This study investigates both conventional and Islamic investors' problems as to whether the inclusion of Islamic and conventional asset classes may expand the frontier of their respective portfolios. Our sample covers the global U.S. portfolios and Malaysian portfolios with multiple asset classes, as well as the portfolios with a specific asset class in several regions. This study uses the recent mean-variance spanning test in multiple regimes, which not only accounts for tail risk but also identifies the source of value added (tangency portfolio or global minimum variance).For intra-asset allocation, our findings show that both Islamic and conventional fund managers of a specific asset class can benefit from conventional and Islamic asset classes, respectively, in several regimes. For inter-asset allocation, conventional institutional investors cannot obtain any value added from Islamic asset classes. On the contrary, the U.S. Islamic institutional investors can expand their tangency portfolio by investing in U.S. TIPSs and REITs, and reduce their global minimum variance by allocating on U.S. high-yield bonds. Moreover, the Malaysian Islamic institutional investors can obtain risk reduction by investing in conventional bonds only in the high term premium regime. For the remaining asset classes, the opportunity sets are sufficient for Islamic investors to invest complying with Shariah rules. We provide some policy implications for the global Islamic financial industry.