Problem

The increasing number of investors in the Indonesia Stock Exchange since the COVID-19 pandemic highlights the importance of effective portfolio optimization. However, the widely used classical mean-variance optimization (MVO) model relies on historical estimates of return and risk that are prone to uncertainty, often leading to suboptimal portfolios. This uncertainty stems from the fact that past observations may not accurately predict future market conditions, creating a need for more robust methods that can account for market fluctuations and worst-case scenarios.

Method

To address the limitations of classical MVO, this study employs robust optimization, which incorporates uncertainty sets to improve portfolio reliability. The research constructs these uncertainty sets using two distinct methods: the moving-window method and the bootstrapping method. The moving-window approach involves selecting a fixed-size sub-sample of data (90 days, corresponding to quarterly periods) to calculate the mean vector and covariance matrix, making the uncertainty set more reflective of recent market conditions. In contrast, the bootstrapping method utilizes random resampling from the entire historical dataset (247 trading days) to generate new samples and their corresponding mean vectors and covariance matrices. The robust optimization model is then solved in MATLAB using Indonesian banking stock data from March 2022 to March 2023, with varying risk-aversion parameters (gamma values of 5, 50, and 100) to observe their effect on optimal portfolio solutions.

Results

The numerical simulations showed that robust optimization using the moving-window method consistently provided a more favorable risk-return trade-off compared to the bootstrapping approach, as indicated by lower objective function values. Under both good and poor market conditions, the moving-window method generated profits, especially for investors with a lower risk-aversion parameter (gamma = 5), yielding Rp. 11,715.00 profit in good conditions and Rp. 735.00 in poor conditions for a Rp. 100,000.00 investment. In contrast, the bootstrapping method often resulted in lower profits or even losses. While the moving-window method was superior for risk-taking investors, for higher risk-aversion coefficients (gamma = 50 and 100), classical mean-variance optimization sometimes yielded greater profits.

Implications

The findings suggest that robust optimization, particularly when combined with the moving-window method for constructing uncertainty sets, offers a promising approach for managing investment portfolios in volatile markets like Indonesia. The moving-window method proved effective in generating resilient portfolios that could achieve positive returns even under adverse market conditions, especially benefiting risk-tolerant investors. This highlights its potential for developing more effective and stable portfolio strategies for Indonesian banking stocks by reflecting current market dynamics more accurately. Future research could explore a broader sensitivity analysis with additional risk-aversion parameter values to further understand its applicability across a wider spectrum of investor preferences.