Nested dynamic network data envelopment analysis models with infinitely many decision making units for portfolio evaluation

Portfolio performance evaluation is a major data envelopment analysis (DEA) application in the finance field. Most proposed DEA approaches focus on single-period portfolio performance assessment based on aggregated historical data. However, such an evaluation setting may result in the loss of valuable information in past individual time periods, and violate real-world portfolio managers’ and investors’ decision making, which generally involves multiple time periods. Furthermore, to our knowledge, all proposed DEA approaches treat the financial assets comprising a portfolio as a “black box”: thus there is no information about their individual performance. Moreover, ideal portfolio evaluation models should enable the target portfolio to compare with all possible portfolios, i.e., enabling full diversification of portfolios across all financial assets. Hence, this research aims at developing nested dynamic network DEA models, an additive model being nested within a slacks-based measure (SBM) DEA model, that explicitly utilizes the information in each individual time period to fully and simultaneously measure the multi-period efficiency of a portfolio and its comprised financial assets. The proposed nested dynamic network DEA models, referred to as NDN DEA models, are linear programs with conditional value-at-risk (CVaR) constraints, and infinitely many decision making units (DMUs). In conducting the empirical study, this research applies the NDN DEA models to a real-world case study, in which Markov chain Monte Carlo Bayesian algorithms are used to obtain future performance forecasts in today's highly volatile investment environments.