Financial Risk Measurement Research Articles

An Optimal Three-Way Stable and Monotonic Spectrum of Bounds on Quantiles: A Spectrum of Coherent Measures of Financial Risk and Economic Inequality

A spectrum of upper bounds (Qα(X ; p) αε[0,∞] on the (largest) (1-p)-quantile Q(X;p) of an arbitrary random variable X is introduced and shown to be stable and monotonic in α, p, and X , with Q0(X ;p) = Q(X;p). If p is small enough and the distribution of X is regular enough, then Qα(X ; p) is rather close to Q(X ; p). Moreover, these quantile bounds are coherent measures of risk. Furthermore, Qα(X ; p) is the optimal value in a certain minimization problem, the minimizers in which are described in detail. This allows of a comparatively easy incorporation of these bounds into more specialized optimization problems. In finance, Q0(X;p) and Q1(X ; p) are known as the value at risk (VaR) and the conditional value at risk (CVaR). The bounds Qα(X ; p) can also be used as measures of economic inequality. The spectrum parameter α plays the role of an index of sensitivity to risk. The problems of the effective computation of the bounds are considered. Various other related results are obtained.

Extended robust support vector machine based on financial risk minimization.

Financial risk measures have been used recently in machine learning. For example, ν-support vector machine ν-SVM) minimizes the conditional value at risk (CVaR) of margin distribution. The measure is popular in finance because of the subadditivity property, but it is very sensitive to a few outliers in the tail of the distribution. We propose a new classification method, extended robust SVM (ER-SVM), which minimizes an intermediate risk measure between the CVaR and value at risk (VaR) by expecting that the resulting model becomes less sensitive than ν-SVM to outliers. We can regard ER-SVM as an extension of robust SVM, which uses a truncated hinge loss. Numerical experiments imply the ER-SVM's possibility of achieving a better prediction performance with proper parameter setting.

A HYBRID MULTIPLE CRITERIA DECISION-MAKING MODEL FOR INVESTMENT DECISION MAKING

Investments are accompanied by risks. How investors choose the right investment tools to assist in the selection of investment targets is a topic worth exploring. Therefore, this study aimed to develop an investment decision-making process to deal with this issue. Firstly, we proposed a globalized modified grey relational analysis to select the representative indicators including the financial indicators and risk measurement indicators. Then we combined financial and risk evaluation indicators, and divided companies into low, moderate and high-risk groups through the grey clustering analysis. Finally, Vlse Kriterijumska Optimizacija Kompromisno Resenje (VIKOR) combined with the grey entropy weighting method was applied to business performance evaluation and sorting of each grouping. In order to verify this study, a combination of 21 financial ratios and four risk indicators was utilized in order to verify the evaluation and decision-making process in the operating performance of 62 listed opto-electronics companies in Taiwan. The results of ranking the operating performance for each group can be made available to company managers as a reference in order to enhance competitiveness and business performance. The results can also be used as the basis for decision-making to aid investors who are facing many investment portfolios.

Returns of Dividend vs. Non-Dividend-Paying Stocks and Their Relations With Financial Distress and Market Risk Measures

This study investigates whether risks and returns of dividend-paying stocks differ from non-dividend-paying stocks. It also examines the financial health and market risk exposure of dividend vs. non-dividend paying firms. The descriptive statistics show that average risks and return of non-dividend paying stocks are higher than dividend-paying stocks. However, tests of equality of means and variances fail to support the conventional view that dividend paying stocks’ returns and risks differ from non-dividend paying stocks over time. The Altman financial stress test shows that the average Z-score of non-dividend-paying stocks is higher and is more volatile than non-dividend paying firms. However, the results strongly reject the argument that dividend and non-dividend paying firms are equally exposed to financial risks. Furthermore, the tests of equality of mean and variance of market risk of dividend paying vs. non-dividend paying stocks are strongly rejected.

Using financial risk measures for analyzing generalization performance of machine learning models

We propose a unified machine learning model (UMLM) for two-class classification, regression and outlier (or novelty) detection via a robust optimization approach. The model embraces various machine learning models such as support vector machine-based and minimax probability machine-based classification and regression models. The unified framework makes it possible to compare and contrast existing learning models and to explain their differences and similarities.In this paper, after relating existing learning models to UMLM, we show some theoretical properties for UMLM. Concretely, we show an interpretation of UMLM as minimizing a well-known financial risk measure (worst-case value-at risk (VaR) or conditional VaR), derive generalization bounds for UMLM using such a risk measure, and prove that solving problems of UMLM leads to estimators with the minimized generalization bounds. Those theoretical properties are applicable to related existing learning models.

Financial Risk Measurement and Joint Extreme Events: The Normal, Student-T, and Mixture of Normals

We all know that the normal distribution does a poor job of representing the tails of the distribution for financial returns or P&L in the univariate case - observed distributions have fat tails. What receives less attention is that for a joint normal distribution events in the tails look as if they are independent: Extreme events will not occur together, whatever the correlation (except for the boundary cases of ±1). This has important implications because it is precisely the occurrence of joint losses in multiple assets that are most important for generating large overall losses. And it is generally accepted that, empirically, financial assets do exhibit joint extreme behavior.

Is the Distribution of Financial Returns Symmetric? Empirical Evidence from the International Exchange Market

The presence of asymmetry in the distribution of financial returns is an important factor that should be considered in optimal portfolio allocation and is also closely related to the recognition and measurement of financial risk. This study adopts a method based on bootstrapping proposed by Lisi (2007) to test asymmetry in the daily return distributions of eight major global exchange rates. The results show that all returns except for the daily return distribution of the CNY/USD rate, which has an evident asymmetry, can be considered symmetric at a high confidence level. In addition, the results also affirm that test methods based on the coefficient of skewness are not suitable for auto-correlative financial return series. This study provides new information relevant to asymmetry evaluation in the marginal distribution of financial time series and the study of the distribution properties of price volatility in the international exchange market.

Financial risk perceptions: a consciousness perspective

Purpose– The purpose of this paper is to investigate the implications of human consciousness relative to financial risk perceptions.Design/methodology/approach– After conceptually identifying that risk perceptions qualify as a Qualia, survey data are gathered from investment experts to clarify the implications.Findings– Financial risk perceptions are Qualia and as such should have a strong affective influence on risk perceptions. This suggests that aggregate market measures of financial risk may be difficult to obtain and utilize.Research limitations/implications– Sample size could be larger and more complete implications need to be investigated. Sample unlikely to exhibit significant bias.Practical implications– Going to be difficult to devise aggregate measures of financial risk across market participants.Social implications– Risk is going to be heavily affective in orientation and interpersonal Trust is a financial risk attribute.Originality/value– Is quite original as the author has never seen another paper look to the implications of consciousness for financial risk perceptions or even Trust. Breaks new ground!

Is the Distribution of Returns Symmetric?—Empirical Evidence from Agricultural Futures Market of China

The presence of asymmetry in the distribution of financial returns is not only an important factor which should be considered in the process of optimal portfolio allocation, but also one of the variables having close relationship with the recognition and measurement of financial risk. This paper adopts a method based on bootstrap to measure asymmetry in the distribution of financial returns, as proposed by Lisi (2007). Results of asymmetry test on the distribution of four representative price index series coming from agricultural futures market in China are presented, and the four indexes are hard wheat index, cotton index, sugar index and soybean oil index. The results indicate that, except for the distribution of soybean oil index return which has an evident asymmetry characteristic, the other three ones all can be considered symmetric at a high confidence level. This paper contributes to asymmetry evaluation in the marginal distribution of financial returns, as well as the study of distribution characteristics in agricultural futures index returns of China, in the way of providing new empirical evidence.

From the Editors

From the Editors

Retracted: Sublinear Expectation Nonlinear Regression for the Financial Risk Measurement and Management

Retracted: Sublinear Expectation Nonlinear Regression for the Financial Risk Measurement and Management

Nowcasting and forecasting global financial sector stress and credit market dislocation

We introduce a new international model for the systematic distress risk of financial institutions from the US, the European Union, and the Asia-Pacific region. Our proposed dynamic factor model can be represented as a nonlinear, non-Gaussian state space model with parameters that we estimate using Monte Carlo maximum likelihood methods. We construct measures of global financial sector risk and of credit market dislocation, where credit market dislocation is defined as a significant and persistent decoupling of the credit risk cycle from macro-financial fundamentals in one or more regions. We show that, in the past, such decoupling has preceded episodes of systemic financial distress. Our new measure provides a risk-based indicator of credit conditions, and as such, complements earlier quantity-based indicators from the literature. In an extensive comparison with such quantity-based systemic risk indicators, we find that the behaviour of the new indicator is competitive with that of the best quantity-based indicators.

Risk Management in Production Planning of Perishable Goods

In food supply chain planning, the trade-off between expected profit and risk is emphasized by the perishable nature of the goods that it has to handle. In particular, the risk of spoilage and the risk of revenue loss are substantial when stochastic parameters related to the demand, the consumer behavior, and the spoilage effect are considered. This paper aims to expose and handle this trade-off by developing risk-averse production planning models that incorporate financial risk measures. In particular, the performance of a risk-neutral attitude is compared to the performance of models taking into account the upper partial mean and the conditional value-at-risk. Insights from an illustrative example show the positive impact of the risk-averse models in operational performance indicators, such as the amount of expired products. Furthermore, through an extensive computational experiment, the advantage of the conditional value-at-risk model is evidenced, as it is able to dominate the solutions from the upper...

Consistency of Risk Measure Estimates

Recently there has been renewed debate about the relative merits of VaR and CVaR as measures of financial risk. VaR is not coherent and does not quantify the risk beyond VaR, while CVaR shows some computational instabilities and is not 'elicitable' (Gneiting 2010, Ziegel 2013). It is argued in this paper that such questions are best addressed from the point of view of probability forecasting or Dawid's 'prequential statistics.' We introduce a concept of 'consistency' of a risk measure, which is close to Dawid's 'strong prequential principle,' and show that VaR indeed has special properties not shared by any other risk measure.

Preface: Special issue on learning and robustness

The proliferation of huge amounts of datasets brings with it a series of special theoretical and computational challenges. This data avalanche arises in a wide range of scientific and commercial applications. With rapid advances in algorithms, computer and information technologies, many of these challenges are beginning to be addressed. Machine learning, knowledge discovery algorithms and optimization have become central to data analysis. In this special issue of CMS the authors have considered several issues of machine learning and non-convex optimization algorithms with several applications in finance. In the paper “Numerical Study of Learning Algorithms on Stiefel Manifold” by Takafumi Kanamori and Akiko Takeda non-convex optimization problems in machine learning are presented. Extensive computational results using different approaches are reported. The next paper “Calibrating Probability Distributions with Convex-ConcaveConvex Functions:Application toCDOPricing” byAlexanderVeremyev, Peter Tsyurmasto, Stan Uryasev, and R. Tyrrell Rockafellar, the authors apply the proposed methodology for the problem of calibrating probabilities of credit environments (market states) in the implied copula CollateralizedDebtObligations (CDO) pricingmodel. The third paper “Interaction between Financial RiskMeasures andMachine LearningMethods” by Jun-ya Gotoh, Akiko Takeda, and Rei Yamamoto the authors demonstrate how the financial risk measures relate to the machine learning methods, especially to support vector machines. In addition, they introduce the class of coherent risk-based methods and report extensive computational results. The paper by Theodore B. Trafalis, Indra Adrianto, Michael B. Richman, and S. Lakshmivarahan on “Machine-learning classifiers for imbalanced tornado data” deals with an important application of tornado prediction.

Robust risk measurement and model risk

Financial risk measurement relies on models of prices and other market variables, but models inevitably rely on imperfect assumptions and estimates, creating model risk. Moreover, optimization decisions, such as portfolio selection, amplify the effect of model error. In this work, we develop a framework for quantifying the impact of model error and for measuring and minimizing risk in a way that is robust to model error. This robust approach starts from a baseline model and finds the worst-case error in risk measurement that would be incurred through a deviation from the baseline model, given a precise constraint on the plausibility of the deviation. Using relative entropy to constrain model distance leads to an explicit characterization of worst-case model errors; this characterization lends itself to Monte Carlo simulation, allowing straightforward calculation of bounds on model error with very little computational effort beyond that required to evaluate performance under the baseline nominal model. This approach goes well beyond the effect of errors in parameter estimates to consider errors in the underlying stochastic assumptions of the model and to characterize the greatest vulnerabilities to error in a model. We apply this approach to problems of portfolio risk measurement, credit risk, delta hedging and counterparty risk measured through credit valuation adjustment.

Security portfolio management based on combined entropic risk measures

A combined entropic financial risk measure that is a convex combination of the entropic risk measure and the CVaR measure is considered. The effectiveness of the proposed measure in the formation of security portfolios is analyzed. Results of computational experiments are presented.

An Improved Historical Simulation Method to Estimate the Amount of Refined Oil Retail Value at Risk VaR

The international crude oil market is complicated in itself and with the rapid development of China in recent years, the dramatic changes of the international crude oil market have brought some risk to the security of Chinas oil market and the economic development of China. Value at risk (VaR), an effective measurement of financial risk, can be used to assess the risk of refined oil retail sales as well. However, VaR, as a model that can be applied to complicated nonlinear data, has not yet been widely researched. Therefore, an improved Historical Simulation Approach, historical stimulation of genetic algorithm to parameters selection of support vector machine, HSGA-SVMF, in this paper, is proposed, which is based on an approach the historical simulation with ARMA forecasts, HSAF. By comparing it with the HSAF and HSGA-SVMF approach, this paper gives evidence to show that HSGA-SVMF has a more effective forecasting power in the field of amount of refined oil.

Mean Failure Cost as a Measurable Value and Evidence of Cybersecurity

Addressing Cybersecurity within e-Learning systems becomes empowered to make online information more secure. Certain competences need to be identified as necessary skills to manage security online such the ability to assess sources and architectural components, understanding the privacy, confidentiality and user authentication. Security management approaches quantifying security threats in e-learning are common with other e-services. It is of our need to adopt a quantitative security risk management process in order to determine the worthiest attack and the ignored one, based on financial business risk measure which is the measure of the mean failure cost.This paper proposes a cyber security measure called the Mean Failure Cost (MFC) suitable for e-Learning systems. It is based on the identification of system’s architecture, the well-defined classes of stakeholders, the list of possible threats and vulnerabilities and the specific security requirements related to e-Learning systems and applications. In the mean time, security requirements are considered as appropriate mechanisms for preventing, detecting and recovering security attacks, for this reason an extension of the MFC measure is presented in order to detect the most critical security requirements. Also this paper highlights the security measures and guidelines for controlling e-Learning security policies regarding the most critical security requirements.

Interaction between financial risk measures and machine learning methods

The purpose of this article is to review the similarity and difference between financial risk minimization and a class of machine learning methods known as support vector machines, which were independently developed. By recognizing their common features, we can understand them in a unified mathematical framework. On the other hand, by recognizing their difference, we can develop new methods. In particular, employing the coherent measures of risk, we develop a generalized criterion for two-class classification. It includes existing criteria, such as the margin maximization and \(\nu \)-SVM, as special cases. This extension can also be applied to the other type of machine learning methods such as multi-class classification, regression and outlier detection. Although the new criterion is first formulated as a nonconvex optimization, it results in a convex optimization by employing the nonnegative \(\ell _1\)-regularization. Numerical examples demonstrate how the developed methods work for bond rating.