It has long been site policy that answering one's own questions is both allowed and encouraged.
It has been established on our Meta:
Where does it say that a user can't ask a question they know the answer to?
And on the sitewide Meta:
Can I answer my own questions, even if I knew the answer before asking?
It has even been stated explicitly by Jeff Atwood:
To be crystal clear, it is not merely OK to ask and answer your own question, it is explicitly encouraged.
However, the reality of the situation (on this and many other sites) is very different. Self-answered questions meet with a lukewarm reception at best (particularly if one mentions that reception!). If a question is self-answered within a short period of being posted, particularly if one uses the "Answer your own question" button, a cascade of downvotes is very likely.
Would a phoenix Horcrux be indestructible?
Did Dumbledore make a horcrux?
At the end of Zootopia, are Nick and Judy an item? (though there are other reasons here).
People do intentionally downvote merely because a question is self-answered, as mentioned recently in chat.
Some users have suggested that the policy mentioned in our Meta might not be valid, since it was made too long ago.
Given that the practical policy seems to be that self-answers are heavily discouraged, should we revisit the policy that they are allowed and encouraged?