Given the current situation, $20k seems pretty far away, and $40k doesn't look real at all given what timeframe you placed it. The effects of halving have so far come after halving, not before. I think you should look at halving 2016, nothing significant has happened before, but we have the big pump in December 2017, although the price was slowly rising throughout the whole year before that.

Expect the unexpected is something to consider when it comes to Bitcoin, maybe it just happens the opposite of what most expected.