shares in those publicly traded companies (in fact, I own shares in several of them).
What it does mean is that I must be aware of insider trading regulations and cannot allow my ownership to compromise my professional obligations with regards to each company.
I don't see why it would be any different for a MP.
If they run afoul of insider trading laws, then they should be charged (just like I would be).
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