Real estate investment trusts, or REITs, are divided into two main varieties -- equity REITs, which invest in properties, and mortgage REITs, which buy pools of mortgage-backed securities. Mortgage REITs are further separated into two types -- agency and non-agency. How mortgage REITs operate. The basic business model of a mortgage REIT is to buy mortgage backed securities (MBS) in order to collect the interest payments from the underlying loans.