scholarly journals A Bi-Objective Portfolio Optimization with Conditional Value-at-Risk

2010 ◽  
Vol 4 (2) ◽  
pp. 47-69 ◽  
Author(s):  
Bartosz Sawik
Keyword(s):  
Value At Risk ◽  
Stock Exchange ◽  
Risk Measure ◽  
Performance Measure ◽  
Conditional Value At Risk ◽  
Programming Approach ◽  
Expected Return ◽  
Worst Case ◽  
Warsaw Stock Exchange ◽  
The Relationship

This paper presents a bi-objective portfolio model with the expected return as a performance measure and the expected worst-case return as a risk measure. The problems are formulated as a bi-objective linear program. Numerical examples based on 1000, 3500 and 4020 historical daily input data from the Warsaw Stock Exchange are presented and selected computational results are provided. The computational experiments prove that the proposed linear programming approach provides the decision maker with a simple tool for evaluating the relationship between the expected and the worst-case portfolio return.

Risk Measures for Natural Resource Management: Description, Simulation Testing, and R Code With Fisheries Examples

2012 ◽  
Vol 3 (1) ◽  
pp. 150-157 ◽  
Author(s):  
Suresh Andrew Sethi ◽  
Mike Dalton
Keyword(s):  
Natural Resource ◽  
Value At Risk ◽  
Risk Measures ◽  
Risk Measure ◽  
Policy Decision ◽  
Performance Measure ◽  
Small Sample ◽  
Conditional Value At Risk ◽  
Management Scenarios ◽  
Resource Systems

Abstract Traditional measures that quantify variation in natural resource systems include both upside and downside deviations as contributing to variability, such as standard deviation or the coefficient of variation. Here we introduce three risk measures from investment theory, which quantify variability in natural resource systems by analyzing either upside or downside outcomes and typical or extreme outcomes separately: semideviation, conditional value-at-risk, and probability of ruin. Risk measures can be custom tailored to frame variability as a performance measure in terms directly meaningful to specific management objectives, such as presenting risk as harvest expected in an extreme bad year, or by characterizing risk as the probability of fishery escapement falling below a prescribed threshold. In this paper, we present formulae, empirical examples from commercial fisheries, and R code to calculate three risk measures. In addition, we evaluated risk measure performance with simulated data, and we found that risk measures can provide unbiased estimates at small sample sizes. By decomposing complex variability into quantitative metrics, we envision risk measures to be useful across a range of wildlife management scenarios, including policy decision analyses, comparative analyses across systems, and tracking the state of natural resource systems through time.

scholarly journals The Case of “Less is More”: Modelling Risk-Preference with Expected Downside Risk

2017 ◽  
Vol 17 (2) ◽  
Author(s):  
Mihály Ormos ◽  
Dusán Timotity
Keyword(s):  
Value At Risk ◽  
Utility Theory ◽  
Risk Measure ◽  
Negative Relationship ◽  
Downside Risk ◽  
Psychological Explanation ◽  
Conditional Value At Risk ◽  
Expected Return ◽  
Linear Predictor ◽  
Less Is More

AbstractThis paper discusses an alternative explanation for the empirical findings contradicting the positive relationship between risk (variance) and reward (expected return). We show that these contradicting results might be due to the false definition of risk-perception, which we correct by introducing Expected Downside Risk (EDR). The EDR parameter, similar to the Expected Shortfall or Conditional Value-at-Risk, measures the tail risk, however, fits and better explains the utility perception of investors. Our results indicate that when using the EDR as risk measure, both the positive and negative relationship between expected return and risk can be derived under standard conditions (e. g. expected utility theory and positive risk-aversion). Therefore, no alternative psychological explanation or additional boundary condition on utility theory is required to explain the phenomenon. Furthermore, we show empirically that it is a more precise linear predictor of expected return than volatility, both for individual assets and portfolios.

scholarly journals Taming Tail Risk: Regularized Multiple β Worst-Case CVaR Portfolio

Symmetry ◽  
2021 ◽  
Vol 13 (6) ◽  
pp. 922
Author(s):  
Kei Nakagawa ◽  
Katsuya Ito
Keyword(s):  
Value At Risk ◽  
Risk Measures ◽  
Risk Measure ◽  
Downside Risk ◽  
Superior Performance ◽  
Conditional Value At Risk ◽  
Worst Case ◽  
Tail Risk ◽  
Promising Alternative ◽  
Investment Process

The importance of proper tail risk management is a crucial component of the investment process and conditional Value at Risk (CVaR) is often used as a tail risk measure. CVaR is the asymmetric risk measure that controls and manages the downside risk of a portfolio while symmetric risk measures such as variance consider both upside and downside risk. In fact, minimum CVaR portfolio is a promising alternative to traditional mean-variance optimization. However, there are three major challenges in the minimum CVaR portfolio. Firstly, when using CVaR as a risk measure, we need to determine the distribution of asset returns, but it is difficult to actually grasp the distribution; therefore, we need to invest in a situation where the distribution is uncertain. Secondly, the minimum CVaR portfolio is formulated with a single β and may output significantly different portfolios depending on the β. Finally, most portfolio allocation strategies do not account for transaction costs incurred by each rebalancing of the portfolio. In order to improve these challenges, we propose a Regularized Multiple β Worst-case CVaR (RM-WCVaR) portfolio. The characteristics of this portfolio are as follows: it makes CVaR robust with worst-case CVaR which is still an asymmetric risk measure, it is stable among multiple β, and against changes in weights over time. We perform experiments on well-known benchmarks to evaluate the proposed portfolio.RM-WCVaR demonstrates superior performance of having both higher risk-adjusted returns and lower maximum drawdown.

scholarly journals Multi-stage stochastic model in portfolio selection problem

Filomat ◽  
2018 ◽  
Vol 32 (3) ◽  
pp. 991-1001
Author(s):  
Shokoofeh Banihashemi ◽  
Ali Azarpour ◽  
Marziye Kaveh
Keyword(s):  
At Risk ◽  
Portfolio Selection ◽  
Value At Risk ◽  
Risk Measures ◽  
Risk Measure ◽  
Selection Problem ◽  
Conditional Value At Risk ◽  
Expected Return ◽  
Portfolio Selection Problem ◽  
Multi Stage

This paper is a novel work of portfolio-selection problem solving using multi objective model considering four parameters, Expected return, downside beta coefficient, semivariance and conditional value at risk at a specified confidence level. Multi-period models can be defined as stochastic models. Early studies on portfolio selection developed using variance as a risk measure; although, theories and practices revealed that variance, considering its downsides, is not a desirable risk measure. To increase accuracy and overcoming negative aspects of variance, downside risk measures like semivarinace, downside beta covariance, value at risk and conditional value at risk was other risk measures that replaced in models. These risk measures all have advantages over variance and previous works using these parameters have shown improvements in the best portfolio selection. Purposed models are solved using genetic algorithm and for the topic completion, numerical example and plots to measure the performance of model in four dimensions are provided.

scholarly journals Worst-Case Higher Moment Coherent Risk Based on Optimal Transport with Application to Distributionally Robust Portfolio Optimization

Symmetry ◽  
2022 ◽  
Vol 14 (1) ◽  
pp. 138
Author(s):  
Wei Liu ◽  
Yang Liu
Keyword(s):  
Portfolio Optimization ◽  
Value At Risk ◽  
Optimal Transport ◽  
Risk Measure ◽  
Conditional Value At Risk ◽  
Worst Case ◽  
Tail Risk ◽  
Coherent Risk ◽  
The Asymmetry ◽  
Distributionally Robust

The tail risk management is of great significance in the investment process. As an extension of the asymmetric tail risk measure—Conditional Value at Risk (CVaR), higher moment coherent risk (HMCR) is compatible with the higher moment information (skewness and kurtosis) of probability distribution of the asset returns as well as capturing distributional asymmetry. In order to overcome the difficulties arising from the asymmetry and ambiguity of the underlying distribution, we propose the Wasserstein distributionally robust mean-HMCR portfolio optimization model based on the kernel smoothing method and optimal transport, where the ambiguity set is defined as a Wasserstein “ball” around the empirical distribution in the weighted kernel density estimation (KDE) distribution function family. Leveraging Fenchel’s duality theory, we obtain the computationally tractable DCP (difference-of-convex programming) reformulations and show that the ambiguity version preserves the asymmetry of the HMCR measure. Primary empirical test results for portfolio selection demonstrate the efficiency of the proposed model.

Portfolio selection with robust estimators considering behavioral biases in a causal network

2019 ◽  
Vol 53 (2) ◽  
pp. 577-591 ◽  
Author(s):  
Omid Momen ◽  
Akbar Esfahanipour ◽  
Abbas Seifi
Keyword(s):  
Portfolio Selection ◽  
Value At Risk ◽  
Stock Exchange ◽  
Risk Measure ◽  
Risk Attitude ◽  
Conditional Value At Risk ◽  
Causal Network ◽  
Robust Estimators ◽  
Behavioral Biases ◽  
Additive Risk

In this study, we develop a behavioral portfolio selection model that incorporates robust estimators for model inputs in order to reduce the need to change the portfolio over consecutive periods. It also includes Conditional Value at Risk as a sub-additive risk measure, which is preferable in behavioral portfolio selection. Finally, we model a varying risk attitude in a causal network in which investor behavioral biases and latest realized return are related to using a causation algorithm. We also provide a case study in Tehran Stock Exchange, where the results disclose that albeit our model is not mean-variance efficient, it selects portfolios that are robust, well diversified, and have less utility loss compared to a well-known behavioral portfolio model.

OPTIMAL REINSURANCE FROM THE VIEWPOINTS OF BOTH AN INSURER AND A REINSURER UNDER THE CVAR RISK MEASURE AND VAJDA CONDITION

2021 ◽  
pp. 1-29
Author(s):  
Yanhong Chen
Keyword(s):  
Loss Function ◽  
Value At Risk ◽  
Numerical Study ◽  
Risk Measure ◽  
Convex Combination ◽  
Weighting Factor ◽  
Loss Functions ◽  
Conditional Value At Risk ◽  
Optimal Reinsurance ◽  
The Impact

ABSTRACT In this paper, we study the optimal reinsurance contracts that minimize the convex combination of the Conditional Value-at-Risk (CVaR) of the insurer’s loss and the reinsurer’s loss over the class of ceded loss functions such that the retained loss function is increasing and the ceded loss function satisfies Vajda condition. Among a general class of reinsurance premium principles that satisfy the properties of risk loading and convex order preserving, the optimal solutions are obtained. Our results show that the optimal ceded loss functions are in the form of five interconnected segments for general reinsurance premium principles, and they can be further simplified to four interconnected segments if more properties are added to reinsurance premium principles. Finally, we derive optimal parameters for the expected value premium principle and give a numerical study to analyze the impact of the weighting factor on the optimal reinsurance.

scholarly journals Portfolio Optimization Constrained by Performance Attribution

2021 ◽  
Vol 14 (5) ◽  
pp. 201
Author(s):  
Yuan Hu ◽  
W. Brent Lindquist ◽  
Svetlozar T. Rachev
Keyword(s):  
Portfolio Optimization ◽  
Asset Allocation ◽  
Value At Risk ◽  
Risk Measures ◽  
Risk Measure ◽  
Selection Effect ◽  
Conditional Value At Risk ◽  
Positive Role ◽  
Performance Attribution ◽  
Dow Jones Industrial Average

This paper investigates performance attribution measures as a basis for constraining portfolio optimization. We employ optimizations that minimize conditional value-at-risk and investigate two performance attributes, asset allocation (AA) and the selection effect (SE), as constraints on asset weights. The test portfolio consists of stocks from the Dow Jones Industrial Average index. Values for the performance attributes are established relative to two benchmarks, equi-weighted and price-weighted portfolios of the same stocks. Performance of the optimized portfolios is judged using comparisons of cumulative price and the risk-measures: maximum drawdown, Sharpe ratio, Sortino–Satchell ratio and Rachev ratio. The results suggest that achieving SE performance thresholds requires larger turnover values than that required for achieving comparable AA thresholds. The results also suggest a positive role in price and risk-measure performance for the imposition of constraints on AA and SE.

scholarly journals Risk-Averse Multi-Stage Stochastic Programming to Optimizing Vaccine Allocation and Treatment Logistics for Effective Epidemic Response

2021 ◽  
Author(s):  
Xuecheng Yin ◽  
Esra Buyuktahtakin
Keyword(s):  
Value At Risk ◽  
Virus Disease ◽  
Risk Measure ◽  
Adverse Outcomes ◽  
Mixed Integer ◽  
Conditional Value At Risk ◽  
Risk Averse ◽  
Expected Number ◽  
Multi Stage ◽  
Stochastic Mixed Integer Programming

Existing compartmental-logistics models in epidemics control are limited in terms of optimizing the allocation of vaccines and treatment resources under a risk-averse objective. In this paper, we present a data-driven, mean-risk, multi-stage, stochastic epidemics-vaccination-logistics model that evaluates various disease growth scenarios under the Conditional Value-at-Risk (CVaR) risk measure to optimize the distribution of treatment centers, resources, and vaccines, while minimizing the total expected number of infections, deaths, and close contacts of infected people under a limited budget. We integrate a new ring vaccination compartment into a Susceptible-Infected-Treated-Recovered-Funeral-Burial epidemics-logistics model. Our formulation involves uncertainty both in the vaccine supply and the disease transmission rate. Here, we also consider the risk of experiencing scenarios that lead to adverse outcomes in terms of the number of infected and dead people due to the epidemic. Combining the risk-neutral objective with a risk measure allows for a trade-off between the weighted expected impact of the outbreak and the expected risks associated with experiencing extremely disastrous scenarios. We incorporate human mobility into the model and develop a new method to estimate the migration rate between each region when data on migration rates is not available. We apply our multi-stage stochastic mixed-integer programming model to the case of controlling the 2018-2020 Ebola Virus Disease (EVD) in the Democratic Republic of the Congo (DRC) using real data. Our results show that increasing the risk-aversion by emphasizing potentially disastrous outbreak scenarios reduces the expected risk related to adverse scenarios at the price of the increased expected number of infections and deaths over all possible scenarios. We also find that isolating and treating infected individuals are the most efficient ways to slow the transmission of the disease, while vaccination is supplementary to primary interventions on reducing the number of infections. Furthermore, our analysis indicates that vaccine acceptance rates affect the optimal vaccine allocation only at the initial stages of the vaccine rollout under a tight vaccine supply.

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