Carbon allowances traded in the EU-Emission Trading Scheme (EU-ETS) were initially designed as an economic motivation for efficiently curbing greenhouse as emissions, but now it mimics quite a few characteristics of financial assets, and have now been used as a candidate product in building financial portfolios. In this study, we examine the time-varying correlations between carbon allowance prices with other financial indices, during the third phase of EU-ETS. The results show that, at the beginning of this period, carbon price was still strongly corrected with other financial indices. However, this connection was weakened over time. Given the relative independence of carbon assets from other financial assets, we argue for the diversification benefits of including carbon assets in financial portfolios, and building such portfolios, respectively, with the traditional global minimum variance (GMV) strategy, the mean-variance-OGARCH (MV-OGARCH) strategy, and the dynamic conditional correlation (DCC) strategy. It is shown that the portfolio built with the MV-OGARCH strategy far out-performs the others and that including carbon assets in financial portfolios does help reduce investment risks.