In this paper, a dependence-switching copula model is used for the first time to analyse the dependence structure between sectoral equity markets and crude oil prices for India, one of the largest oil importing countries. Specifically, we investigate the dependence and tail dependence for four distinctive states of the market, i.e. rising oil prices—rising equity markets, declining oil prices—declining equity markets, rising oil prices—declining equity markets, and declining oil prices—rising equity markets. Our results reveal that the tail dependence is symmetric (asymmetric) in positive (negative) correlation regimes. Based on the copula results, we estimate the systemic crude oil price risk to different sectors using CoVaR and delta CoVaR. A fleeting positive sectoral CoVaR and delta CoVaR across all sectors implies a time-varying oil price systemic risk. Yet, little difference between CoVaR and VaR across the sectors reveals that a bearish oil market does not add additional systemic risk to a bearish sectoral equity market. The carbon sector is found to be the safe haven investment when both the equity and the oil markets are in a downward phase.

We examine the energy-food nexus using the dependence-switching copula model. Specifically, we look at the dependence for four distinct market states, such as, increasing oil–increasing commodity, declining oil–declining commodity, increasing oil–declining commodity, as well as declining oil–increasing commodity markets. Our results support the argument that the crash of oil markets and agricultural commodities happen at the same time, especially during crisis period. However, the same is not true during times of normal economic conditions, implying that investors cannot make excess profits in both agricultural and oil markets at once. Furthermore, our analysis suggests that the return chasing effect dominates for all commodities on maximum occasions. The CoVaR and ΔCoVaR results indicate important risk spillover from oil to agricultural markets, especially around the financial crisis.