This paper investigates the surge and the eventual slowdown in global REITs in the 2000s. Further, it offers some investment strategies that this sector could offer to the investors. The paper contributes to the literature on the predictability of real estate securities returns over short to medium horizons. An evolutionary (genetic) algorithm is applied to optimize the investment strategies. Our findings suggest that momentum effects have been present during the 2000-2008 period. However, in contrast with prior studies, momentum portfolio returns are insignificant during the boom years, but are highly significant during the downturn periods.