Big name University examples:

• Cambridge Clare Student Investment Fund
• Charles R. Blyth Fund at Stanford University
• Oxford Alpha Fund (seems like a virtual fund, with no money invested -- I'm curious to see Nassim Nicholas-Taleb's take on their Oxonian approach)

Oddly specific examples:

• Front Row Ventures is a Canadian student-run, university-focused venture capital fund
• Black Gen Capital is a 100% minority-owned student investment fund in the US
• Student Investment Funds exist at: University of Waterloo, University of New Brunswick,  Mount Royal University and many more Canadian Universities (honestly, I didn't even know these last two places had universities -- aside: maybe this is why anti-Toronto sentiment runs high in small town Canada!)

Someone wrote How to Start and Run a Student-Managed SRI Fund. What's the case for  Why to Start and Run a Student-Managed Fund? 
Given the amounts involved, its hard to see these investment funds meaningfully influencing new venture formation, but maybe students with experience running Student Investment Funds are marginally more likely to be hired into similar roles at companies and institutions managing large sums of money. How might that compare to some other student activity such as running an EA group or joining a Sports Team?