Risks

20 pages, 1284 KiB

Open AccessArticle

Improving Credit Risk Assessment in Uncertain Times: Insights from IFRS 9

by Petr Jakubik and Saida Teleu

Risks 2025, 13(2), 38; https://doi.org/10.3390/risks13020038 - 19 Feb 2025

Cited by 1 | Viewed by 737

This study highlights the superior performance of Bayesian Model Averaging (BMA) in credit risk modeling under IFRS 9, particularly during economic uncertainty, such as the COVID-19 pandemic. Using granular bank-level data from Malta, spanning 2017–2023, the analysis integrates macroeconomic scenarios and sector-specific transition [...] Read more.

This study highlights the superior performance of Bayesian Model Averaging (BMA) in credit risk modeling under IFRS 9, particularly during economic uncertainty, such as the COVID-19 pandemic. Using granular bank-level data from Malta, spanning 2017–2023, the analysis integrates macroeconomic scenarios and sector-specific transition matrices to assess credit risk dynamics. Key findings demonstrate BMA’s ability to outperform Single-Equation Models (SEM) in predictive accuracy, robustness, and adaptability. The results emphasize BMA’s resilience to structural economic changes, making it a critical tool for regulatory stress testing and provisioning in small open economies highly exposed to external shocks. This work underscores the importance of forward-looking, flexible frameworks for credit risk management and policy decisions. Full article

(This article belongs to the Special Issue Innovative Quantitative Methods for Financial Risk Management)

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27 pages, 974 KiB

Open AccessArticle

Longevity Risk and Annuitisation Decisions in the Absence of Special-Rate Life Annuities

by Jorge de Andrés-Sánchez and Laura González-Vila Puchades

Risks 2025, 13(2), 37; https://doi.org/10.3390/risks13020037 - 19 Feb 2025

Viewed by 425

Abstract

Longevity risk affecting older adults can be transferred to the insurance market by purchasing a lifetime annuity. Special-rate life annuities, which are priced, among other factors, on the basis of health and lifestyle factors, go beyond traditional considerations of age and sex by [...] Read more.

Longevity risk affecting older adults can be transferred to the insurance market by purchasing a lifetime annuity. Special-rate life annuities, which are priced, among other factors, on the basis of health and lifestyle factors, go beyond traditional considerations of age and sex by using modified mortality tables. However, they are not available in many countries. In regions where life annuities are priced solely via standard mortality tables, retirees with below-average life expectancy may face unfair pricing. This study aims to quantify this actuarial unfairness and proposes an alternative annuitisation strategy for these retirees. The strategy allows them to transfer longevity risk by acquiring a life annuity on the basis of their actual mortality probabilities, thereby mitigating actuarial inequities. Additionally, the paper examines how tax incentives can exacerbate actuarial unfairness and, specifically for Spanish tax regulations, compares different alternatives under two scenarios related to the sources used for purchasing life annuities. Full article

(This article belongs to the Special Issue Applied Financial and Actuarial Risk Analytics)

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18 pages, 378 KiB

Open AccessArticle

Insurers’ Loss Portfolio Similarity and Climate Risk Insurance Cost: A Spatial Analysis of US Homeowners Insurance Market

by Tao Sun

Risks 2025, 13(2), 36; https://doi.org/10.3390/risks13020036 - 18 Feb 2025

Viewed by 365

Abstract

This study examines the geographical spillover of the state-level average homeowners insurance cost for 48 US contiguous states. We estimate a panel spatial Durbin model with state and year fixed effect for data between 2001 and 2018. We found a significant positive spillover [...] Read more.

This study examines the geographical spillover of the state-level average homeowners insurance cost for 48 US contiguous states. We estimate a panel spatial Durbin model with state and year fixed effect for data between 2001 and 2018. We found a significant positive spillover of average homeowners insurance cost as indicated by a large spatial autoregressive coefficient in the baseline model. We also found a positive relationship between underwriters’ loss portfolio similarity and the average homeowners insurance cost. We conduct several robustness tests and show that the baseline results are robust if against potential biases due to heterogenous state-level insurance regulation, an alternatively defined spatial weighting matrix, and the usage of average homeowners cost for the dominant policy form (the HO3 policy). We also adopt the generalized spatial two-step least squares to mitigate the bias due to endogenous explanatory variables and find that the results are consistent with these reported for the baseline model. Full article

(This article belongs to the Special Issue Risk Analysis in Insurance and Pensions)

25 pages, 572 KiB

Open AccessArticle

Uncertainty in Pricing and Risk Measurement of Survivor Contracts

by Kenrick Raymond So, Stephanie Claire Cruz, Elias Antonio Marcella, Jeric Briones and Len Patrick Dominic Garces

Risks 2025, 13(2), 35; https://doi.org/10.3390/risks13020035 - 18 Feb 2025

Viewed by 486

Abstract

As life expectancy increases, pension plans face growing longevity risk. Standardized longevity-linked securities such as survivor contracts allow pension plans to transfer this risk to capital markets. However, more consensus is needed on the appropriate mortality model and premium principle to price these [...] Read more.

As life expectancy increases, pension plans face growing longevity risk. Standardized longevity-linked securities such as survivor contracts allow pension plans to transfer this risk to capital markets. However, more consensus is needed on the appropriate mortality model and premium principle to price these contracts. This paper investigates the impact of the mortality model and premium principle choice on the pricing, risk measurement, and modeling of survivor contracts. We present a framework for evaluating risk measures associated with survivor contracts, specifically survivor forwards (S-forward) and survivor swaps (S-swaps). We analyze how the mortality model and premium principle assumptions affect pricing and risk measures (value-at-risk and expected shortfall). Four mortality models (Lee–Carter, Renshaw–Haberman, Cairns–Blake–Dowd, and M6) and eight premium principles (Wang, proportional hazard, dual power, Gini, exponential, standard deviation, variance, and median absolute deviation) are considered. Our analysis highlights the need to refine mortality models and premium principles to enhance pricing accuracy and risk management. We also suggest regulators and practitioners incorporate expected shortfall alongside value-at-risk to capture tail risks and improve capital allocation. Full article

(This article belongs to the Special Issue Applied Financial and Actuarial Risk Analytics)

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14 pages, 364 KiB

Open AccessArticle

The Impact of Cyber Governance Quality on Dividend Policy in Mitigating Cybersecurity Breaches

by Manar Al-Mohareb

Risks 2025, 13(2), 34; https://doi.org/10.3390/risks13020034 - 17 Feb 2025

Viewed by 555

Abstract

This study investigates the relationship between cyber risks and dividend policy, as well as how boards, as a governance mechanism, affect the dividend policy under cyber risk. This study collected firm-level financing, corporate governance, and control variables from the Bloomberg database during the [...] Read more.

This study investigates the relationship between cyber risks and dividend policy, as well as how boards, as a governance mechanism, affect the dividend policy under cyber risk. This study collected firm-level financing, corporate governance, and control variables from the Bloomberg database during the period 2013–2022. This paper measures of cyber risk through publicly available corporate disclosures on Form 10-K. The findings confirmed that cyber risks significantly impact dividend policy by posing challenges to corporate technical communication and financial transparency. Effective boards play a critical role in guiding companies toward governance strategies that enhance dividend policy and improve cybersecurity. This study involves policy and practical implications, where research findings suggest the need to strengthen regulatory frameworks that encourage the adoption of strong governance practices and advanced cybersecurity practices within companies. On the practical level, companies should adopt a proactive approach to managing cyber risks by enhancing investments in this area and developing flexible dividend policies. Full article

18 pages, 586 KiB

Open AccessFeature PaperArticle

A Bivariate Model for Correlated and Mixed Outcomes: A Case Study on the Simultaneous Prediction of Credit Risk and Profitability of Peer-to-Peer (P2P) Loans

by Yan Wang, Xuelei Sherry Ni, Huan Ni and Sanad Biswas

Risks 2025, 13(2), 33; https://doi.org/10.3390/risks13020033 - 12 Feb 2025

Viewed by 672

Abstract

In the peer-to-peer (P2P) lending market, current studies focus on two categories of approaches to evaluate the loans, thus providing investment suggestions to the investors: credit scoring (i.e., predicting the credit risk) and profit scoring (i.e., predicting the profitability). However, relying on a [...] Read more.

In the peer-to-peer (P2P) lending market, current studies focus on two categories of approaches to evaluate the loans, thus providing investment suggestions to the investors: credit scoring (i.e., predicting the credit risk) and profit scoring (i.e., predicting the profitability). However, relying on a single scoring approach may bias the loan evaluation conclusion. In this paper, we propose a bivariate model based on the integration of two scoring approaches. We first formulate the loan evaluation task as a multi-target problem, in which loan_status (i.e., default or not default) is used as the discrete outcome for the credit risk measure while the annualized rate of return (ARR) is used as the continuous outcome for the profitability measure. Then to solve the multi-target problem, we design a novel loss function based on the assumption that the discrete outcome follows a Bernoulli distribution, and the continuous outcome is normally distributed conditional on the discrete output. The effectiveness of the proposed model is examined using the real-world P2P data from the Lending Club. Results indicate that our approach outperforms the sole scoring methods by identifying loans with higher profit and lower default risk. Therefore, the proposed method can serve as an alternative for loan evaluation. Full article

(This article belongs to the Special Issue Computational Methods and Models in the Financial Risk Management Process)

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19 pages, 974 KiB

Open AccessArticle

The Saint Petersburg Paradox and Its Solution

by Claudio Mattalia

Risks 2025, 13(2), 32; https://doi.org/10.3390/risks13020032 - 11 Feb 2025

Viewed by 629

Abstract

This article describes the main historical facts concerning the Saint Petersburg paradox, the most important solutions proposed thus far, and the results of new experimental evidence and a simulation of the game that shed light on a solution for this paradox. The Saint [...] Read more.

This article describes the main historical facts concerning the Saint Petersburg paradox, the most important solutions proposed thus far, and the results of new experimental evidence and a simulation of the game that shed light on a solution for this paradox. The Saint Petersburg paradox has attracted the attention of important mathematicians and economists since it was first formulated 300 years ago, and it has strongly influenced the development of new concepts in the economic and social sciences. The main conclusion of this study is that the behavior of the individuals playing the game is not paradoxical at all, and the paradox is intrinsic to the game. Full article

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24 pages, 1644 KiB

Open AccessFeature PaperArticle

On GARCH and Autoregressive Stochastic Volatility Approaches for Market Calibration and Option Pricing

by Tao Pang and Yang Zhao

Risks 2025, 13(2), 31; https://doi.org/10.3390/risks13020031 - 10 Feb 2025

Viewed by 855

Abstract

In this paper, we carry out a comprehensive comparison of Gaussian generalized autoregressive conditional heteroskedasticity (GARCH) and autoregressive stochastic volatility (ARSV) models for volatility forecasting using the S&P 500 Index. In particular, we investigate their performance using the physical measure (also known as [...] Read more.

In this paper, we carry out a comprehensive comparison of Gaussian generalized autoregressive conditional heteroskedasticity (GARCH) and autoregressive stochastic volatility (ARSV) models for volatility forecasting using the S&P 500 Index. In particular, we investigate their performance using the physical measure (also known as the real-world probability measure) for risk management purposes and risk-neutral measures for derivative pricing purposes. Under the physical measure, after fitting the historical return sequence, we calculate the likelihoods and test the normality for the error terms of these two models. In addition, two robust loss functions, the MSE and QLIKE, are adopted for a comparison of the one-step-ahead volatility forecasts. The empirical results show that the ARSV(1) model outperforms the GARCH(1, 1) model in terms of the in-sample and out-of-sample performance under the physical measure. Under the risk-neutral measure, we explore the in-sample and out-of-sample average option pricing errors of the two models. The results indicate that these two models are considerably close when pricing call options, while the ARSV(1) model is significantly superior to the GARCH(1, 1) model regarding fitting and predicting put option prices. Another finding is that the implied versions of the two models, which parameterize the initial volatility, are not robust for out-of-sample option price predictions. Full article

(This article belongs to the Special Issue Valuation Risk and Asset Pricing)

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19 pages, 1583 KiB

Open AccessArticle

Retirement Readiness in the Baltics: The Roles of Financial Literacy, Product Ownership, and Advisory Confidence

by Ramona Rupeika-Apoga and Janis Priede

Risks 2025, 13(2), 30; https://doi.org/10.3390/risks13020030 - 8 Feb 2025

Viewed by 772

Abstract

This study examined the relationships between financial literacy, financial product ownership, confidence in financial advisers, and confidence in retirement readiness across Estonia, Latvia, and Lithuania. By using data from the Flash Eurobarometer 525 survey (March 2022) and applying categorical data analysis methods, including [...] Read more.

This study examined the relationships between financial literacy, financial product ownership, confidence in financial advisers, and confidence in retirement readiness across Estonia, Latvia, and Lithuania. By using data from the Flash Eurobarometer 525 survey (March 2022) and applying categorical data analysis methods, including chi-square tests and Cramér’s V, the findings revealed that a higher financial literacy and confidence in financial advisers are significantly associated with greater retirement preparedness. The ownership of financial products, particularly among active investors, is also strongly correlated with improved retirement outcomes. These results highlight the importance of financial education, accessible advisory services, and policies promoting financial literacy and product ownership to mitigate retirement risks and enhance financial security in the Baltic region. Full article

(This article belongs to the Special Issue Risk Analysis in Insurance and Pensions)

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24 pages, 576 KiB

Open AccessArticle

Tax Risk and Cost of Debt: The Role of Tax Avoidance—Evidence from the Iraqi Stock Market

by Hussen Amran Naji Al-Refiay, Jasim Idan Barrak, Asif Isam Elaibi Al-Tameemi and Mohammadreza Pazhohi

Risks 2025, 13(2), 29; https://doi.org/10.3390/risks13020029 - 7 Feb 2025

Viewed by 932

Abstract

Taxes represent a significant expense for many companies, prompting a strong incentive to minimize tax liabilities through strategies known as tax avoidance. This research explores the impact of tax avoidance and tax risk disclosure on the cost of debt among companies listed on [...] Read more.

Taxes represent a significant expense for many companies, prompting a strong incentive to minimize tax liabilities through strategies known as tax avoidance. This research explores the impact of tax avoidance and tax risk disclosure on the cost of debt among companies listed on the Iraqi Stock Exchange. This study analyzes data from 33 firms from 2016 to 2021, employing multivariate linear regression and the generalized least squares (GLS) model to test the hypotheses. The findings indicate that tax avoidance significantly and positively affects the cost of debt, suggesting that firms engaging in tax avoidance may experience greater borrowing costs. Additionally, tax risk disclosure is shown to directly and significantly influence the cost of debt. Importantly, this study reveals that tax risk disclosure negatively moderates the relationship between accrual tax avoidance and the cost of debt, indicating that higher tax risk disclosure can reduce uncertainties associated with tax avoidance, reducing borrowing costs. These results imply that tax avoidance and its influence on corporate debt levels can affect the overall risk profile of a country's financial system. Understanding this relationship is crucial for governance measures aimed at managing tax risks effectively. Given the limited research in this area, this study contributes to the literature by examining how tax risk and tax avoidance relate to the cost of debt in an emerging market context. Full article

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25 pages, 521 KiB

Open AccessFeature PaperArticle

Efficient Positive Semidefinite Matrix Approximation by Iterative Optimisations and Gradient Descent Method

by Vali Asimit, Runshi Wang, Feng Zhou and Rui Zhu

Risks 2025, 13(2), 28; https://doi.org/10.3390/risks13020028 - 7 Feb 2025

Viewed by 560

Abstract

We devise two algorithms for approximating solutions of PSDisation, a problem in actuarial science and finance, to find the nearest valid correlation matrix that is positive semidefinite (PSD). The first method converts the PSDisation problem with a positive semidefinite constraint and other linear [...] Read more.

We devise two algorithms for approximating solutions of PSDisation, a problem in actuarial science and finance, to find the nearest valid correlation matrix that is positive semidefinite (PSD). The first method converts the PSDisation problem with a positive semidefinite constraint and other linear constraints into iterative Linear Programmings (LPs) or Quadratic Programmings (QPs). The LPs or QPs in our formulation give an upper bound of the optimal solution of the original problem, which can be improved during each iteration. The biggest advantage of this iterative method is its great flexibility when working with different choices of norms or with user-defined constraints. Second, a gradient descent method is designed specifically for PSDisation under the Frobenius norm to measure how close the two metrices are. Experiments on randomly generated data show that this method enjoys better resilience to noise while maintaining good accuracy. For example, in our experiments with noised data, the iterative quadratic programming algorithm performs best in more than 41% to 67% of the samples when the standard deviation of noise is 0.02, and the gradient descent method performs best in more than 70% of the samples when the standard deviation of noise is 0.2. Examples of applications in finance, as well as in the machine learning field, are given. Computational results are presented followed by discussion on future improvements. Full article

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19 pages, 476 KiB

Open AccessArticle

On the Curvature of the Bachelier Implied Volatility

by Elisa Alòs and David García-Lorite

Risks 2025, 13(2), 27; https://doi.org/10.3390/risks13020027 - 3 Feb 2025

Viewed by 932

Abstract

Our aim in this paper is to analytically compute the at-the-money second derivative of the Bachelier implied volatility curve as a function of the strike price for correlated stochastic volatility models. We also obtain an expression for the short-term limit of this second [...] Read more.

Our aim in this paper is to analytically compute the at-the-money second derivative of the Bachelier implied volatility curve as a function of the strike price for correlated stochastic volatility models. We also obtain an expression for the short-term limit of this second derivative in terms of the first and second Malliavin derivatives of the volatility process and the correlation parameter. Our analysis does not need the volatility to be Markovian and can be applied to the case of fractional volatility models, both with

H < 1 / 2

and

H > 1 / 2 .

More precisely, we start our analysis with an adequate decomposition formula of the curvature as the curvature in the uncorrelated case (where the Brownian motions describing asset price and volatility dynamics are uncorrelated) plus a term due to the correlation. Then, we compute the curvature in the uncorrelated case via Malliavin calculus. Finally, we add the corresponding correlation correction and we take limits as the time to maturity tends to zero. The presented results can be an interesting tool in financial modeling and in the computation of the corresponding Greeks. Moreover, they allow us to obtain general formulas that can be applied to a wide class of models. Finally, they provide us with a precise interpretation of the impact of the Hurst parameter H on this curvature. Full article

(This article belongs to the Special Issue Integrating New Risks into Traditional Risk Management)

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33 pages, 2866 KiB

Open AccessArticle

Exploring Corporate Capital Structure and Overleveraging in the Pharmaceutical Industry

by Samar Issa and Hussein Issa

Risks 2025, 13(2), 26; https://doi.org/10.3390/risks13020026 - 2 Feb 2025

Viewed by 1209

Abstract

This paper applies an empirical model of corporate capital structure, optimal debt, and overleveraging to estimate overleveraging measured as the difference between actual and optimal debt. Estimated using a sample of the twenty largest pharmaceutical firms, covering the time span from 2000 to [...] Read more.

This paper applies an empirical model of corporate capital structure, optimal debt, and overleveraging to estimate overleveraging measured as the difference between actual and optimal debt. Estimated using a sample of the twenty largest pharmaceutical firms, covering the time span from 2000 to 2018, the model sheds light on an industry-specific default risk. The analysis presented in this paper reveals a concerning trend in the pharmaceutical industry, with corporate excess debt steadily increasing over the past two decades, particularly peaking during the 2008 crisis and after 2013. These findings underscore the critical role of excess debt in exacerbating financial instability and highlight the pharmaceutical sector’s unique challenges, including high R&D intensity and regulatory pressures. By quantifying overleveraging and linking it to financial risk, the paper offers valuable policy implications, emphasizing the need for proactive management of optimal debt levels to mitigate default risks and enhance macroeconomic resilience. Full article

(This article belongs to the Special Issue Risk Analysis in Financial Crisis and Stock Market)

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25 pages, 937 KiB

Open AccessArticle

An IID Test for Functional Time Series with Applications to High-Frequency VIX Index Data

by Xin Huang, Han Lin Shang and Tak Kuen Siu

Risks 2025, 13(2), 25; https://doi.org/10.3390/risks13020025 - 30 Jan 2025

Viewed by 640

Abstract

To address a key issue in functional time series analysis on testing the randomness of an observed series, we propose an IID test for functional time series by generalizing the Brock–Dechert–Scheinkman (BDS) test, which is commonly used for testing nonlinear independence. Similarly to [...] Read more.

To address a key issue in functional time series analysis on testing the randomness of an observed series, we propose an IID test for functional time series by generalizing the Brock–Dechert–Scheinkman (BDS) test, which is commonly used for testing nonlinear independence. Similarly to the BDS test, the proposed functional BDS test can be used to evaluate the suitability of prediction models as a model specification test and to detect nonlinear structures as a nonlinearity test. We establish asymptotic results for the test statistic of the proposed test in a generic separate Hilbert space and show that it enjoys the same asymptotic properties as those for the univariate case. To address the practical issue of selecting hyperparameters, we provide the recommended range of the hyperparameters. Using empirical data on the VIX index, empirical studies are conducted that feature the applications of the proposed test to evaluate the adequacy of the fAR

(1)

and fGARCH

(1, 1)

models in fitting the daily curves of cumulative intraday returns (CIDR) of the index. The results reveal that the proposed test remedies some shortcomings of the existing independence test. Specifically, the proposed test can detect nonlinear temporal structures, while the existing test can only detect linear structures. Full article

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72 pages, 1225 KiB

Open AccessArticle

Sectoral Counter-Cyclical Approach to Financial Risk Management Based on CSR for Sustainable Development of Companies

by Uran Zh. Ergeshbaev, Dilobar M. Mavlyanova, Yulia G. Leskova, Elena G. Popkova and Elena S. Petrenko

Risks 2025, 13(2), 24; https://doi.org/10.3390/risks13020024 - 30 Jan 2025

Viewed by 1184

Abstract

This research determines the contribution of Corporate Social Responsibility (CSR) to reducing financial risks and, consequently, to the sustainable development of companies in different sectors of the economy and at different phases of the economic cycle (using Russia as an example). The informational [...] Read more.

This research determines the contribution of Corporate Social Responsibility (CSR) to reducing financial risks and, consequently, to the sustainable development of companies in different sectors of the economy and at different phases of the economic cycle (using Russia as an example). The informational and empirical base comprises data on the dynamics of stock prices of sectoral indices of the Moscow Exchange’s total return “gross” (in Russian rubles): oil and gas, electricity, telecommunications, metals and mining, finance, consumer sector (retail trade), chemicals and petrochemicals, and transportation, as well as the “Responsibility and Openness” index in 2019 (before the crises), in 2020 (COVID-19 crisis), 2022 (sanction crisis), and 2024 (Russia’s economic growth). Economic–mathematical models, compiled through regression analysis, showed that the contribution of CSR to reducing the financial risks of companies is highly differentiated among economic sectors and phases of the economic cycle. The research presents a new sectoral perspective on counter-cyclical management of the financial risks of companies through CSR, enabling a deeper study of the cause-and-effect relationships of such management for the sustainable development of companies from different economic sectors. This is the theoretical significance of this research, its novelty, and its contribution to the literature. The research has practical significance, revealing previously unknown best practices for the sustainable development of companies from different economic sectors of Russia across different phases of the economic cycle. The systematized experience will be useful for forecasting the financial risks of companies during future economic crises in Russia and improving the practice of planning and organizing the financial risk management of Russian companies through CSR. The authors’ conclusions have managerial significance because they will help enhance the flexibility and efficiency of corporate financial risk management by considering the sectoral specifics and cyclical nature of the economy when implementing CSR. Full article

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19 pages, 4067 KiB

Open AccessArticle

Redesigning Home Reversion Products to Empower Retirement for Singapore’s Public Flat Owners

by Koon Shing Kwong, Jing Rong Goh, Jordan Jie Xin Lee and Ting Lin Collin Chua

Risks 2025, 13(2), 23; https://doi.org/10.3390/risks13020023 - 30 Jan 2025

Viewed by 653

Abstract

This paper introduces an innovative sell-type home reversion product aimed at monetizing Singapore’s public flats, serving as a new alternative to the existing Singapore Lease Buyback Scheme (LBS). This new product not only retains the LBS’s guaranteed period of residence in the property [...] Read more.

This paper introduces an innovative sell-type home reversion product aimed at monetizing Singapore’s public flats, serving as a new alternative to the existing Singapore Lease Buyback Scheme (LBS). This new product not only retains the LBS’s guaranteed period of residence in the property along with life annuity incomes but also enhances the product features to meet specific homeowner needs, including the ability to age in place, flexibility in retaining part of the property, options for bequests, and guaranteed principal return. By incorporating these additional features, the new product seeks to stimulate greater demand for monetizing public flats among asset-rich but cash-poor homeowners. An actuarial pricing model is developed to establish a transparent and fair framework for justifying the cost of each product feature. Additionally, we present a cost–benefit analysis from both the provider and consumer perspectives to highlight the major contributions of the new product when compared to the LBS. Full article

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27 pages, 3247 KiB

Open AccessArticle

A Different Risk–Return Relationship

by Aydin Selim Oksoy, Matthew R. Farrell and Shaomin Li

Risks 2025, 13(2), 22; https://doi.org/10.3390/risks13020022 - 27 Jan 2025

Viewed by 833

Abstract

We challenge the widely accepted premise that the valuation of an early-stage firm is simply the capital invested (USD) divided by the equity received (%). Instead, we argue that this calculation determines the break-even point for the investor; for example, investing USD 1.0 [...] Read more.

We challenge the widely accepted premise that the valuation of an early-stage firm is simply the capital invested (USD) divided by the equity received (%). Instead, we argue that this calculation determines the break-even point for the investor; for example, investing USD 1.0 in exchange for a 10% equity sets a firm-level free cash flow target of USD 10.0, resulting in a 0% return for the investor. The design of our study is that of a descriptive analysis of the phenomenon, based on three assumptions: that angel investing is a two-issue negotiation, that negotiation positions are communicated sequentially from capital to equity, and that the capital is fixed to a strategic trajectory. We note that when pausing the negotiation once a strategic trajectory (and thus capital) has been defined, utilizing the break-even point as the main reference point provides a structure that can serve as a guiding barometer for negotiators, as they evaluate their options across the full range of equity greater than 0% and less than 100%. We draw attention to the diminishing benefit of the marginal equity percentage point [diminishing at a rate of (−1/x²)] for the investor to break even on their investment. This relationship tracks to the equation [value = 1/equity], which presents the full option set for any offer, once the capital is determined. Our study provides the practitioner with the subtle benefit of situational awareness and the scholar with a logical foundation for future research. Full article

(This article belongs to the Special Issue Risk Management for Capital Markets)

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23 pages, 1263 KiB

Open AccessArticle

Turning Points in the Core–Periphery Displacement of Systemic Risk in the Eurozone: Constrained Weighted Compositional Clustering

by Anna Maria Fiori and Germà Coenders

Risks 2025, 13(2), 21; https://doi.org/10.3390/risks13020021 - 24 Jan 2025

Viewed by 823

Abstract

Investigating how systemic risk originates and spreads across the financial system poses an inherently compositional question, i.e., a question concerning the joint distribution of relative risk share across several interdependent contributors. To address this question, we propose a weighted compositional clustering approach aimed [...] Read more.

Investigating how systemic risk originates and spreads across the financial system poses an inherently compositional question, i.e., a question concerning the joint distribution of relative risk share across several interdependent contributors. To address this question, we propose a weighted compositional clustering approach aimed at tackling the trajectories and turning points of systemic risk in the Eurozone, from both a chronological and a geographical perspective. The cluster profiles emerging from our analysis indicate a progressive shift from Northern Europe towards the Euro-Mediterranean region in the coordinate center of systemic risk compositions. This shift matures as the outcome of complex interactions between core and peripheral EU countries that compositional methods have the merit of capturing and unifying in a self-contained multivariate framework. Full article

(This article belongs to the Special Issue Systemic Risk in the Financial System: New Developments and Challenges)

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16 pages, 1521 KiB

Open AccessArticle

Data Mining for the Adjustment of Credit Scoring Models in Solidarity Economy Entities: A Methodology for Addressing Class Imbalances

by Ivan Mauricio Bermudez Vera, Jaime Mosquera Restrepo and Diego Fernando Manotas-Duque

Risks 2025, 13(2), 20; https://doi.org/10.3390/risks13020020 - 22 Jan 2025

Cited by 1 | Viewed by 1133

Abstract

This study addresses the quantification of credit risk in solidarity economy entities, proposing a new methodology to redefine the concept of a “default” in the frequent situations of extreme class imbalances. The objective is to develop and evaluate credit scoring models that enhance [...] Read more.

This study addresses the quantification of credit risk in solidarity economy entities, proposing a new methodology to redefine the concept of a “default” in the frequent situations of extreme class imbalances. The objective is to develop and evaluate credit scoring models that enhance risk management by incorporating internal and external data to assess default risk. Data mining techniques are applied to address class imbalances, redefining the term “default” to include external credit information and increasing the representation of the minority class. The effectiveness of machine learning and statistical models is evaluated using class-balancing methods such as under-sampling, over-sampling, and the Synthetic Minority Over-sampling Technique (SMOTE). The evaluation is based on the Balanced Accuracy metric and the holding power of the performance, ensuring a consistent predictive power of the model while avoiding overfitting. While machine learning methods can improve credit scoring, logistic regression-based models remain effective, especially when combined with class-balancing techniques. It is concluded that a balanced sample in a class size is essential to improve predictive performance. Full article

(This article belongs to the Special Issue Applied Financial and Actuarial Risk Analytics)

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24 pages, 689 KiB

Open AccessFeature PaperArticle

Modeling the Inter-Arrival Time Between Severe Storms in the United States Using Finite Mixtures

by Ilana Vinnik and Tatjana Miljkovic

Risks 2025, 13(2), 19; https://doi.org/10.3390/risks13020019 - 21 Jan 2025

Viewed by 884

Abstract

When inter-arrival times between events follow an exponential distribution, this implies a Poisson frequency of events, as both models assume events occur independently and at a constant average rate. However, these assumptions are often violated in real-insurance applications. When the rate at which [...] Read more.

When inter-arrival times between events follow an exponential distribution, this implies a Poisson frequency of events, as both models assume events occur independently and at a constant average rate. However, these assumptions are often violated in real-insurance applications. When the rate at which events occur changes over time, the exponential distribution becomes unsuitable. In this paper, we study the distribution of inter-arrival times of severe storms, which exhibit substantial variability, violating the assumption of a constant average rate. A new approach is proposed for modeling severe storm recurrence patterns using a finite mixture of log-normal distributions. This approach effectively captures both frequent, closely spaced storm events and extended quiet periods, addressing the inherent variability in inter-event durations. Parameter estimation is performed using the Expectation–Maximization algorithm, with model selection validated via the Bayesian information criterion (BIC). To complement the parametric approach, Kaplan–Meier survival analysis was employed to provide non-parametric insights into storm-free intervals. Additionally, a simulation-based framework estimates storm recurrence probabilities and assesses financial risks through probable maximum loss (PML) calculations. The proposed methodology is applied to the Billion-Dollar Weather and Climate Disasters dataset, compiled by the U.S. National Oceanic and Atmospheric Administration (NOAA). The results demonstrate the model’s effectiveness in predicting severe storm recurrence intervals, offering valuable tools for managing risk in the property and casualty insurance industry. Full article

(This article belongs to the Special Issue Advancements in Actuarial Mathematics and Insurance Risk Management)

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Risks, Volume 13, Issue 2 (February 2025) – 20 articles

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