In this paper, we contribute to the old debate on the dynamic correlation between gold and stock markets by considering a spectral approach within the framework of portfolio hedging. Specifically, we consider eight MENA stock markets (Tunisia, Egypt, Morocco, Jordan, UAE, Saudi Arabia, Qatar, and Oman) and examine the optimal composition between gold and the stock market index, with a minimum portfolio risk and a high expected return. Based on the spectral approach, we propose seven portfolio structures and evaluate them through a comparison with the conventional DCC-GARCH method and the most best 10 portfolios constructed by using wavelet approach. The main results show that the spectral-based approach outperforms the DCC-GARCH and the wavelet methods. In fact, the optimal gold-stock composition depends on the spectral density of each stock market index, where a stock market index with a stable spectral density requires more investments in gold than a stock market index with an unstable spectral density.