He doesn't have to.
He is allowed to invest out right in stocks, bonds, etc.
He does have a financial portfolio and he is allowed to control it, its not in a trust.
If your wondering about conflict of interest...check out the 1982 court case "Lewis v. United States".
Greenspan can do whatever the heck he pretty much wants with his own money and whatever information he gets or has or knows.
I don't think that those are the kind of "inside tips" that Alan "The G" Greenspan is giving her. You need to get your mind INTO the gutter. ;->