Aug 2026· Digital Business and Entrepreneurship Journal· Vol 4, pp. 89-99· 0 citations
Abstract
Constructing an optimal portfolio is a crucial step for investors in balancing the trade-off between expected return and investment risk. This study aims to construct an optimal portfolio comprising two stocks, EMDE and MTDL, by applying the Markowitz mean-variance model to minimize return variance at a specific return level. The methodology employs mean-variance optimization, estimating expected return, variance, and covariance based on historical return data for both stocks to determine efficient portfolio weights. The analysis reveals that the optimal portfolio consists of 19.27% EMDE stock and 80.73% MTDL stock. This combination yields an expected portfolio return of 1.33% with a return standard deviation of 8.43%, reflecting a more efficient risk-return profile compared to an allocation in a single stock. These findings indicate that diversification between EMDE and MTDL can improve portfolio risk characteristics without significantly sacrificing returns. Consequently, investors are advised to consider this combination as part of their asset allocation strategy, particularly those with moderate risk preferences who prioritize mean-variance efficiency. This study provides empirical evidence regarding the application of the Markowitz model in the Indonesian stock market and serves as a reference for future research involving a broader range of assets and data periods.
Portfolio optimization is a fundamental aspect of investment management that focuses on constructing a portfolio capable of delivering the highest possible return while minimizing investment risk. Modern Portfolio Theory (MPT), introduced by Harry Markowitz, provides a quantitative framework for selecting an optimal combination of assets based on their expected returns, variances, and correlations. This study examines the application of Modern Portfolio Theory in optimizing investment portfolios by evaluating the trade-off between risk and return across different asset classes. Historical financial data are analyzed to estimate expected returns, standard deviations, and covariance among selected securities. The efficient frontier is generated to identify portfolios that maximize returns for a given level of risk, while diversification is employed to reduce unsystematic risk. The findings demonstrate that a well-diversified portfolio designed using MPT can significantly improve investment performance compared to investing in individual assets. The study also highlights the practical significance of portfolio optimization in assisting investors, financial analysts, and portfolio managers in making informed investment decisions aligned with their financial objectives and risk tolerance. Overall, the research emphasizes that Modern Portfolio Theory remains a valuable and effective approach for achieving efficient asset allocation and enhancing long-term portfolio performance in dynamic financial markets. Keywords: Portfolio Optimization, Modern Portfolio Theory (MPT), Investment Management, Risk-Return Trade-off, Asset Allocation, Portfolio Diversification, Efficient Frontier.
K. Naveen, Amita Johar, T. Meghana· International Journal of Dat...· 0 citations
The capital market plays an important role in the economy by providing investment instruments for investors and financing sources for companies. A capital market portfolio consists of a collection of financial assets, such as stocks, constructed to achieve an optimal return while reducing investment risk. Mean-variance portfolio construction is highly sensitive to parameter estimation errors. Therefore, a robust estimation approach is employed to obtain more stable parameter estimates by minimizing the influence of outliers. This study aims to construct an optimal stock portfolio through diversification, determine stock weights using a two-constraint mean-variance model with robust S-estimation, calculate the expected return and risk, and evaluate portfolio performance. The analysis was conducted using the closing prices of stocks included in the IDX30 Index from October 2024 to September 2025. The results identified nine stocks with positive expected returns from five different sectors. Based on the stock selection criteria, two optimal portfolios were constructed. Portfolio 1 consists of ASII, BRPT, INDF, PGAS, and TLKM, whereas Portfolio 2 consists of ASII, ANTM, INDF, PGAS, and TLKM. Portfolio 1 generates an expected return of 0.137% with a risk of 2.226%, while Portfolio 2 generates an expected return of 0.097% with a risk of 1.319%. Based on the Sharpe and Treynor ratios, Portfolio 1 demonstrates relatively better performance than Portfolio 2.
Anis Faiqo Tuzzainiyah, E. Sulistianingsih, Nurfitri Imro'ah· Jambura Journal of Mathemati...· 0 citations
In mean-variance portfolio analysis, the efficient frontier represents the optimal trade-off between expected return and risk, assuming stable underlying parameters. This paper investigates portfolio fragility: the instability of optimal weights, risk-adjusted performance, and diversification when model inputs and construction choices are jointly perturbed. Combining constrained Markowitz optimization with variance-based global sensitivity analysis (Sobol indices), we map out how input uncertainty and portfolio-construction choices propagate along the target-return dimension. Using an empirical universe of multi-asset exchange-traded funds (ETFs), we find a distinct transition in the sensitivity structure: in the baseline experiment, lower target returns are dominated by l2 regularization, whereas aggressive return requirements become increasingly sen- sitive to the weight cap and expected-return perturbations. This shift coincides with a sharp drop in effective diversification and a rise in weight dispersion. We extend the analysis to a multi-universe fragility atlas, showing that under a com- mon absolute concentration rule, the smallest universe is weight-cap-driven in the aggressive return region, while larger sampled universes remain more often regularization-driven. The fragile frontier serves as a direct diagnostic tool to evaluate the structural robustness of constrained optimizers without altering the underlying allocation rule.
Stefano Pellegrino, Giulia Vannucci, R. Siciliano· 0 citations
Portfolio optimization is a systematic investment approach for balancing expected return and investment risk through diversification. This research paper examines the application of the Markowitz Mean-Variance Model to selected Information Technology and Banking sector companies listed on the National Stock Exchange (NSE) of India. The study uses secondary historical stock-price data for ten companies, comprising five IT companies—TCS, Infosys, Wipro, HCL Technologies and Tech Mahindra—and five banking companies—HDFC Bank, ICICI Bank, Axis Bank, State Bank of India and Kotak Mahindra Bank. Daily returns, average returns, variance, standard deviation, covariance, correlation, portfolio weights, portfolio return and portfolio risk are used to evaluate the risk-return profile. The analysis indicates that Tech Mahindra recorded the highest positive average daily return among the selected IT companies, while SBIN recorded the highest positive average daily return among the selected banks. Wipro and Kotak Mahindra Bank recorded the highest volatility within their respective sectors. The optimized IT portfolio generated a daily return of -0.000478 with portfolio risk of 0.013807, while the optimized banking portfolio generated a daily return of -0.000247 with portfolio risk of 0.013648. The study concludes that the Markowitz framework provides a structured basis for diversification, risk measurement and portfolio construction.
Nikhil Reddy Y, Nagaraj Chippolu· EPRA International Journal o...· 0 citations
Indonesia’s growing capital market provides investors with diverse opportunities; however, differences in stock returns and risks require systematic portfolio selection. This study aimed to identify LQ45 stocks that formed an optimal portfolio and determine their investment proportions during 2021–2025 using the Single Index Model. A quantitative descriptive approach was employed using secondary data obtained from the Indonesia Stock Exchange and Bank Indonesia, including monthly closing stock prices, Composite Stock Price Index (CSPI) data, and the BI Rate. Stocks were selected through purposive sampling and analyzed based on expected return, beta, residual variance, Excess Return to Beta (ERB), Cut-Off Point, and fund allocation proportion. The findings identified eight stocks as optimal portfolio constituents, namely ASII, TLKM, TOWR, PGAS, UNTR, ANTM, UNVR, and MEDC, with a Cut-Off Point value of 0.01335. PGAS achieved the highest ERB value of 6.4313, indicating the highest return efficiency relative to systematic risk. However, ASII received the largest portfolio allocation at 19%, followed by TLKM at 17%, TOWR at 15%, PGAS and UNTR at 14% each, ANTM at 8%, UNVR at 7%, and MEDC at 6%. The study concluded that the Single Index Model effectively generated a diversified, rational, and risk-conscious investment portfolio for Indonesia’s post-pandemic market and provided practical allocation guidance for investors and investment managers seeking efficient investment decisions.
Ratih Paramitasari· Eduvest - Journal Of Univers...· 0 citations
The rapid growth of retail investors in Indonesia, from 2.48 million in 2019 to over 20 million by 2025, underscores an urgent need for empirically grounded portfolio optimization frameworks adoptable into practical tools such as robo-advisory systems. This study applies the Markowitz Mean-Variance model to construct and evaluate an optimal stock portfolio from the LQ45 index over January 2022 to December 2025, a post-pandemic period characterized by predominantly adverse risk-adjusted returns. Using daily closing price data for 27 consistently listed LQ45 stocks (958 trading days) from the Indonesia Stock Exchange (IDX), with sample consistency verified through official BEI constituent evaluation announcements, this study constitutes an ex-post empirical analysis designed to isolate the mathematical efficacy of the Mean-Variance model under adverse market conditions. The analysis encompasses individual return and risk profiling, construction of a 27x27 covariance matrix, efficient frontier derivation via constrained quadratic optimization using Microsoft Excel Solver (GRG Nonlinear), and Sharpe ratio-based performance evaluation against a risk-free rate of 5.3281% per annum (average BI Rate 2022-2025). The core finding is that 19 of 27 sample stocks (70.4%) generated negative Sharpe ratios, confirming the inadequacy of undiversified single-stock strategies in adverse markets. In contrast, the tangency portfolio achieved a Sharpe ratio that materially surpasses all 27 individual stocks, establishing that quantitative portfolio optimization delivers superior risk-adjusted outcomes precisely when markets are most challenging. These results validate the enduring relevance of Modern Portfolio Theory in Indonesia's capital market and provide a transparent, replicable framework for investors and practitioners.
Irfan Andi Pramudya, Intan Shaferi· The International Conference...· 0 citations
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