Conditional Value-at-risk Model Research Articles

Geopolitical Risk and Extreme Risk Connectedness Among Energy and Other Strategic Commodities: Fresh Sight Using the High‐Dimensional CoVaR Model

ABSTRACTExisting studies on commodity market risk spillovers recognize the pivotal role of geopolitical risk (GPR), but scarcely address how it drives tail risk spillover networks. This study adopts the Tail‐Event driven NETwork methodology to explore high‐dimensional Conditional Value at Risk (CoVaR) spillovers within energy and other strategic commodity markets. Our findings indicate that (1) In both lower and upper tail networks, metal and food commodities primarily act as net risk transmitters, whereas energy commodities are mainly net risk receivers. Additionally, these roles undergo short‐term reversals during periods of heightened market uncertainty. (2) There exists an asymmetrical pattern of CoVaR co‐movements in these commodity markets. The total connectedness (TC) in both the upper and lower tails demonstrates distinct responses to various extreme events. GPR tends to weaken the lower tail TC and strengthen the upper tail. (3) Incorporating GPR substantially improves the effectiveness of Minimum Connectedness Portfolio (MCoP) for these strategic commodities.

Risk Analysis of Electricity Demand at Public Electric Vehicle Charging Stations (SPKLU): CVaR Model Approach

The electricity demand at Public Electric Vehicle Charging Stations (SPKLUs) exhibits significant volatility, which is driven by several aspects including electricity demand patterns at specific time intervals, load variability, SPKLU capacity, and other related factors. The variability of these swings can present hazards for SPKLU operators in relation to energy administration as well as operational and financial hazards. The objective of this study is to assess the risk associated with energy demand fluctuation at SPKLUs by employing the Conditional Value-at-Risk (CVaR) model technique. CVaR, or Conditional Value at Risk, is a quantitative measure of risk that calculates the predicted loss value in the most unfavorable situation. It is commonly employed to enhance the risk management approach of SPKLUs. The electricity demand at SPKLU exhibits significant volatility, with an average fluctuation of 10.15% and a standard deviation of 49.67%. The CVAR, calculated at -121.19% for a confidence interval of 1%, represents the maximum potential loss that could be experienced during worst-case electrical demand conditions, highlighting the substantial fluctuations in demand. The study initially implemented the CVaR model to analyze power demand at SPKLU, providing novel perspectives on risk reduction for critical infrastructure and proposing unique strategies for managing demand fluctuations in a reliable and efficient manner. The results also offer comprehensive insights into risk exposure and facilitate the formulation of well-informed and strategic risk management plans.

Analyzing the Influence of Risk Models and Investor Risk-Aversion Disparity on Portfolio Selection in Community Solar Projects: A Comparative Case Study

This study examines the impact of risk models and investors’ risk aversion on the selection of community solar portfolios. Various risk models to account for the volatility in the electrical power output of community solar, namely variance (Var), SemiVariance (SemiVar), mean absolute deviation (MAD), and conditional value at risk (CVaR), were considered. A statistical model based on modern portfolio theory was employed to simulate investors’ risk aversion in the context of community solar portfolio selection. The results of this study showed that the choice of risk model that aligns with investors’ risk-aversion level plays a key role in realizing more return and safeguarding against volatility in power generation. In particular, the findings of this research revealed that the CVaR model provides higher returns at the cost of greater volatility in power generation compared to other risk models. In contrast, the MAD model offered a better tradeoff between risk and return, which can appeal more to risk-averse investors. Based on the simulation results, a new approach was proposed for optimizing the portfolio selection process for investors with divergent risk-aversion levels by averaging the utility functions of investors and identifying the most probable outcome.

Supplier selection and order allocation problems considering regional and supplier disruptions with a risk-averse strategy

This paper studies optimal supplier selection and order allocation problems considering regional and supplier disruptions. We suggest a pricing policy that takes into account disruption probability, which reflects the trade-off relationship between cost and risk. We present a risk-neutral model considering the expected cost and a risk-averse model considering the conditional value-at-risk (CVaR) measure. We also present a weighted CVaR model that considers various tolerance levels simultaneously. Several multi-objective models that consider both risk-averse and risk-neutral models are proposed. We develop methodologies to solve multi-objective models by applying a convex combination or a modified augmented Tchebycheff distance. Finally, we show the performance of solution approaches through numerical experiments and present the supplier dependency ratio, which can construct an appropriate portfolio. We offer a Pareto frontier as the result of the multi-objective model and derive managerial insights, suggesting a decision-making criterion between disruption risk and the expected cost.

A sustainable NEV manufacturer-retailer system under the Nash bargaining framework: considering the impact of the COVID-19 epidemic under the CVaR criterion

Suppose a new energy vehicle (NEV) manufacturer-retailer system where the wholesale price and the order quantity are determined through a negotiation procedure. Considering the impact of the COVID-19 epidemic, the manufacturer and the retailer are both assumed to be risk averse with Conditional Value-at-Risk (CVaR) as their performance measure. With the uniform distribution assumption, we derive the equilibrium solutions as well as the players’ profit shares in the Stackelberg game and Nash bargaining framework. We quantitatively address the impacts of the players’ confidence levels and government subsidy on the equilibrium order quantity, wholesale price and profit allocation in both negotiation frameworks. We find that, in both negotiation frameworks and considering the impact of the COVID-19 epidemic, a more risk-averse (i.e., with lower confidence level in CVaR model) manufacturer or retailer tends to occupy a higher profit share. On the other hand, a higher government subsidy aiming at offsetting the epidemic’s impact leads to a higher profit share for the manufacturer and a lower one for the retailer. A quantitive comparison of the equilibriums in the two negotiation frameworks indicates that more NEVs are ordered by the retailer and a higher system profit is generated in the Nash bargaining framework than the Stackelberg game. Thus, we analytically prove that the Nash bargaining framework is superior to the Stackelberg game for the NEV manufacturer-retailer system in terms of both quantity and profit with consideration of the epidemic impact. In addition, a series of numerical experiments is carried out to illustrate the effects of some significant parameters on the equilibrium order quantity and the system profit allocation in different negotiation frameworks. These numerical experiments also further demonstrate the superiority of the Nash bargaining framework for either NEV player—no matter how the epidemic trend and the government subsidy vary—and provide a quantitative scope for the retailer’s bargaining power to sustainably maintain the win-win cooperation between the NEV manufacturer and retailer in the superior Nash bargaining framework within the epidemic environment. From the perspective of policy, the government should increase subsidy within the epidemic environment to offset the negative effect and can degenerate subsidy when the epidemic dissipates. Furthermore, as the subsidy degenerates, both model results and numerical experiments show that the manufacturer suffers a more unfavorable effect, so the government can preferentially support the manufacturer by adjusting the subsidy to a higher level to alter players’ relative powers and profit shares.

CSP-IES economic dispatch strategy with generalized energy storage and a conditional value-at-risk model

To promote the efficient use of energy storage and renewable energy consumption in the integrated energy system (IES), an economic dispatch strategy for the concentrating solar power (CSP)-IES with generalized energy storage and a conditional value-at-risk (CVaR) model is proposed. First, considering the characteristics of energy storage and distributed power supply timing, a CSP-IES configuration is established by using a CSP plant to achieve thermal decoupling of the combined heat and power unit and by defining the thermal storage system of the CSP plant and the battery as the actual energy storage. Second, the fuzzy response of the logistic function is used to optimize the time-of-use tariff to guide load shifting, and the load shifting is defined as virtual energy storage. Third, the CSP-IES economic dispatch model is established to consider the carbon emission allowance model. Finally, considering the system uncertainty, a fuzzy chance constraint is used to relax the system power balance constraint, and then the trapezoidal fuzzy number is transformed into a deterministic equivalence class, and the CVaR model is used as a risk assessment index to quantify the risk cost of the system due to uncertainty. The CSP-IES economic dispatch model with CVaR is constructed. The feasibility and effectiveness of the proposed optimization model are verified by comparing various scenarios.

Risk measurement of China's green financial market based on B-spline quantile regression

To accurately measure the spillover effect of China's green financial carbon emission market, a new measurement of conditional value at risk (CoVaR) based on the B-spline quantile methods is proposed. Firstly, the variable coefficient CoVaR model is constructed, and the model coefficients are estimated by the B-spline quantile method. Then, the relationship between Δconditional value at risk (ΔCoVaR) and value at risk (VaR) is considered. In the empirical analysis, we investigate five carbon trading quota risk measurements of the carbon emission projects in China from 2014 to 2022, and verify the B-spline superiority by Monte Carlo simulation. The empirical results show that B-spline method has the highest risk fitting success rate and the smallest error.

Portfolio Selection Problem Using CVaR Risk Measures Equipped with DEA, PSO, and ICA Algorithms

Investors always pay attention to the two factors of return and risk in portfolio optimization. There are different metrics for the calculation of the risk factor, among which the most important one is the Conditional Value at Risk (CVaR). On the other hand, Data Envelopment Analysis (DEA) can be used to form the optimal portfolio and evaluate its efficiency. In these models, the optimal portfolio is created by stocks or companies with high efficiency. Since the search space is vast in actual markets and there are limitations such as the number of assets and their weight, the optimization problem becomes difficult. Evolutionary algorithms are a powerful tool to deal with these difficulties. The automotive industry in Iran involves international automotive manufacturers. Hence, it is essential to investigate the market related to this industry and invest in it. Therefore, in this study we examined this market based on the price index of the automotive group, then optimized a portfolio of automotive companies using two methods. In the first method, the CVaR measurement was modeled by means of DEA, then Particle Swarm Optimization (PSO) and the Imperial Competitive Algorithm (ICA) were used to solve the proposed model. In the second method, PSO and ICA were applied to solve the CVaR model, and the efficiency of the portfolios of the automotive companies was analyzed. Then, these methods were compared with the classic Mean-CVaR model. The results showed that the automotive price index was skewed to the right, and there was a possibility of an increase in return. Most companies showed favorable efficiency. This was displayed the return of the portfolio produced using the DEA-Mean-CVaR model increased because the investment proposal was basedon the stock with the highest expected return and was effective at three risk levels. It was found that when solving the Mean-CVaR model with evolutionary algorithms, the risk decreased. The efficient boundary of the PSO algorithm was higher than that of the ICA algorithm, and it displayed more efficient portfolios.Therefore, this algorithm was more successful in optimizing the portfolio.

A risk measure of the stock market that is based on multifractality

By studying the parameters of the multifractal spectrum and their economic significance, a new multifractal measure Rf is constructed, which extracts price fluctuation information from different various levels. To evaluate the performance of the new multifractal measure, using 1-min high-frequency data from the US S&P 500 index and China’s CSI 300 index as the research samples, we empirically compare Rf with the mainstream risk measure model — conditional value at risk (CVaR). We apply the Spearman rank correlation test to the two measures, formulate investment strategies under the two measures according to a uniform investment standard, and simulate investments. The results show that Rf has risk identification capability and that its average prediction accuracy, investment benefit and Sharpe ratio are higher than those of the CVaR model.

Identifying Systemically Important Banks in Indonesia: CoVaR Approach

The Global Financial Crisis of 2008 had a significant impact on banks' bailout decisions due to its high cost of Rp. 6.76 trillion (USD 499.5 million). That shifted the focus from analyzing bank size to a broader notion of systemic risk. Therefore, this research aims to systemically identify important banks in Indonesia using Conditional Value-at-Risk (CoVaR) approach. We conduct the following three steps measurement for population-based on all commercial banks data. Firstly, this study uses Merton Model to gauge the probability of default of commercial banks. Secondly, this study quantifies the value at risk of each bank, including its contribution to the whole banking systemic risk. Finally, this study measures financial linkage among banks and the individual bank value at risk contribution, conditional on other banks being in financial distress, i.e., at its Value at Risk (ΔCoVaR A|B). A threshold of 20% ΔCoVaR (A|B) was used to determine 12 out of 119 Indonesian commercial banks that are systemically important and the size ability to affect CoVaR positively. The novelty of the research is to integrate Probability of Default derived from the Merton Model into the CoVaR Model developed by Adrian & Brunnermeier.

Designing a closed-loop supply chain for reusable packaging materials: A risk-averse two-stage stochastic programming model using CVaR

Reusable packaging material (RPM) provide a circular and sustainable way of transporting parts/products safely along the various stages of supply chain. In the present work, we study a multi-echelon closed-loop supply chain network design problem for wooden RPMs. Initially, a mixed-integer programming model under deterministic setting is proposed to determine the optimal configuration of the manufacturing facilities and distribution centers of RPMs. Further, a risk-averse two-stage stochastic programming model is developed to incorporate the uncertainties associated with the demand, initial inventory and level of reusability of the RPMs. The developed model utilizes conditional-value-at-risk (CVaR) as risk measure since it provides more robust solutions compared to a risk-neutral approach in presence of uncertainty. The applicability of the model is explained using a real-life example of the prevalent supply chain of wooden pallets in several automobile manufacturers and their suppliers in India. The results suggest trade-off among various cost components such as fixed cost of opening facilities and capacity installation, manufacturing, acquisition, refurbishing, and environmental cost. Several managerial insights are drawn by carrying out sensitivity analysis of deterministic model and running the stochastic model with different values of CVaR parameters. Finally, we present numerical results to discuss how incorporating a risk measure affects the computational performance and solution of the CVaR model.

Risk-Perception-Aware Control Design Under Dynamic Spatial Risks

This letter proposes a novel Risk-Perception-Aware (RPA) control design using non-rational perception of risks associated with uncertain dynamic spatial costs. We use Cumulative Prospect Theory (CPT) to model the risk perception of a Decision Maker (DM) and use it to construct perceived risk functions that transform the uncertain dynamic spatial cost to deterministic perceived risks of a DM. These risks are then used to build safety sets which can represent risk-averse to risk-insensitive perception. Using these sets, we define novel notions of “inclusiveness” and “versatility” which can be employed to compare and evaluate any risk models in the context of RPA safety-critical controls. We then prove that CPT is the most “inclusive” and “versatile” model w.r.t. Conditional Value at Risk (CVaR) and Expected Risk (ER). Given a RPM, we construct a class of Control Barrier Functions (CBFs) and generate perceived-safety-critical controls using a Quadratic Program (QP) to guide an agent safely to a goal. For a class of truncated-Gaussian costs, we provide sufficient geometric conditions for the above QP to be feasible. We also prove that CPT-equipped RPA controller has both a larger feasible control set and more accurate stabilization w.r.t CVaR and ER models. We present simulations in a 2D environment to illustrate the proposed controller.

BP-CVaR: A novel model of estimating CVaR with back propagation algorithm

We propose a more flexible and useful model, BP-CVaR, to estimate conditional value-at-risk (CVaR) using back propagation (BP) algorithm, which can capture the change of markets and use the information to adjust the next CVaR result. We use three samples including S&P 500 index, Nasdaq index, DIJA index and compare the results by back-testing approaches. We find that (i) BP-CVaR is more reliable and has higher accuracy than Monte Carlo CVaR model and (ii) BP-CVaR can react to the change of markets more quickly than traditional CVaR model.

An empirical analysis of the cardinality constrained expectile-based VaR portfolio optimization problem

Expectiles are asymmetric generalizations of mean that are extensively employed by statisticians in regression analysis. In the last decade, the coherence and elicitability characteristics of expectiles have attracted attention of the researchers in risk management field. Recently, expectile has been recommended as an alternative risk measure to value-at-risk (VaR) and conditional value-at-risk (CVaR). As an analogy to VaR and CVaR, expectile is defined as a risk measure called expectile-based value-at-risk (EVaR). In this study, EVaR optimization model is extended with a set of practical constraints such as no short-selling, target return, proportional bounds, and portfolio cardinality constraints. The ex-ante and ex-post risk-adjusted return performances of the proposed model are compared with those of CVaR model by using historical data of the stocks listed in the BIST 100 and the S&P 100 indices. Furthermore, we perform an extensive numerical investigation to reveal the impact of important parameters on the performances of the models. The obtained results show the potential benefits of using EVaR model in practical investment decisions.

Beyond Value at Risk for Developing Markets

The standard metric for assessing risk in the financial realm has been the Value-at-Risk (VaR) with several parametric and non-parametric approaches and its derivatives which is Conditional Value-at-Risk (CVaR). The inability of VaR to tell loss severity beyond the confidence threshold and its incoherency gave birth to CVaR which accounted for both shortcomings and is also sub-additive. However, backtesting a 1-day CVaR model is almost impossible and VaR estimates gives better accuracy for fat tails than CVaR which makes CVaR also defective. Hence, there is need for a better measure which will capture the shortcomings of both metrics. This research will employ other risk measures beyond the conventional VaR and CVaR using the historical return of developing markets; South African Stock exchange (JTOPI-40) and the Nigerian Stock Exchange (NSE-30). In Particular, we will consider Hull-White Value-at-Risk (HWVaR) and Bubble Value-at-Risk (BVaR) and finally compare and contrast them with the two conventional metrics.

Is Being “Robust” Beneficial? A Perspective from the Indian Market

Motivated by the progress made towards incorporating robust optimization in the framework of risk minimization, this work focuses on assessing the practical usefulness of the robust optimization approaches for the minimization of downside risk measures, such as Value-at-Risk (VaR) and Conditional Value-at-Risk (CVaR). Accordingly, we perform empirical analysis of the performance of VaR and CVaR models with respect to their robust counterparts, namely, Worst-Case VaR and Worst-Case CVaR, using both simulated data and market data involving the Indian indices of S&P BSE 30 and S&P BSE 100. Additionally, we provide relevant insights regarding the viability of these robust models over their classical formulations from the perspective of an investment practitioner. We conclude by noting the superior performance of Worst-Case VaR and Worst-Case CVaR with respect to their classical versions in the cases involving higher number of stocks and simulated setup respectively.

Designing a multi-period credit portfolio optimization model a nonlinear multi-objective fuzzy mathematical modeling approach (Case study: Ansar banks affiliated to Sepah Bank)

This study aims to design a multi-period credit portfolio optimization model with a nonlinear multi-objective fuzzy mathematical modeling approach. In terms of data collection, this study is a descriptive-survey research and in terms of the nature and purpose of the research, it is an applied one. The statistical population of the research includes all facility files of the last 10 years as well as the statements of financial position of Ansar Bank branches affiliated with Sepah Bank, selected by census method. The risk criteria used in the models include Average Value at Risk (AVaR), Conditional Value at Risk (CVAR) and Semi-Entropy. First, having reviewed the research literature, the objectives and indices of the portfolio optimization issue were investigated based on the practical character of this issue and the main indices were selected. Then, each of the objectives and constraints were specified in a state of uncertainty and ambiguity, based on the principles of fuzzy credibility theory, for a state in which the expected rate of stock return is a triangular fuzzy number. Finally, three multi-objective fuzzy models were designed based on the selected criteria. Research models were implemented using MOPSO algorithm. The software used in conducting the research was MATLAB software. The results indicated that the CVAR model performed better than the other two models, i.e. AVAR and Semi-Entropy, in evaluating optimal portfolios.

Portfolio Construction by Using Different Risk Models: A Comparison among Diverse Economic Scenarios

We aim to construct portfolios by employing different risk models and compare their performance in order to understand their appropriateness for effective portfolio management for investors. Mean variance (MV), semi variance (SV), mean absolute deviation (MaD) and conditional value at risk (CVaR) are considered as risk measures. The price data were extracted from the Pakistan stock exchange, Bombay stock exchange and Dhaka stock exchange under diverse economic conditions such as crisis, recovery and growth. We take the average of GDP of the selected period of each country as a cut-off point to make three economic scenarios. We use 40 stocks from the Pakistan stock exchange, 92 stocks from the Bombay stock exchange and 30 stocks from the Dhaka stock exchange. We compute optimal weights using global minimum variance portfolio (GMVP) for all stocks to construct optimal portfolios and analyze the data by using MV, SV, MaD and CVaR models for each subperiod. We find that CVaR (95%) gives better results in each scenario for all three countries and performance of portfolios is inconsistent in different scenarios.

Convergence Analysis of the Approximation Problems for Solving Stochastic Vector Variational Inequality Problems

In this paper, we consider stochastic vector variational inequality problems (SVVIPs). Because of the existence of stochastic variable, the SVVIP may have no solutions generally. For solving this problem, we employ the regularized gap function of SVVIP to the loss function and then give a low-risk conditional value-at-risk (CVaR) model. However, this low-risk CVaR model is difficult to solve by the general constraint optimization algorithm. This is because the objective function is nonsmoothing function, and the objective function contains expectation, which is not easy to be computed. By using the sample average approximation technique and smoothing function, we present the corresponding approximation problems of the low-risk CVaR model to deal with these two difficulties related to the low-risk CVaR model. In addition, for the given approximation problems, we prove the convergence results of global optimal solutions and the convergence results of stationary points, respectively. Finally, a numerical experiment is given.

Select a Training Plan to Succession on Highly-skills Using Portfolio Optimization

In the manufacturing industry, Highly-skills are recognized as one of the company’s strengths. So, how to inherit Highly-skills is one of the most important issues. But, there is no standard model for education. Currently, training is based on the experience of each instructor. Therefore, we propose to formulate a training plan using portfolio optimization. We adopted the LPM (Lower Partial Moment) and CVaR (Conditional Value at Risk) models. By using standard model, it is possible to objectively evaluate the succession of Highly-skills, and to create an efficient training plan.