In the world of finance, the emergence of Islamic finance has led to many Islamic financial products and services. Access to professional fund managers who specialize in forming portfolios that fulfil the needs of Muslim investors to trade in investments that do not violate their Islamic principles and rules is now commonly available in both Muslim and non-Muslim countries. Islamic stock market indices (ISMI) have also been established. This thesis consists of three self-contained empirical essays that focus on important financial issues for Muslim investors: (1) the empirical support for orthodox asset pricing models when applied to Islamic stocks; (2) the volatility of Islamic stock market indices and the relevance of oil to this volatility; and (3) seasonality in an Islamic stock market. In addition, each empirical essay compares the findings of ISIM to those of an appropriate counterpart conventional stock market index (CSMI). The findings firstly demonstrated that ISMI can be exposed to different risk factors from those proposed by previous empirical works on CSMI. Secondly, the statistical results established that ISMI proves to be a safe investment during the oil market turbulences contrary to CSMI. Thirdly, the last empirical essay found out that the emergence of ISMI in the non-Muslim countries can bring about another calendar anomaly or at least change the effect of an existing one such as Friday effect. The general conclusion to be drawn from the findings of the whole thesis is that there are variations between ISMI and CSMI in the way they react towards the same exogenous variables. This is despite the fact that previous studies failed to find significant differences between them in terms of performance, and merely observed that investors lose nothing by restricting themselves to ISMI.