I am considering setting up a personal kind of hedge fund / stock portfolio among friends.
I am trying to figure out what kind of a legal agreement I should have them sign for investing with me to define what their responsibilities and expectations of such a relationship are.
I tried to search online for such information but I am unsure of what these documents would be called. What should I be looking for?
Sounds like you are starting an investment club.
What you need is an investment club partnership agreement. Have a look at this free document.
EDIT
Based on OP's comments, it appears that the OP will be acting as an adviser/manager of a private investment fund. If the fund is not open to the public, it may still be treated as a type of investment club, but different rules -- including possibly having to register with the SEC -- may apply (quoted from the first link):
If the adviser is compensated for providing the advice regarding the club's investments, the adviser may need to register according to the Investment Advisers Act of 1940. Also, if one person selects investments for the club, that person may have to register as an investment adviser.
In general, a person who has $25 million or more in assets under management is required to register with the SEC under the Investment Advisers Act of 1940.
A person managing less than $25 million may be required to register under the securities laws of the state or states in which the adviser transacts business.
You have to register with the SEC as an Investment Company. The SEC has a "Investment Company Regulation and Registration Package", available here: http://www.sec.gov/divisions/investment/invcoreg121504.htm
I found that off their overall page for funds and advisors: http://www.sec.gov/divisions/investment.shtml
Finally, bear in mind that your state may have various requirements as well.
