From a ‘Dash’;

The Sophistry: Rising interest rates will undermine higher stock prices – yet another overly simple heuristic.
The Reality: The relationship between the P/E multiple and stocks is a bit complicated. I have often described it is curvilinear. If interest rates are too low, it reflects deflationary fears. Since no one really believe the “E” in the earnings forecasts, the multiple is low. As the economy improves – the stage where we are now – stock multiples actually move higher. The logic is quite clear, but hardly anyone understands it. You can look at my research, or if that is not convincing, you can look at this chart from JP Morgan.

As you can clearly see, rising interest rates are consistent with higher stock prices, until the 10-Year Treasury Yield gets to 5% or so.