Integrating fuzzy logic into portfolio optimization: Enhancing risk management and return maximization

Modern Portfolio Theory (MPT), or mean-variance analysis, is built on principles of risk and return. A core assumption in MPT is investor risk aversion, which significantly influences investment choices. In evidence, highly risk-averse investors often choose safer investments with lower returns over riskier options that may yield higher returns. This study seeks to optimize investment portfolio utility scores by modelling risk aversion using fuzzy logic. Introduced by Lotfi Zadeh, fuzzy logic addresses human reasoning and decision-making under uncertainty and ambiguity. Thus, this logic is suitable to model investors' diverse utility preferences and to reflect their subjective and varied perceptions of risk. Traditional utility scoring uses fixed risk aversion coefficients from 1 to 5, with higher values indicating greater risk aversion. Here, we propose a more granular approach, measuring risk aversion on a 0-100 scale, where 0 indicates total risk tolerance and 100 signifies complete risk aversion. We categorize investors as low (5-45), moderate (45-75), or high (75-95) risk-averse, acknowledging that no investor is entirely risk-seeking or risk-averse. Each risk aversion category is modelled with Trapezoidal and Cauchy distributions using a linear combination of their respective fuzzy membership functions. A sensitivity analysis was conducted, over short, mid and long-term timeframes, on a portfolio consisting of 10 assets which is optimized with fuzzy risk aversion coefficient then compared to the same portfolio optimized with fixed coefficients. Findings showed that fuzzy logic consistently provided superior risk-adjusted returns, particularly in mid-term and long-term scenarios. Although fuzzy-optimized portfolios had higher betas and variances, those risks were offset by enhanced returns. The Treynor ratios were similar across both methods, yet the fuzzy approach delivered higher overall returns, highlighting its effectiveness in managing volatility and risk.