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'Unrealized' is simply an adjective referring to something that could be thought of as on paper or not real. For example, if you bought stock ABC at $5/share and it is now trading at $20/share but you still hold your shares, there is an unrealized gain of $15/share. If you sell the stock you realize the gain as you'd then have money instead of the stock. An unrealized return would be the return on paper or what you could realize assuming you could sell everything without moving the market.

That clear things up? http://www.investorwords.com/u1.htm#unrealized is a link for a textbook answer if you want that form too.

JB
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