||Real Estate Investment Trusts (REITs) have been an available investment in the U.S. since the 1960s. REITs are publicly traded unit funds which invest primarily in income-producing real estate assets. Only 5 years after the first introduction in Japan, the REITs market in Asia doubles each year. Within 5 years REITs controlled 27 billion US dollar In 2005 observers expected that until 2010 the REITs could control about 160 billion US dollar in real estates. Shares of companies going public for the first time are typically at a price below that achieved on their first day of trading, giving subscribing investors large positive returns (Ibbotson and Ritter, 1995; Loughran, Ritter and Rydqvist, 1994). Therefore, either the offering price is set too low or the investors systematically overvalue IPOs on the first trading day. Since the results of studies indicate few if any departures from efficiency in the aftermarket (Ibbotson, 1975) positive initial returns can be attributed to a downward bias in the offering price, that is, IPOs are underpriced. No complete explanation of the underpricing phenomenon exists, though various theories based on different rationales shed light on the factors that may be influential. First information asymmetry (Baron,1982; Rock, 1986), second signalling (Allen and Faulhaber, 1989; Grinblatt and Hwang, 1989; Welch, 1989; Benveniste and Spindt, 1989), third legal liability and litigation risk (Tinic, 1988; Hughes and Thakor, 1992) and finally information cascade effects (Welch, 1992). The evidence for Real Estate Investment Trust (REIT) IPOs is less consistent. Early studies found evidence of overpricing; a 1990s study found underpricing. So far there is few works pointing out the existence of REITs underpricing of IPO in Asia. The author's preliminary study try to examine the IPOs of the REITs in Hong Kong, Japan, Korea, Malaysia, Singapore and investigate the evidence for either underpricing or overpricing of IPO units over the first 10 and 20 days of trading."