Inverse DEA for Portfolio Volatility Targeting: Industry Evidence from Taiwan Stock Exchange

This work develops an inverse data envelopment analysis (Inverse DEA) framework for portfolio optimization, treating return as a desirable output and volatility as an undesirable output. Using 20 industry-level portfolios from the Taiwan Stock Exchange (1365 stocks; FY-2020), we first evaluate efficiency with a directional-distance DEA model and identify 7 inefficient industries. We then formulate an Inverse DEA model that holds inputs and desirable outputs fixed and estimates the maximum feasible reduction in volatility. Estimated reductions range from 0.000827 to 0.007610, and substituting these targets into the base model drives each portfolio’s inefficiency score to zero (ϕ=0), thereby making them efficient. To test robustness, we extend the analysis to a calm pre-crisis year (2019) and a recovery year (2021), which confirm that inefficiency and volatility-reduction targets behave logically across regimes, smaller cuts in stable markets, larger cuts in stressed conditions, and intermediate adjustments during recovery. We interpret these targets as theoretical envelopes that inform risk-reduction priorities rather than investable guarantees. The approach adds a forward-planning layer to DEA-based performance evaluation and provides portfolio managers with quantitative, regime-sensitive volatility-reduction targets at the industry level.