Incidentally, if there is a crash, how is the Fed going to respond, since interest rates are practically as low as they can go? Will we see negative interest rates and asset purchases of equities and perhaps even real estate?
The Fed has been raising rates and is expected to raise rates in each of the next two quarters. They hope they can raise rates high enough, fast enough to give them leverage for when there is a crash. Of course they don’t want to raise rates too fast else the rate raising will be the cause of the next crash.
It's more accurate to say that bonds are uncorrelated with the stock market. You can verify this yourself by plotting a broad bond ETF like BND against the S&P 500 or DJIA. You won't get a magic bump in bonds when the market goes into a recession, you just won't lose a bunch of money, either.