Multi-objective portfolio optimization of mutual funds under downside risk measure using fuzzy theory

This paper addresses group multi-objective optimization under a new perspective. For each point in the feasible decision set, satisfaction or dissatisfaction from each group member is determined by a multi-criteria ordinal classification approach, based on comparing solutions with a limiting boundary between classes “unsatisfactory” and “satisfactory”. The whole group satisfaction can be maximized, finding solutions as close as possible to the ideal consensus. The group moderator is in charge of making the final decision, finding the best compromise between the collective satisfaction and dissatisfaction. Imperfect information on values of objective functions, required and available resources, and decision model parameters are handled by using interval numbers. Two different kinds of multi-criteria decision models are considered: (i) an interval outranking approach and (ii) an interval weighted-sum value function. The proposal is more general than other approaches to group multi-objective optimization since (a) some (even all) objective values may be not the same for different DMs; (b) each group member may consider their own set of objective functions and constraints; (c) objective values may be imprecise or uncertain; (d) imperfect information on resources availability and requirements may be handled; (e) each group member may have their own perception about the availability of resources and the requirement of resources per activity. An important application of the new approach is collective multi-objective project portfolio optimization. This is illustrated by solving a real size group many-objective project portfolio optimization problem using evolutionary computation tools.

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Modeling and Optimizing the Multi-Objective Portfolio Optimization Problem with Trapezoidal Fuzzy Parameters

Mathematical and Computational Applications ◽

10.3390/mca26020036 ◽

2021 ◽

Vol 26 (2) ◽

pp. 36

Author(s):

Alejandro Estrada-Padilla ◽

Daniela Lopez-Garcia ◽

Claudia Gómez-Santillán ◽

Héctor Joaquín Fraire-Huacuja ◽

Laura Cruz-Reyes ◽

...

Keyword(s):

Steady State ◽

Portfolio Optimization ◽

Optimization Problem ◽

Solution Process ◽

Density Estimator ◽

Nsga Ii ◽

Spatial Spread ◽

Multi Objective ◽

Significant Difference ◽

Portfolio Optimization Problem

A common issue in the Multi-Objective Portfolio Optimization Problem (MOPOP) is the presence of uncertainty that affects individual decisions, e.g., variations on resources or benefits of projects. Fuzzy numbers are successful in dealing with imprecise numerical quantities, and they found numerous applications in optimization. However, so far, they have not been used to tackle uncertainty in MOPOP. Hence, this work proposes to tackle MOPOP’s uncertainty with a new optimization model based on fuzzy trapezoidal parameters. Additionally, it proposes three novel steady-state algorithms as the model’s solution process. One approach integrates the Fuzzy Adaptive Multi-objective Evolutionary (FAME) methodology; the other two apply the Non-Dominated Genetic Algorithm (NSGA-II) methodology. One steady-state algorithm uses the Spatial Spread Deviation as a density estimator to improve the Pareto fronts’ distribution. This research work’s final contribution is developing a new defuzzification mapping that allows measuring algorithms’ performance using widely known metrics. The results show a significant difference in performance favoring the proposed steady-state algorithm based on the FAME methodology.

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Portfolio Optimization Constrained by Performance Attribution

Journal of Risk and Financial Management ◽

10.3390/jrfm14050201 ◽

2021 ◽

Vol 14 (5) ◽

pp. 201

Author(s):

Yuan Hu ◽

W. Brent Lindquist ◽

Svetlozar T. Rachev

Keyword(s):

Portfolio Optimization ◽

Asset Allocation ◽

Value At Risk ◽

Risk Measures ◽

Risk Measure ◽

Selection Effect ◽

Conditional Value At Risk ◽

Positive Role ◽

Performance Attribution ◽

Dow Jones Industrial Average

This paper investigates performance attribution measures as a basis for constraining portfolio optimization. We employ optimizations that minimize conditional value-at-risk and investigate two performance attributes, asset allocation (AA) and the selection effect (SE), as constraints on asset weights. The test portfolio consists of stocks from the Dow Jones Industrial Average index. Values for the performance attributes are established relative to two benchmarks, equi-weighted and price-weighted portfolios of the same stocks. Performance of the optimized portfolios is judged using comparisons of cumulative price and the risk-measures: maximum drawdown, Sharpe ratio, Sortino–Satchell ratio and Rachev ratio. The results suggest that achieving SE performance thresholds requires larger turnover values than that required for achieving comparable AA thresholds. The results also suggest a positive role in price and risk-measure performance for the imposition of constraints on AA and SE.

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Investigation and Comparison of the Performance of Multi-Objective Evolutionary Algorithms Based on Decomposition and Dominance in Portfolio Optimization

Electrical Engineering (ICEE), Iranian Conference on ◽

10.1109/icee.2018.8472663 ◽

2018 ◽

Cited By ~ 1

Author(s):

Mahsa Rajabi ◽

Hamid Khaloozadeh

Keyword(s):

Evolutionary Algorithms ◽

Portfolio Optimization ◽

Multi Objective

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