An integrated fuzzy-grey relational analysis approach to portfolio optimization

Area of Science:

• Quantitative Finance
• Decision Science
• Financial Engineering

Background:

• Investor expectations are often imprecise and subjective.
• Traditional risk measures may not fully capture individual investor preferences.
• Modeling uncertain asset returns requires robust mathematical frameworks.

Purpose of the Study:

• To develop a novel risk measure for portfolio optimization that incorporates subjective investor expectations.
• To quantify an investor's perception of risk based on the proximity of portfolio returns to ideal returns.
• To combine Fuzzy set theory and Grey Relational Analysis for enhanced financial modeling.

Main Methods:

• Utilized Fuzzy set theory and Credibility theory to formalize imprecise investor expectations.
• Employed Grey Relational Analysis to measure the similitude between actual and ideal portfolio return sequences.
• Developed a maximization-type risk measure based on closeness to ideal returns.
• Applied a genetic algorithm for solving the portfolio optimization problem.

Main Results:

• The proposed risk measure effectively quantifies investor risk perception.
• Case studies on NASDAQ-100 and NIFTY-50 indices demonstrated the model's applicability.
• Out-of-sample analysis showed portfolios achieved healthy growth and superior performance compared to existing methods.

Conclusions:

• The novel risk measure is intuitive, easy to calculate, and reduces estimation risk.
• The integrated approach offers a superior method for portfolio optimization under uncertainty.
• The model's effectiveness is validated through empirical analysis of major stock market indices.