This study examines the direction and extent of asymmetric volatility connectedness between the oil and commodity markets, using five-minute interval data from the oil, natural gas and 21 commodity futures markets. We also analyze the positive and negative volatility connectedness through network diagrams to determine the magnitude and strength of the volatility spillover. We suggest optimal portfolios for several oil-commodity pairs minimizing value-at-risk and conditional value-at-risk with higher hedge effectiveness. The results are of significant interest to investors and policymakers.