Stock and oil relationship is usually time-varying and depends on the current economic conditions. In this study, we propose a new Dynamic Stochastic Mixed data sampling (DSM) copula model, that decomposes the stock-oil relationship into a short-run dynamic stochastic component and a long-run component, governed by related macro-finance variables. Inference and prediction is carried out using a novel Bayesian estimation strategy, that can efficiently estimate the latent states and delivers an estimate of the log marginal likelihood used for model comparison. We find that inflation/interest rate, uncertainty and liquidity factors are the main drivers of the long-run co-dependence. We show that the multi-step-ahead variance covariance forecasts constructed using the proposed approach are closer to the true values as compared to the benchmark model. Finally, investment portfolios, based on the proposed DSM copula model, are more accurate and produce better economic outcomes as compared to other alternatives.