Institutional investors aiming to enhance the sustainability of their portfolios often use value-weighted stock market indices as benchmarks for their active equity strategies. However, recent research reveals that these indices exhibit a carbon bias, primarily because carbon-intensive companies, often from capital-intensive sectors, are more likely to be publicly listed. This bias exposes investors to carbon transition risks. To mitigate these risks, investors can consider strategies like transitioning to green assets, which may reduce returns but also reduce exposure to climate risks. It's essential to inform clients and fund participants about the potential impacts of adopting a low-carbon strategy on their portfolio's risk-return profile.