This study is an initial attempt investigating the extent to which portfolio diversification benefits are available at different investment horizons to Turkish conventional and Shari'ah compliant investors in Southeast Asian conventional and Islamic stock markets. We apply multivariate-generalized autoregressive conditional heteroscedastic (MGARCH-DCC) and Wavelet techniques on daily data spanning from 2007 to 2018. The findings tend to suggest that Turkish investors would likely not invest in Singapore stock markets. At the same time, investing in stock indices of Indonesia and Thailand present moderate diversification benefits overall. The results highly recommend that Turkish conventional and Islamic investors would rather opt for Malaysia stock markets for higher diversification benefits, especially for the short-run investment horizons up to 16 days, as well as for long-term investment periods exceeding 128 days. In addition, Turkish conventional investors could also consider investing in Thailand Islamic equities in short-run holding periods up to 16 days. As for the medium investing horizons from 16 to 128 days, it is advised to avoid investing in all the equities because of very low diversification benefits for Turkish investors ...