Classical portfolio theory frequently assumes frictionless markets, but in reality, transaction costs, like fees and market impact, can erode returns and cause excessive turnover. Incorporating these costs transforms rebalancing from a mechanical rule into a strategic decision: determining exactly when and how much to trade to restore desirable exposures efficiently. This study proposes a dynamic rebalancing framework that explicitly models proportional transaction costs within a multi-period optimization setting. By introducing a transaction cost function, portfolio adjustment becomes a rigorous optimization problem balancing expected returns, risk exposure, and total rebalancing costs. This cost-aware framework empowers investors to avoid unnecessary trading, preserving risk control while improving net performance. To solve this, specific algorithmic procedures are designed to enhance computational efficiency in realistic, multi-asset scenarios. Empirical evaluations using historical financial data compare this cost-aware strategy against conventional periodic and threshold-based methods. Performance is assessed across metrics including cumulative return, portfolio volatility, turnover rate, and net returns after costs. The empirical results demonstrate that explicitly integrating transaction costs into optimization significantly improves strategy performance. The proposed model successfully reduces unnecessary trading activity and lowers portfolio turnover while maintaining competitive risk-adjusted returns. Furthermore, sensitivity analyses reveal that transaction cost levels dictate the optimal rebalancing frequency and adjustment magnitude. Overall, this study provides a systematic modeling framework and strong empirical evidence for cost-aware dynamic portfolio rebalancing, offering practical insights for investors navigating complex environments.
The global stock market is a critical mechanism for the allocation of scarce financial resources to productive economic activities. However, investors continuously face the dual challenge of minimising risk while simultaneously maximising returns. This tension becomes particularly acute during catastrophic events such as pandemics, which can severely disrupt market stability and undermine conventional investment strategies. The COVID-19 pandemic, for instance, caused significant downturns across major stock markets worldwide, highlighting the vulnerability of concentrated investment portfolios and reinforcing the importance of sound portfolio diversification strategies. This study applies Markowitz’s Modern Portfolio Theory (MPT) to nine selected stocks listed on the United States (US) stock market, spanning sectors including Technology, E-commerce, Energy, Health, Automobile, Transport, and Entertainment. Stock performance is evaluated over two distinct periods: before the pandemic (January 2018 to December 2019) and during the pandemic (January 2020 to December 2021), using data obtained from Yahoo Finance. The expected returns of the selected stocks are estimated using the Capital Asset Pricing Model (CAPM). A diversified portfolio is then formulated, the Sharpe ratio is computed for risk-adjusted performance evaluation, and the efficient frontier is constructed using Monte Carlo simulation implemented in Python. The simulation generates 2,000 portfolio scenarios to identify the optimal risky portfolio. The results demonstrate that a well-diversified portfolio can yield superior risk-adjusted returns, with the optimal portfolio achieving a Sharpe ratio of 1.21 at a return of 27.02% and a standard deviation of 22.36%. These findings underscore the effectiveness of MPT and Monte Carlo simulation as practical tools for optimal portfolio selection, particularly in the context of catastrophic market events.
D. Arhinful, I. Ampofi, Ebenezer Asiedu· American Journal of Applied...· 0 citations
Investment portfolio optimization has become essential for managing risk and maximizing returns in increasingly complex and volatile financial markets. Traditional portfolio selection methods often relied on intuition, whereas modern analytical models use quantitative techniques such as mean-variance optimization, Capital Asset Pricing Model (CAPM), multi-factor models, and stochastic optimization to support informed investment decisions. This study presents a comprehensive analytical framework that integrates financial data preprocessing, risk estimation, portfolio optimization, and performance evaluation using metrics such as expected return, portfolio variance, Sharpe ratio, Value at Risk (VaR), and diversification efficiency. The framework enables dynamic portfolio rebalancing by continuously analyzing market conditions and adjusting investment strategies. Experimental results demonstrate that analytical optimization methods outperform traditional allocation approaches by improving returns, reducing risk, enhancing diversification, and increasing investment stability. The study concludes that combining mathematical optimization with statistical financial analysis provides a reliable foundation for intelligent portfolio management, while future integration with Artificial Intelligence (AI), Big Data, Reinforcement Learning, and sustainable investment strategies will further enhance investment decision-making.
Johan Håstad's mentor Arne Andersson· International Journal of Com...· 0 citations
This paper investigates optimal portfolio choice for a risk-averse investor who is operating in a
financial market characterized by continuous time usage and with explicit attention being paid to
the investor's sensitivity to market movements. The investor's preferences are described by a
power utility function of constant relative risk aversion, which promotes economically interesting
behavior over wealth levels. The market consists of a risk-free asset and many risky assets,
evolving under stochastic differential equations. By allowing the investor to adjust portfolio
positions according to the changes in the processes of risky assets, the model can extend
traditional portfolio optimization frameworks. Aiming to self-assemble against dynamic
programming and the Hamilton-Jacobi-Bellman equation, exploiting Itô's calculus, we got
analytical representations of the optimal portfolio strategy and its expected terminal utility. The
quantification of the explicit sensitivity effect parameter allowed the activation of market
responsiveness to additional advantage. Numerical simulations, with Python, demonstrate the
role of market signals on a market-responsive portfolio. Two- and three-dimensional numerical
figure analyses also depict the behavior, in terms of the optimal investment decisions, of risk
aversion, asset volatility, and sensitivity parameters.
C. Achudume· International Journal of Com...· 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
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.
Zahra Rohadatul Aisylah, Ferdiansyah Saputra, Arief Surya Lesmana et al.· Digital Business and Entrepr...· 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