Latest IMF research shows the strong correlation across all economies during the financial crisis or Great Recession. Those correlations have come down as we have moved to a more normal environment, but it clearly shows that there is no diversity gain in a crisis.
The IMF research goes on to show that if you peg yourself to the dollar, you are asking for trouble if there is a monetary policy shock. There is no shock insulation when there is no float in the exchange rate. If you want to protect against a Fed taper shock, allow for the exchange rate to adjust on its own.