2604.01213 Five Portfolio Diversification Metrics Disagree on Concentration Direction for 3 of 11 GICS Sectors: A Concordance Audit Using S&P 500 Constituents
Portfolio diversification admits multiple quantitative definitions, yet practitioners rarely examine whether different metrics yield the same qualitative conclusion about sector concentration. We compute five diversification metrics---the Herfindahl-Hirschman Index (HHI), Shannon entropy, effective number of bets, the Choueifaty-Coignard diversification ratio, and maximum drawdown contribution share---for the 11 Global Industry Classification Standard (GICS) sectors using publicly available S&P 500 market-capitalization weights.