Traditional Mean-Variance (MV) portfolio optimization faces significant challenges. It assumes normal return distributions, often underestimating risk during market stress due to financial returns exhibiting fat tails and skewness. The model is highly sensitive to input estimation errors, leading to unstable and extreme portfolio allocations. Furthermore, MV often results in corner solutions, where portfolios are concentrated in a few assets, undermining diversification. This study assess whether Fuzzy Semi-Mean Absolute Deviation (FSMAD) models can overcome these shortcomings.

We adapted Fuzzy Semi-Mean Absolute Deviation (FSMAD) Models 1 and 2, initially designed for the energy sector, to public financial markets. Their performance is compared against the classical Mean-Variance (MV) model using a real-world quarterly financial data set spanning 2000-2025. The study employed a structured evaluation framework: diversification was assessed quantitatively using the Herfindahl-Hirschman Index (HHI), robustness was evaluated through a split-sample testing approach across two distinct periods (2000-2012 and 2013-2025).

The Mean-Variance (MV) model demonstrated superior diversification with lower Herfindahl-Hirschman Index (HHI) values and broader asset inclusion, making it the better choice when stability is a priority. FSMAD1 offered less diversification than MV, but more than FSMAD2; in terms of robustness, FSMAD1 performed better than MV, but worse than FSMAD2. In contrast, FSMAD2, despite its high concentration due to linear constraints, proved most robust, maintaining stable frontiers and consistent allocations amid market shifts. These results highlight key trade-offs: while MV is suitable for unstable environments demanding diversification, FSMAD2 excels in uncertain markets, offering the best robustness among all models. While the tested fuzzy models did not outperform the classical MV model in terms of diversification, the results indicate potential advantages regarding robustness. To confirm these findings, additional testing with larger and more diverse datasets is needed. The inferior diversification observed, particularly in FSMAD2, could be mitigated by refining the model parameters or extending its formulation. Also, out-of-sample testing is needed before confirming superiority.