This paper examines the dynamic dependence structure of crude oil and East Asian stock markets at multiple frequencies using wavelet and copulas. We also investigate risk management implications and diversification benefits of oil-stock portfolios by calculating and comparing risk and tail risk hedging performance. Our results provide strong evidence of time-varying dependence and asymmetric tail dependence between crude oil and East Asian stock markets at different frequencies. The level and fluctuation of their dependencies increase as time scale increases. Furthermore, we find the time-varying hedging benefits differ at investment horizons and reduced over the long run.