Well logically due to supply and demand this should happen but sometimes there doesn't seem to be much logic at all in the valuation of bitcoin. It goes up and it goes down without any obvious reason but I'm hoping the halving does push the price up I just hope there's more demand for the coins by then.
True, there is really no evident relation between coin reward and price. We were at $1100 when the reward was 25 BTC per block. And now we're at $225 when the reward is.... the same 25 BTC, lol.
But what I hope is that the DEMAND for the coins will increase regardless of the block reward. And due to more demand, the ask price should eventually go UP. But this is just a speculative hope. Nothing can be predictable in the world of crypto currency.