An approach to large-scale portfolio optimization for asset returns represented by factor models is disclosed. Factor models can be used within general portfolio optimization problems, such as mean-variance optimization, expected utility maximization, and mean-risk optimization, with various measures of risk, including conditional Value-at-Risk, as well as the representation of risk constraints and constraints on higher moments of the asset return distribution. Both expected utility maximization and mean-risk optimization are more general than mean-variance optimization and can consider fat tails in the asset return distribution and, thus, allow for better control of downside risk. Explicit risk constraints especially constraints on conditional Value-at-Risk, limit downside risk in either mean-variance optimization, expected utility maximization, or mean-risk optimization. Constraints on higher moments limit fat tails of the asset return distribution. Equilibrium returns in expected utility maximization and mean-variance optimization based on factor models of asset returns are obtained. Active management of portfolios of financial assets based on factor exposures is provided.
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