write conclusion for master thesis: 1.	Multivariate analysis

1.1.	Introduction

In today’s increasingly complex and competitive business environment, understanding the multifaceted relationships between various financial and non-financial metrics is crucial for informed decision-making. Multivariate analysis offers a robust framework for examining such intricate dynamics, allowing researchers and professionals to simultaneously consider multiple variables and their interdependencies. This analytical approach not only provides deeper insights into the underlying patterns but also enhances the predictive accuracy of the models.
The objective of this study is to employ multivariate analysis to explore and quantify the determinants impacting a critical financial measure, PD2023 (presumably a performance metric for the year 2023). By analyzing a comprehensive dataset that includes both traditional financial metrics and environmental performance indicators, this study aims to identify key determinants and understand their relationships with PD2023. Specifically, the analysis will focus on the following:
1. Control Variables: Previous year’s performance (PD2022), firm size (size_2023), leverage (LV_2023), return on assets (ROA_2023), capital expenditure (CAPEX_2023), and other control variables considered traditionally influential in financial performance analysis.
2. Physical Risk: Composite scores at four scenarios (low, medium, medium-high, and high levels of physical risk) across three time horizons: 2030, 2040, and 2050, to assess how varying physical risks influence PD2023.
3. Environmental Performance: Absolute emissions (LN_EMISIONES_2022) and relative emissions (LN_EMISSIONSREL_2022). These variables are vital given the increasing regulatory scrutiny and stakeholder interest in corporate sustainability practices.
4. Environmental Initiatives (ENV_INV_INI_2022) and Compensation for Sustainability (COMP_SUST_2022): These variables to capture the impact of companies’ proactive environmental actions and sustainability-related compensation practices on PD2023.
1.1.1. Hypotheses and Analytical Approach
The hypotheses driving this study are centered around the anticipated impact of financial metrics and environmental performance on PD2023:
- H1: Control variables such as PD2022, size_2023, LV_2023, ROA_2023, and CAPEX_2023 significantly influence PD2023.
- H2: Physical risk levels (low, medium, medium-high, high) in different time horizons (2030, 2040, 2050) have a significant impact on PD2023.
- H3: Emissions and environmental actions significantly influence PD2023, with potential differential effects based on the company’s environmental responsibility.
To test these hypotheses, this study estimates a series of twelve multivariate regression models. The models vary in complexity, with some focusing solely on financial metrics and others incorporating emission variables. This approach enables the identification of consistent patterns and robust relationships, facilitating a nuanced understanding of how different factors contribute to financial performance.
1.2.	Estimated models
1.2.1.	General Model with Control variables:
Interpretation:
1. Intercept: The intercept is statistically significant in Models 1, 2, and 3, indicating baseline factors affecting PD2023 that are not captured by the included variables, suggesting that while the chosen variables explain a substantial part of PD2023’s variability, other influential factors might be omitted.
2. PD2022: The high significance and positive coefficients across all models emphasize the strong continuity in performance metrics from year to year, making PD2022 a critical predictor as firms performing well in 2022 are likely to sustain this performance in 2023.
3. size_2023: Negative coefficients suggest that larger firms tend to perform worse on PD2023, with consistent significance across models underscoring the robustness of this finding, indicating that larger firms may face scalability challenges or more rigorous scrutiny.
4. BTM_2023: Positive coefficients for the book-to-market ratio indicate firms with higher book value relative to market value see better PD2023 performance, suggesting that undervalued firms or firms with solid fundamentals but lower market valuation may experience better financial outcomes.
5. LV_2023: Positive coefficients indicate that higher leverage (more debt) is associated with higher PD2023, reflecting more aggressive growth strategies or higher risk-taking behavior leading to higher returns, aligning with the idea that debt-financed investments may drive better short-term performance.
6. ROA_2023: The negative relationship suggests that higher return on assets, indicative of higher profitability, correlates inversely with PD2023, which could signal differing accounting practices or prioritization of balance sheet strength over aggressive revenue growth.
7. Asset_turnover_2023 and CAPEX_2023: The significance of asset turnover and capital expenditure in some models illustrates their conditional importance, with CAPEX being positive and significant, suggesting that firms investing in capital improvements see better future performance.
8. R-squared Values: The R-squared values indicate a consistent explanatory power of the models, with higher values in some models suggesting a better fit and a more comprehensive explanation of the variability in PD2023.
Conclusion:
Models 3 and 4 exhibit higher explanatory power, indicating their utility in further analyses. Both models will be used to explore additional layers such as physical risk, emissions, and environmental initiatives to assess their impacts on PD2023.
1.2.2.	Model Including Physical Risk Scenarios
Interpretation:
Models with Intercept:
2030 Scenarios: For the year 2030, it is observed that companies under the LOW physical risk scenario have a lower Probability of Default (PD) compared to those under the HIGH physical risk scenario. This suggests that in the low physical risk scenario, PD is significantly reduced, which makes sense since lower risk scenarios result in lower probabilities of default.
2040 Scenarios: In the year 2040, PD appears relatively stable across different physical risk scenarios. This stability indicates that companies have effectively adapted to the varying degrees of physical risks from previous years, thereby maintaining a consistent PD regardless of the level of physical risk.
2050 Scenarios: For the year 2050, the relationship reverses, with the LOW physical risk scenarios exhibiting a higher PD than the HIGH physical risk scenarios. Economically, this is somewhat counterintuitive, as higher risk scenarios would typically lead to higher PD. However, at such long-term horizons, the economic rationale might become less straightforward due to the uncertainty and potential changes in risk management practices over time.
General Insight: Across all scenarios, it is evident that a higher composite score reduces the probability of default. This finding underscores the importance of enhancing a company’s risk management practices, indicating that as companies improve their risk scores or management strategies, their PD decreases significantly, leading to better financial outcomes and increased stability.

Models without Intercept:
In the models without intercept, the coefficients for the physical risk scenarios (e.g., LOW_30, MEDIUM_30, MEDIUMHIGH_30, and HIGH_30) become statistically insignificant. This indicates that physical risk scenarios do not significantly explain the variability in PD2023 when the intercept is excluded, highlighting the importance of baseline factors. However, in these models, it seems that PD decreases as the physical risk scenario increases.
General Insight: The significant drop in the explanatory power of physical risk variables in the absence of the intercept underscores the crucial role of baseline factors in explaining PD2023. The consistent insignificance of physical risk scenarios in models without intercept highlights the fundamental importance of including comprehensive baseline variables for precise analysis.
1.2.3.	Model Including Emissions and Environmental Actions