As investment portfolios become increasingly diversified and financial asset risks grow more complex, accurately forecasting the risk of multiple asset classes through mathematical modeling and identifying their heterogeneity has emerged as a critical topic in financial research. This study examines the volatility and tail risk of gold, crude oil, Bitcoin, and selected stock markets. Methodologically, we propose two improved Value at Risk (VaR) forecasting models that combine the autoregressive (AR) model, Exponential Generalized Autoregressive Conditional Heteroskedasticity (EGARCH) model, Extreme Value Theory (EVT), skewed heavy-tailed distributions, and a rolling window estimation approach. The model’s performance is evaluated using the Kupiec test and the Christoffersen test, both of which indicate that traditional VaR models have become inadequate under current complex risk conditions. The proposed models demonstrate superior accuracy in predicting VaR and are applicable to a wide range of financial assets. Empirical results reveal that Bitcoin and the Chinese stock market exhibit no leverage effect, indicating distinct risk profiles. Among the assets analyzed, Bitcoin and crude oil are associated with the highest levels of risk, gold with the lowest, and stock markets occupy an intermediate position. The findings offer practical implications for asset allocation and policy design.

After a period of rapid growth, China’s pharmaceutical industry is facing multiple challenges, including insufficient innovation and severe pollution. Current research on the efficiency of pharmaceutical companies in China primarily focuses on financial or innovation aspects. Therefore, a holistic approach to operational efficiency is needed. To measure the operational efficiency of pharmaceutical companies in China more accurately and holistically, while accounting for environmental pollution, this study employs a three-stage Data Envelopment Analysis (DEA) model with undesirable outputs to evaluate efficiency across five dimensions: market performance, profitability, financial risk control, innovation, and sustainability. This approach integrates financial, innovation, and sustainability indicators to provide a more industry-specific framework for efficiency measurement. Furthermore, integrating with Stochastic Frontier Analysis (SFA) allows for revealing the impact of environmental factors on efficiency. The results show that both technical efficiency (TE) and pure technical efficiency (PTE) are relatively low in the first and third stages, with significant regional disparities. After excluding environmental factors, some regions—typically economically developed areas—showed improved overall efficiency. This indicates that the local environment in these regions is not conducive to the development of pharmaceutical enterprises. The SFA results further demonstrate that investments in education and high-level talent significantly enhance efficiency, whereas pollutant emissions and per capita income reduce operational efficiency. The findings suggest that local governments should enhance the operational efficiency of pharmaceutical enterprises by investing in education, attracting skilled talent, and improving waste infrastructure. Additionally, less efficient firms are encouraged to optimize resource allocation to achieve higher efficiency.

The pharmaceutical industry plays a vital role in safeguarding public health and enhancing industrial competitiveness. However, pharmaceutical industry in China faces persistent challenges, including high pollution, insufficient innovation, and limited profit margins, which constrain its global competitiveness. The current researches on the operational efficiency were either from financial or innovation aspects-lacking a comprehensive assessment framework. Moreover, the impact of environments on efficiency relied on limited indicators and lacked in multicollinearity research. Finally, there was an absence of research on internal resource allocation affects operation efficiency. To fill this, this study aims to evaluate the current operation efficiency of the listed pharmaceutical enterprises in China from finance, innovation, and sustainability, and to reveal the influence environments on efficiency and the impact of the internal resource allocation on efficiency. To achieve these objectives, the study adopts a Three-stage Data Envelopment Analysis with undesirable outputs, integrated with Principal Component Analysis and Tobit regression, to comprehensively evaluate the operational efficiency of Chinese listed pharmaceutical enterprises over the ten-year period from 2013 to 2022 across the aforementioned three dimensions. The findings reveal generally low efficiency with significant regional disparities. North and Northwest China benefit from favorable environmental conditions, while Northeast China suffers from negative impacts. Improvements in external factors, such as innovation, living standards, labor supply, and openness level reduce costs, whereas internal uncontrollable factors, such as state-owned enterprise attributes, increase costs and suppress research and development. In terms of resource allocation, higher management expenses, and personnel allocations decrease efficiency, while increased sales expenditures and improved staff quality enhance efficiency. This study constructs a comprehensive framework for evaluating the operational efficiency and reveals the impact of external environments and internal resource allocation on efficiency. It provides empirical support for policymakers and operation managers seeking to improve the efficiency of the pharmaceutical companies.

The pharmaceutical industry is a cornerstone of national economies and plays a critical role in public health. However, China’s pharmaceutical industry faces significant challenges, including regional disparities in development. The existing research on operational efficiency evaluation primarily focuses on financial or innovation metrics, lacking a comprehensive approach. Moreover, studies on the environmental impact on operational efficiency often rely on a limited set of indicators, failing to offer a holistic understanding of how environmental factors influence efficiency. This study aims to address these gaps by comprehensively evaluating operational efficiency and analyzing the impact of broader environmental factors on efficiency. To achieve these objectives, the study employs a Three-Stage Data Envelopment Analysis method combined with Principal Component Analysis to evaluate the operational efficiency of the pharmaceutical industry across 31 provinces in China, considering both financial and innovation dimensions.The findings reveal that overall efficiency has improved annually, with regional disparities gradually narrowing. Specifically, innovation capability and innovation environment have a positive impact on operational efficiency, while living standards and openness exhibit a negative correlation. Additionally, the current environmental conditions in the northwestern region are found to be conducive to the development of the pharmaceutical industry. This study is the first to integrate three-stage data envelopment analysis with principal component analysis, constructing a comprehensive framework for analyzing the relationship between environmental factors and operational efficiency. The results provide empirical evidence for policymakers aiming to enhance the efficiency of the pharmaceutical industry.

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