Market Risk Measurement and Backtesting of Stock Portfolios (China A-Shares) Based on VaR and ES

Construction of High-order Dynamic Portfolio Models Based on VAR-ICA-MGARCH

The aim of the study is to prove that dynamic portfolios can effectively reflect the temporal dynamics of current risks of a higher order, providing greater reliability and stability compared to traditional portfolios. The subject is the economic imbalance in portfolio models, which occurs when different participants have different level of knowledge about market conditions and the performance of assets. In an environment where traditional portfolios have shown low returns due to the pronounced peaks and sharp declines in financial asset returns, as well as their inability to account for dynamic changes in financial risks. This study incorporates higher-order short-term risks into traditional portfolios in order to mitigate the effects of deviations from the normal distribution. The methodology is based on the concept of multiple financial time series and the VAR-ICA-GARCH model. This model effectively captures the conditional mean, the covariance matrix, the mutual asymmetry matrix, and the mutual kurtosis matrix, thereby characterizing temporal changes at higher-order moments. Due to the inherent nonlinearities of dynamic portfolio optimization tasks, we use a genetic algorithm to solve the dynamic portfolio model. The results of the study show that dynamic portfolios can effectively reflect the changing dynamics of current higher-order risks, while providing greater reliability and stability than traditional portfolios. Even when exposed to such complex risks, dynamic portfolios perform better. The practical significance of this research lies in determining the time-varying weighting coefficients for the portfolio and conducting both simulation experiments and empirical analysis.

Evaluation of individual stock portfolio performance on the Indonesia stock exchange using the Ortiz, Jorion, and Markowitz approaches

Background: Indonesia's capital market has experienced a sustained increase in investor participation, creating a stronger need for systematic and implementable portfolio construction methods. This study evaluates estimation risk in mean-variance optimization by comparing traditional Markowitz optimization with two mean-shrinkage approaches: the parameter-focused Bayes-Stein estimator of Jorion and the decision-focused optimal shrinkage of means proposed by Ortiz et al. Methods: The study uses monthly individual stock data from the Indonesia Stock Exchange over January 2006-December 2025. Excess returns are calculated relative to a monthly risk-free proxy, and portfolios are evaluated using a 120-month rolling-window out-of-sample backtest under long-only constraints. The sample is a balanced panel of 74 stocks with complete monthly data, and the monthly deposit insurance rate of the Indonesia Deposit Insurance Corporation (LPS) is used as the risk-free proxy. Portfolio performance is assessed using monthly and annualized Sharpe ratios, while weight stability is assessed using average weight volatility and turnover. Newey-West tests are used to evaluate whether differences across methods are statistically significant. Findings: The Ortiz approach consistently selects an optimal shrinkage intensity of zero, making its weights and performance effectively identical to the traditional Markowitz portfolio. Markowitz and Ortiz record an annualized out-of-sample Sharpe ratio of 0.0713, while Jorion records 0.0608. The statistical tests indicate that differences in out-of-sample performance and stability are not significant across the three approaches. In economic terms, the annualized Sharpe ratios of all three methods are very low (below 0.08), indicating that long-only optimization of individual Indonesian stocks delivered only marginal risk-adjusted excess returns over the sample period. Conclusion: In the Indonesian stock market setting, more complex mean-shrinkage methods do not automatically produce superior portfolio outcomes. Novelty/Originality of this article: This article provides Indonesian market evidence on the comparison between parameter-focused and decision-focused shrinkage approaches within a consistent rolling-window portfolio backtesting framework.

Forecasting Extreme Downside Risk in the Nifty 50 Index Using Extreme Value Theory

Stock market crashes are rare but can cause major problems for investors, financial institutions, and policymakers. The standard risk models used tend to assume that stock returns are normally distributed, leading to an underestimation of extreme movements in the stock market. The purpose of this study is to analyse the performance of probability distribution models developed by Extreme Value Theory (EVT) on extreme negative returns of the NIFTY 50 index to check if the prediction of stock market crashes can be improved. The study investigates the characteristics of events with large market losses and provides an estimate of the likelihood of such events based on the Peak Over Threshold (POT) and the Generalised Pareto Distribution (GPD). The results demonstrate that the NIFTY 50 returns are fat-tailed and considerably deviated from normal distribution, implying that extreme losses are not all that rare. Contrary to traditional models like Valueat- Risk (VaR), EVT models can provide more precise estimates of the probability and intensity of extreme market events, resulting in a more holistic approach to risk analysis of financial products. This study contributes to the existing literature on financial risk management in emerging markets by demonstrating the usefulness of EVT in understanding extreme market behaviour and forecasting crashes. The results have implications for investors, portfolio managers, risk managers, and policymakers, as they help them make informed investment decisions, build better risk management strategies, and make the equity market more resilient.

An Analysis of LQ45 Index Volatility Using the GARCH Model and Its Implications for Retail Investment Risk during the 2020-2025 Period

Portfolio Optimization and Risk Estimation of LQ45 Mining Stock Using The ARIMA-GARCH-EVT-COPULA Hybrid Model as Alternative Pension Fund Investment

Economic uncertainty and high commodity market volatility demand more accurate pension fund investment risk management. This study aims to measure risk and determine the optimal portfolio of LQ45 mining stocks as an alternative pension fund investment instrument using a hybrid GARCH-EVT-Copula approach. The data used are daily log returns of ITMG, ADRO, and PTBA stocks for the period June 1, 2020, to June 30, 2025. The ARIMA-GARCH model is used to capture volatility dynamics, while extreme risks are modeled using the EVT approach. Dependencies between stocks are analyzed using the best copula model and Monte Carlo simulations to produce VaR and ES estimates which are then validated using Backtesting. The results show that the best model for ITMG stocks is ARMA(0,0)-GARCH(1,1), for ADRO stocks it has an ARMA(1,1)-GARCH(1,1) model, and for PTBA stocks it has an ARMA(0,1)-GARCH(0,1) model. Based on the EVT estimation, ITMG and ADRO stock have positive GPD shape parameters, indicating a sfat-tailed distribution and a higher potential for extreme risk. In contrast, PTBA stock have negative shape parameters, indicating a limited tail distribution so that extreme risk is relatively more controlled. The scale parameter value also confirms that PTBA's extreme fluctuations are more stable than other stock. The portfolio dependency structure can be modeled using the best copula model, namely the Gumbel Copula, the optimization results give portfolio A a weight of 62.11456% for ITMG stock and 37.88544% for ADRO stock, portfolio B is 19.93126% for ITMG stock and 80.06874% for PTBA stock, while portfolio C is 8.668356% for ADRO stock and 91.33164% for PTBA stock. The results also show that the estimated VaR values ​​obtained are valid at all confidence levels, and the optimal portfolio tends to place PTBA and ITMG stock as dominant stocks to reduce the total portfolio risk. Thus, the ARIMA-GARCH-EVT-Copula approach is proven to be effective in modeling extreme risks and dependency structures between stocks, and can provide a strong basis for making long-term investment decisions for pension fund management.

An Empirical Study of Robust Portfolios Based on Statistical Noise Reduction and Regularization Constraints

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.