Will big funds buy at high price levels?

No.

Big funds got two main methods to make money - Buy low sell high, and sell high buy low.

What will big funds do when they wanna buy if the prices are too high?

Intentionally sell and short the the targetted instrument such as indexes or stocks in order to push it down to low levels, then accummulate.

Actually, current prices are very attractive for big funds to sell instead of buy. Let's continue to watch what will happen.