Summary: In this study we have examined that assets returns in Indian markets do not follow an elliptical dependence structure; asymmetric tail dependence can be observed among asset returns particularly when the assets exhibit downside returns in a bearish market. We have used Elliptical, Archimedean and Canonical Vine copulas to model such dependence structure in large portfolios. Using certain goodness-of-fit tests we find that Archimedean copulas are insufficient to model the dependence among assets in a large portfolio. We have also compared copula models using an out-of-sample Value-at-Risk (VaR) calculation and comparing results to the historical data. It is observed that the Canonical Vine copulas consistently capture the variation in weekly and daily VaR values.