Oil is perceived as a good diversification tool for stock markets. To fully
understand this potential, we propose a new empirical methodology that combines
generalized autoregressive score copula functions with high frequency data and
allows us to capture and forecast the conditional time-varying joint
distribution of the oil -- stocks pair accurately. Our realized GARCH with
time-varying copula yields statistically better forecasts of the dependence and
quantiles of the distribution relative to competing models. Employing a
recently proposed conditional diversification benefits measure that considers
higher-order moments and nonlinear dependence from tail events, we document
decreasing benefits from diversification over the past ten years. The
diversification benefits implied by our empirical model are, moreover, strongly
varied over time. These findings have important implications for asset
allocation, as the benefits of including oil in stock portfolios may not be as
large as perceived