A realized profit is the gain on a position or trade after it has been closed. The value of any trade or position fluctuates with the market, so a trade must be completed and closed out before a profit is counted as realized.
The value of a position can swing between loss and profit many times before it is closed by the trader. Until the trade is settle, all the profits and losses are unrealized. These are called paper profits and losses because they only exist on paper (or, more accurately, on the screen). If the trade is closed at gain, then it becomes a realized profit.
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