The degree of connection and integration between stock market indices is crucial to identifying the potential benefits associated with international diversification. However, there have been no findings on relationships between sustainability indices. The present study analyses the existence of equilibrium between short‐ and long‐term environmentally sustainable investments through Johansen cointegration tests and based on a model of asymmetric multivariate conditional heteroscedasticity. We selected indices for five segments of environmental investment (alternative energy, clean technology, green building, sustainable water, and pollution prevention) and applied a time period of roughly nine years. The obtained results show that over the long term, the indices' behaviour is autonomous, creating opportunities to diversify investment. Over the short term, environmental segments exhibit similar behaviour, approaching behaviours described by conventional indices. Copyright © 2017 John Wiley & Sons, Ltd and ERP Environment