Abstract The study investigates dependence structure and estimates portfolio risk on data from foreign exchange market in India. We specify both marginal models for the foreign exchange returns and a joint model for the dependence. We employ the AR-t-GARCH-EVT models for the marginal distribution of each of five currency returns series. For the joint model, we choose seven copulas with different dependence structure such as Gaussian, Frank, Clayton, Gumbel, BB1, BB2 and BB7 copulas. Using LL, AIC, and BIC values we find BB1 as the best fitted copula. The evidence of tail dependence coefficients suggests that currency markets are more likely to boom together than to crash together. Portfolio risk is measured using VaR and CVaR and global minimum risk portfolio is selected based on efficient frontiers. The evidences have direct implications for investors and risk managers during extreme currency market movements.