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This is very basic but I think it covers what you're looking for: http://www.hedgefundfundamentals.com/media_posts/hedge-funds-count-asse…
AUM is equity. It's the value the investors in the fund could pull out if the whole thing liquidated today. Calculating this shouldn't be difficult for most funds; funds holding securities that are non-traded, non-public, or just very illiquid have a bit more work to do and there is a speculative element to calculating the value of those types of assets.
RAUM is total securities managed w/o deducting liabilities, so if a fund were highly levered, RAUM would greatly exceed investor's equity.
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