Is there a corpus about personal financial portfolios? I.e. data which is anonymous user data and shows financial portfolios for these users.
You can get portfolios that by law are submitted to the US Securities and Exchange Committee (SEC)
Form 13F—Reports Filed by Institutional Investment Managers
An institutional investment manager that uses the U.S. mail (or other means or instrumentality of interstate commerce) in the course of its business, and exercises investment discretion over $100 million or more in Section 13(f) securities (explained below) must report its holdings on Form 13F with the Securities and Exchange Commission (SEC).
The database of company filings is called EDGAR, and it is searchable.
For example, here is a recent 13F from Berkshire Hathaway.
If you want real-time trade data, then check out a social trading network. Maybe you'll even find one with an API.