Despite sustainable investments standing at record highs, it remains a challenge to quantify climate risk. We propose a proxy for a climate risk factor, the pollutive-minus-clean (PMC) portfolio, which captures differences in returns to firms that have high versus low corporate emissions. By regressing individual stock returns on the PMC factor, we obtain estimates of asset-level climate risk exposure: 'carbon beta'. Validation of carbon betas confirms that variation in climate risk exposures aligns with our prior expectations. Our measure has desirable properties regarding availability, coverage, and informativeness compared to conventional climate risk measures. We study the interaction of carbon betas with several proxies for realisations in climate risk. Returns to stocks with high carbon betas are lower during months in which climate change is more frequently discussed in the news, during months in which temperatures are abnormally high, and during exceptionally dry months. Unlike firm emissions and intensities, variation in carbon betas correlates with green patent issuance and forward-looking measures of climate risk.