Robust optimization, one of the most popular topics in the field of optimization and control since the late 1990s, deals with an optimization problem involving uncertain parameters. In this paper, we ...consider the relative robust conditional value-at-risk portfolio selection problem where the underlying probability distribution of portfolio return is only known to belong to a certain set. Our approach not only takes into account the worst-case scenarios of the uncertain distribution, but also pays attention to the best possible decision with respect to each realization of the distribution. We also illustrate how to construct a robust portfolio with multiple experts (priors) by solving a sequence of linear programs or a second-order cone program.
• We change the definition of financial distress in CoVaR. • We consider more severe distress events, backtest CoVaR, and improve its consistency. • Our CoVaR and VaR have a weak relation in the ...cross-section and in the time-series. • Depository institutions contribute the most to systemic risk. • Leverage, size, and equity beta are important in explaining systemic risk.
We modify Adrian and Brunnermeier’s (2011) CoVaR, the VaR of the financial system conditional on an institution being in financial distress. We change the definition of financial distress from an institution being exactly at its VaR to being at most at its VaR. This change allows us to consider more severe distress events, to backtest CoVaR, and to improve its consistency (monotonicity) with respect to the dependence parameter. We define the systemic risk contribution of an institution as the change from its CoVaR in its benchmark state (defined as a one-standard deviation event) to its CoVaR under financial distress. We estimate the systemic risk contributions of four financial industry groups consisting of a large number of institutions for the sample period June 2000 to February 2008 and the 12months prior to the beginning of the crisis. We also investigate the link between institutions’ contributions to systemic risk and their characteristics.
There appears to be a consensus that the recent instability in global financial markets may be attributable in part to the failure of financial modeling. More specifically, it is alleged that current ...risk models have failed to properly assess the risks associated with large adverse stock price behavior. In this paper, we first discuss the limitations of classical time series models for forecasting financial market meltdowns. Then we set forth a framework capable of forecasting both extreme events and highly volatile markets. Based on the empirical evidence presented in this paper, our framework offers an improvement over prevailing models for evaluating stock market risk exposure during distressed market periods.
This paper considers the problem of risk sharing, where a coalition of homogeneous agents, each bearing a random cost, aggregates their costs, and shares the value‐at‐risk of such a risky position. ...Due to limited distributional information in practice, the joint distribution of agents' random costs is difficult to acquire. The coalition, being aware of the distributional ambiguity, thus evaluates the worst‐case value‐at‐risk within a commonly agreed ambiguity set of the possible joint distributions. Through the lens of cooperative game theory, we show that this coalitional worst‐case value‐at‐risk is subadditive for the popular ambiguity sets in the distributionally robust optimization literature that are based on (i) convex moments or (ii) Wasserstein distance to some reference distributions. In addition, we propose easy‐to‐compute core allocation schemes to share the worst‐case value‐at‐risk. Our results can be readily extended to sharing the worst‐case conditional value‐at‐risk under distributional ambiguity.
We study an extension of value-at-risk (VaR) measure, named as Mixed VaR, a weighted sum of multiple VaRs quantified at different confidence levels. Classical VaR or single VaR computed at a fixed ...confidence level corresponds to a single percentile of distribution and therefore, is unable to reveal much information of risk involved in it. As a remedy to this, we propose to investigate the role of Mixed VaR and its deviation version in risk management of extreme events in the portfolio selection problem. We analyze the computational performance of portfolios from optimization models minimizing single VaR and Mixed VaR (and their deviation variants) for different combinations of confidence levels over historical as well as on simulated data in various financial performance parameters including mean value, risk measures (VaR and CVaR values quantified at multiple confidence levels), and risk-reward measures (Sharpe ratio, Sortino ratio, Sharpe with VaR, and Sharpe with CVaR). We also study the numerical comparison between Mixed VaR with its most crucial counterpart, the Mixed conditional value-at-risk (Mixed CVaR). We find that the performance of portfolios from Mixed VaR model is lying between the performance of its single VaR counterparts and rarely yield any worst value in any of the considered performance parameters. A similar observation is concluded for the deviation version of the models. Further, we find that Mixed VaR outperforms Mixed CVaR with respect to risk-reward measures considered in the study on both of the data sets, historical as well as on simulated.
•The Mixed VaR model is introduced.•The Mixed VaR is compared numerically with its strong competitor Mixed CVaR.•Numerical analysis is done using historical as well as simulated data sets.•Simulations are performed with varying dependency as well as marginal structure.•The Mixed Value at Risk model proves out to be more stable and robust compared to the others.
In this study, value at risk and conditional value at risk are used to measure the risks of pilot carbon markets of Beijing, Shanghai, Guangdong, Tianjin, Hubei, Shenzhen and Chongqing in China. ...Regular vine copula-CoES is used to measure the risk spillover effects among carbon markets of Guangdong, Hubei and Shenzhen with high transactions. The empirical results show that compared with the traditional value at risk, conditional value at risk can better measure the risks of carbon markets. Carbon markets of Chongqing, Tianjin and Shenzhen have higher risks than those of Hubei and Guangdong. Risk spillover effects are found between carbon markets of Guangdong and Shenzhen, rather than between those of Hubei and Guangdong.
•Conditional value at risk are used to measure the risks of China's pilot carbon markets.•Regular vine copula-CoES is used to measure the risk spillover effects between carbon markets of Guangdong, Hubei and Shenzhen.•Conditional value at risk can better measure the risks of carbon markets than value at risk.•Risk spillover effects are found between carbon markets of Guangdong and Shenzhen.
A system to calculate Cyber Value-at-Risk Erola, Arnau; Agrafiotis, Ioannis; Nurse, Jason R.C. ...
Computers & security,
February 2022, 2022-02-00, 20220201, Volume:
113
Journal Article
Peer reviewed
Open access
In the face of increasing numbers of cyber-attacks, it is critical for organisations to understand the risk they are exposed to even after deploying security controls. This residual risk forms part ...of the ongoing operational environment, and must be understood and planned for if resilience is to be achieved. However, there is a lack of rigorous frameworks to help organisations reason about how their use of risk controls can change the nature of the potential losses they face, given an often changing threat landscape. To address this gap, we present a system that calculates Cyber Value-at-Risk (CVaR) of an organisation. CVaR is a probabilistic density function for losses from cyber-incidents, for any given threats of interest and risk control practice. It can take account of varying effectiveness of controls, the consequences for risk propagation through infrastructures, and the cyber-harms that result. We demonstrate the utility of the system in a real case study by calculating the CVaR of an organisation that experienced a significant cyber-incident. We show that the system is able to produce predictions representative of the actual financial loss. The presented system can be used by insurers offering cyber products to better inform the calculation of insurance premiums, and by organisations to reason about the effects of using particular risk control setups on reducing their exposure to cyber-risk.
This article studies the optimal portfolio selection of expected utility‐maximizing investors who must also manage their market‐risk exposures. The risk is measured by a so‐called weighted ...value‐at‐risk (WVaR) risk measure, which is a generalization of both value‐at‐risk (VaR) and expected shortfall (ES). The feasibility, well‐posedness, and existence of the optimal solution are examined. We obtain the optimal solution (when it exists) and show how risk measures change asset allocation patterns. In particular, we characterize three classes of risk measures: the first class will lead to models that do not admit an optimal solution, the second class can give rise to endogenous portfolio insurance, and the third class, which includes VaR and ES, two popular regulatory risk measures, will allow economic agents to engage in “regulatory capital arbitrage,” incurring larger losses when losses occur.
Banking on ecosystem services Mundaca, Luis; Heintze, Jan-Niklas
Ecological economics,
October 2024, 2024-10-00, Volume:
224
Journal Article
Peer reviewed
Open access
The COP 15 of the UN Convention on Biological Diversity emphasised the need to monitor, evaluate, and disclose the risks and dependencies of financial institutions on biodiversity. In the light of ...this context, our paper focuses specifically on banks and is framed by the following overarching question: to what extent have banks identified, integrated, measured, and disclosed their dependency and exposure to ecosystem services (ES)? The literature on finance and biodiversity provides various arguments highlighting the urgency and significance of understanding and disclosing banks' ES risk exposure. Despite numerous public and/or private initiatives, banks have been slow to evaluate and integrate their dependency on ES, and related risks, into their operations and performance. Using data from the ten largest European banks, we estimate that for every dollar of equity holding, 26 cents are potentially exposed to high ES dependencies. This figure should be regarded as a lower estimate of the total banks' exposure to ES dependency. To make progress, we argue that banks must become champions of ES to ensure their own resilience and financial sustainability. Governance plays a key role, and we suggest several measures to accelerate this transition.
Recent studies in Lee and Prékopa (Oper Res Lett 45:19–24, 2017) and Lee (Oper Res Lett 45:1204–1220, 2017) showed that a union of partially ordered orthants in Rn can be decomposed only into the ...largest and the second largest chains. This allows us to calculate the probability of the union of such events in a recursive manner. If the vertices of such orthants designate p-level efficient points, i.e., the multivariate quantile or the multivariate value-at-risk (MVaR) in Rn, then the number of them, say N, is typically very large, which makes it almost impossible to calculate the multivariate conditional value-at-risk (MCVaR) introduced by Prékopa (Ann Oper Res 193(1):49–69, 2012). This is because it takes O(2N) in case of N MVaRs in Rn to find the exact value of MCVaR. In this paper, upon the basis of ideas in Lee and Prékopa (Oper Res Lett 45:19–24, 2017) and Lee (Oper Res Lett 45:1204–1220, 2017), together with proper adjustments, we study efficient methods for the calculation of the MCVaR without resorting to an approximation. In fact, the proposed methods not only have polynomial time complexity but also computes the exact value of MCVaR. We also discuss additional benefits MCVaR has to offer over its univariate counter part, the conditional value-at-risk, by providing numerical results. Numerical examples are presented with computing time in both cases of given population and sample data sets.
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