Extends replica analysis to derive macroscopic relations including a Pythagorean theorem for Sharpe ratios and Tobin's separation theorem for portfolios with a risk-free asset.
Shinzato: Physica A: Statistical Mechanics and its Applications 490 (2018) 986
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Macroscopic theorem of the portfolio optimization problem with a risk-free asset
Extends replica analysis to derive macroscopic relations including a Pythagorean theorem for Sharpe ratios and Tobin's separation theorem for portfolios with a risk-free asset.