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Purpose  This study aims to investigate the moderating role of investor demand on the relationship between the investors' divergence of beliefs and the first-day initial public offering (IPO) return.    Design/methodology/approach  The study sample covers the period from 2010 to 2019 and consists of 117 IPOs that are priced using the fixed price and listed on the Malaysian stock exchange (Bursa Malaysia). This study employed both the ordinary least square (OLS) and the quantile regression (QR) methods.    Findings  Investor demand, proxied by the over-subscription ratio (OSR), plays a moderating role in increasing the effect of investors' divergence of beliefs on initial return, and the moderation effects vary across the quantile of initial return. Pure moderation effects are observed at the bottom and top quantiles, suggesting that investor demand is necessary for divergence of beliefs to influence IPO initial return. However, at the middle quantile of initial return, investor demand is a quasi-moderator. That is, the OSR not only moderates the relationship between the divergence of beliefs and initial return but also has a positive effect on the initial return.    Practical implications  Investors' excessive demand for an IPO issue exacerbates the IPO under-pricing issue induced by a divergence of beliefs amongst investors, thus rendering greater equity market inefficiency.    Originality/value  To the authors' knowledge, this study is amongst the first to empirically investigate the moderating role of investor demand on the investors' divergence of beliefs and IPO initial return relationship.

Divergence of beliefs and IPO initial return: the quasi-moderating role of investor demand