Here is E/P compared to interest rate on 10 year government bonds:
Here is E/P compared to interest rate on corporate bonds:
As corporate bond yields go up it really makes sense for stocks to go down. Another way to think about this is that when companies can borrow money really cheaply an easy way to boost earning per share, and possible get executive bonuses, is to just borrow money and buy back some shares. But when interest rates go up they won't do this so much. So a major thing propping up the stock market will go away.