We develop a simple dynamic investment strategy that allows long‐term passive investors to hedge climate risk without sacrificing financial returns. Our proposed hedging strategy goes beyond a simple divestment of high carbon footprint or stranded assets stocks. This is just the first step. The second step is to optimize the composition of the low carbon portfolio so as to minimize the tracking error with the reference benchmark index. We show that tracking error can be almost eliminated even for a low carbon index that has 50% less carbon footprint. The low carbon portfolios in existence that have been constructed in this way have so far matched or outperformed their benchmark. And the low carbon indices that have not yet been launched have similar performance based on back testing. By investing in such an index investors are holding, in effect, a "free option on carbon": as long as the introduction of significant limits on CO2 emissions is postponed they are essentially able to obtain the same returns as on a benchmark index, but the day when CO2 emissions are priced the low carbon index will outperform the benchmark.