Analyst Michael Gorman said economic indicators for those REITs are "increasingly dour," but the stocks are up strongly this year. He downgraded Apartment Investment & Management Co. and Camden Property Trust to "Neutral" from "Outperform," and lowered his target prices as well.

Apartments are rated in multiple categories, with Class A the most desirable, above classes B and C. While REITs that owned Class B apartments did better than Class A REITs during the 2001 recession, Gorman does not think that will happen this year because of threats to credit quality and a slump in the housing industry.

Gorman added that growing levels of vacancies in single-family apartments, along with falling prices, will pressure rental rates.

He said BRE Properties Inc., which owns Class A properties, is his top pick in the sector.