There are shreds of evidence of Islamic securities to behave differently from conventional ones, especially under the influence of certain factors such as oil, gold, economic policy uncertainty, and geopolitical risk. This paper has empirically evaluated such pieces of evidence through Quantile Autoregressive Distributed Lags Error Correction Model. Analysis has been performed on monthly returns from Dow Jones Islamic Market and Dow Jones Conventional Market Indexes for the sample period from January 1997 to July 2019. Results suggest that the Islamic stocks do behave differently from conventional stocks only for the long term in case of oil price influence under bullish market conditions; whereas, under bearish market conditions, economic policy uncertainty causes Islamic securities to behave differently. Hence, investment in Islamic stocks can be used for diversification of conventional securities' portfolio under specific conditions. For instance, under oil price changes Islamic and conventional securities can diversify risk in bullish market trends; such diversification can also be achieved in case of the bearish market trend under economic policy uncertainty shock. The results of this study are significant for policymakers and investors as this will provide a clear picture to the investors regarding their investment with respect to Islamic or conventional markets. A further new basis will be provided to both speculators and portfolio managers of Islamic and conventional markets.