Something strange is happening in the world of global stocks. After years of trading in line with American stocks, Asian equities are no longer moving in tandem.

Asia's regional benchmark has slumped about 6.5 percent in the past year, with the MSCI Asia Pacific Index still not recouping all of the losses during the global market rout if late 2018. By contrast, the U.S. S&P 500 is up 11 percent, hitting all-time highs as recently as Tuesday.

Several themes have been playing out in Asia: