Do any foundations/endowments manage their own investments?

I got a little long winded - the short answer is sure, they are out there, but generally will be the larger ones and in most cases it just doesn't make much sense for them to manage a sleeve internally vs. hiring a manager to do it for them. Anyway - continue on if you'd like. .

For the majority of small to mid sized E&F it would be crazy to have a full blown investment staff to invest their assets. Consider a generalized $100 million dollar endowment. The board will have an investment consultant. They don't necessarily manage the investments (we'll come back to this) but provide a variety of strategic advice on asset allocation, investment lineups, strategy selection and manager selection. If they are a true 'consultant' in many cases they will end up recommending managers and then the entity contracts with them - as, remember, the board is the fiduciary in this case (not the consultant). There may be some internal investment staff (minimal amount) that work with the consultant as well - but it would be pretty lean. If we assume they have a 'traditional' looking portfolio that's 60/40 ish with a mix of private and public investments - you end up with needing quite a few different strategies across international and domestic equiities/fixed income, some privates (VC, PE, HF), some real assets, etc. You get the point. This might cost you somewhere in the neighborhood of 50 to 100 basis points with manager fees, consultant fee, etc. Could be lower as well as fees just keep coming down. It just makes sense in most cases for that type of size to outsource all the management of the various assets - both monetarily and structurally. Easier. Cheaper. Probably more effective. Keep in mind that in many cases you'll see them with lots of passively indexed portions - say for large cap domestic equities - they'll just buy whatever the ETF of the day is and keep going. 

The other option nowadays is to hand over your entire $100m to the consultant and give them the keys, Outsourced chief investment officer is the term, where they have discretion and then manage the portfolio. They select managers, invest the assets with managers, report to the board, etc. basically fully outsourced investment program - think commonfund, FEG, Hirtle + all the major guys like Goldman, SEI, VIAS. 

So back to your question - you'll see some internally managed sleeves in the largest, or rather larger, institutions. Same with pension funds - you will outsource the majority and have some internally managed stuff. It can vary widely. I'd tell you the majority of roes, and situations, you are a true 'allocator' where your job is primarily manager research, investment/performance analysis, strategy and/or allocation research/analysis. You won't often find yourself getting hired to run the Core fixed income sleeve unless, maybe, you ran one at a prior place you were at.