A modified Sharpe framework incorporating carbon exposure

This study proposes the Carbon Adjusted Standardized Sharpe Ratio (CASSR), which combines standardized Sharpe ratios and portfolio carbon exposure using parameters estimated from the feasible portfolio distribution. For Bitcoin, gold, and the S&P 500, CASSR reduces calculated carbon exposure by 33.28% relative to Sharpe optimization, with a 3.51% reduction in the Sharpe ratio. The optimal allocation remains unchanged under the alternative emission estimates examined but varies with gold valuation and investment horizon. In a separate application to eleven S&P 500 sectors using a common carbon metric, CASSR reduces carbon exposure by 93.20%, with a 13.56% reduction in the Sharpe ratio. Moving-block bootstrap results indicate lower average portfolio carbon exposure under CASSR. Comparisons with alternative carbon-optimization approaches place the CASSR solution on both the carbon-efficient and mean-variance-carbon efficient frontiers. The findings are conditional on the selected investment universe and carbon-accounting assumptions.