Jul 2026· Journal of Innovation and Development· 0 citations· 6 references
TL;DR
The results suggest that including a covariance noise or normalization term in the traditional expected value and variance-based approach to portfolio management helps reduce the impact of estimation error and market volatility on portfolio performance.
Abstract
This research paper discusses the issue of out-of-sample robustness of portfolio optimization within a complex market environment. Within the mean-variance framework, we compare four methods for covariance estimation and weighting: a baseline model based on sample covariances, the Ledoit-Wolf shrinkage estimator, Garber's robust covariance estimator, and a minimum-variance model incorporating an L2 regularization term. This study uses data from 60 American stocks from 2019 to 2021, with four rebalancing cycles (5, 20, 60, and 100 days) were established, and a moving-window backtesting method was applied to evaluate the performance of the various methods in terms of returns, risk, and out-of-sample stability. The empirical results indicate that the L2 normalization model generates higher cumulative returns and Sharpe ratios during most rebalancing periods, demonstrating effective stabilization of the weights; Garbner's robust covariance technique demonstrates consistent resilience to downturns in high-volatility market environments; And Reduit-Wolf's contraction estimates also show a relatively stable improvement in sample skewness compared to the benchmark model. These results suggest that including a covariance noise or normalization term in the traditional expected value and variance-based approach to portfolio management helps reduce the impact of estimation error and market volatility on portfolio performance. The period of analysis for this paper is specified. Furthermore, it covers the observation period, highlights limitations related to market comprehensiveness and parameter selection, and provides guidance for future research by incorporating financial data from diverse sources and more advanced robust optimization techniques.
This paper presents a comprehensive review of two foundational portfolio models in modern finance: the Markowitz mean-variance model and the Sharpe single-index model. The study systematically examines their theoretical frameworks, computational requirements, empirical performance, and practical applicability. The Markowitz model, as a model-free optimisation framework, aims to achieve theoretically optimal risk-return trade-offs by fully considering pairwise covariances among assets. However, its high sensitivity to estimation errors and intensive data requirements often limit its empirical usefulness, particularly for large portfolios. In contrast, the index model simplifies covariance estimation by attributing asset return variations to a common market factor, thereby reducing parameter dimensionality and enhancing computational efficiency. Multi-factor extensions further improve explanatory power while maintaining practical feasibility. By reviewing existing literature and empirical evidence, this paper highlights the strengths, limitations, and appropriate application scenarios of both models. The findings provide guidance for investors, portfolio managers, and researchers in selecting or integrating portfolio models to balance theoretical rigor with empirical robustness and operational efficiency.
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
This study asks whether environmental, social, and governance (ESG) screening changes the risk-return profile of an Indian large-cap equity portfolio. The Nifty 100 ESG index is compared with its unscreened parent, the Nifty 100, so the only systematic difference is the ESG screen and reweighting applied to a common constituent universe; the Nifty 50 is a secondary reference. Daily data from January 2021 to May 2026 show significant excess kurtosis and ARCH effects, so a constant-conditional-correlation GARCH(1,1) model with Student's t innovations generates correlated one-year price paths, with tail dependence imposed through a Cholesky-factorized multivariate-t shock. Headline tail-risk figures average five independent 100,000-path runs. A deterministic grid of 1,001 portfolios spanning 0% to 100% ESG weight is assessed on the Sharpe ratio, annualized volatility, Value at Risk and Conditional Value at Risk at 99%, the Sortino ratio, and downside deviation, at a risk-free rate and minimum acceptable return of 6.5%. Against the matched parent, daily returns correlate at 0.978, annualized volatility is 14.5% for both, and mean daily returns are identical to three decimal places (0.0453%). The optimal ESG weight is therefore interior, ranging from 50.7% to 68.1%, and annualized return holds at 11.4% across the efficient set. A Jobson-Korkie test with the Memmel correction finds no difference in Sharpe ratios (z = 0.0045, p = 0.996), corroborated by paired t and Newey-West HAC tests. Against the properly matched benchmark, ESG screening had no measurable effect on return, risk, or tail risk over this sample.
Vasudha Srivatsa, Bhavya Vikas· Journal of Computers, Mechan...· 0 citations
In the context of normalized volatility in the A-share market, traditional VaR models are unable to effectively capture the tail risk of extreme market conditions, while Expected Shortfall (ES) can make up for this deficiency. This paper selects 12 A-shares from two equally weighted stock portfolios within and outside the CSI 300 index, with a sample period from May 2022 to April 2026. It uses three methods—historical simulation, parametric method (normal), and GARCH (1,1)-t—to estimate VaR and ES, and conducts backtesting using the Kupiec POFF test, the Christoffersen conditional coverage test, and the Acerbi-Székely Z2 test. The results show that GARCH (1,1)-t can more accurately characterize tail risk at a 99% confidence level. The historical simulation method is generally robust, while the normal parameter method tends to underestimate systematic risk. ES is greater than VaR in all scenarios, which verifies its stronger ability to capture extreme losses. The conclusion remains unchanged after replacing the confidence level and portfolio weights. This paper recommends that A-share investors and regulatory agencies use ES as an important supplementary indicator to VaR, and prioritize the use of GARCH-t or historical simulation methods for risk measurement.
Yuhui Gao· Advances in Economics, Manag...· 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
This article assesses the performance of various stock market portfolios using a space-filling mixture design and a model for the logratios in the portfolio allocation. Traditional portfolio analysis relies on historical correlations between various returns and adopts various optimization models. However, these methods rely excessively on the assumptions made and often tend to ignore the statistical variability in their optimization procedures. As a result, they may not perform well when implemented on independent future data. Additionally, the constraints and bounds imposed play a crucial role in determining the feasible region and hence the optimal value therein. By integrating a systematic simplex design approach for exploring component mixtures in our portfolio and applying a logratio transformation, we offer a robust framework for analyzing the portfolios and exploring how various portfolios perform relative to each other. An advantage of our method is that we are able to estimate the standard error for each portfolio, and this allows us to incorporate the consideration of volatilities into our decision making. Using publicly available stock market data, we demonstrate the effectiveness of our approach.
R. Khattree, Md Shakhawat Alam· Journal of the Indian Societ...· 0 citations
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