Affective meaings must be judged in context. Everything "real" is not necessarily favourable - e.g. "a real problem", whilst everything "false" may not necessarily be unfavourable - e.g. "false teeth".
I think there is no evidence for any preference for evaluation in cases like "world", "diamond" or "precaution". They can be judged as neutral.
I must thank you for your great help.
But can we understand them in this way? real diamond ---for diamond is sth. rare and valuable, so it carries the meaning favorable; whereas real enemy, for :enemy is sb. people are against , so enemy has the meaning unfavorable??
Semantic prosody is different from its inherent connotation.
The semantic prosody of a word or structure is only achived by large amount of contextulized texts. So it cannot be judged by observing a few intances.