If you take a look at the behaviour of the REI index before, during, and after the 2008 recession and present day. The REIT is in blue, the S&P500 is in red.
Before
REI index is outpacing the S&P500
During
REI index is converging with the S&P500
the indices both fell together with the REI falling more aggressively
After
REI index recovers quicker and begins to outpace the S&P500 again