Climate change has been one of the biggest and most controversial environmental issues of our times. It affects the global economy, environment and human health. Many researchers find that carbon dioxide (CO2) has contributed the most to climate change between 1750 and 2005. In this study, the orthogonal GARCH (OGARCH) model is applied to examine the time-varying correlations in European CO2 allowance, crude oil and stock markets in US, Europe and China during the Protocol's first commitment period. The results show that the correlations between EUA carbon spot price and the equity markets are higher and more volatile in US and Europe than in China. Then the optimal portfolios consisting these five time series are selected by Mean-Variance and Mean-CVAR models. It shows that the optimal portfolio selected by MV-OGARCH model has the best performance.