NAREIT and the double counting part

can you explain to me how equity is component of NAREIT and the double counting part? (bolded part) Thanks!!

“The use of the hedged NAREIT Index could be justified by the concept of eliminating double counting (the equity return component in equity REITs). Additionally, the use of mortgage and hybrid REITs would reduce the redundancy of the more highly correlated equity REITs. Nevertheless, equity REITs compose about 95 percent of the NAREIT Index, so the unhedged data show a significant increase in return with less risk, as demonstrated by the high Sharpe ratio of the NAREIT Index relative to most other asset classes”

REITS trade on the stock exchange - so they have a strong equity market component.

The hedged REIT - uses a hedge to remove the equity market component - and hence the hedged REIT returns would be better representative of “actual” returns that can be expected from the REITs themselves.

when mortgage and hybrid REITs are used - the equity component is further reduced.