This paper examines the relationship between 10 Global sectoral conventional and Islamic assets. For each sector, a conventional, an Islamic stock index and a bond are retained. The analyzed relations are done by taking into account diverse investment horizons by using MODWT and GARCH-DCC-type models. Our results indicate that adding bond indexes into a portfolio composed with conventional stock or Islamic stock is efficient. As for the correlations between conventional and Islamic sectoral indexes, they depend on the sector. Relations between returns of securities are quite similar to the relations between high-frequency part of these series and are very volatile at low frequency.