Climate change is now increasingly recognized as a major financial threat. 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. 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. This Low TE low CO2 strategy can mobilize investors on financial grounds, support disciplining pressure to reduce CO2 emissions, and contribute to build an investor constituency in support of climate change mitigation policies.