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 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 Problem-driven scenario generation: an analytical approach for stochastic programs with tail risk measure

2019 ◽  
Author(s):  
Jamie Fairbrother ◽  
Amanda Turner ◽  
Stein W. Wallace
Keyword(s):  
Portfolio Selection ◽  
Random Vector ◽  
Value At Risk ◽  
Risk Measures ◽  
Risk Measure ◽  
Monte Carlo Sampling ◽  
Conditional Value At Risk ◽  
Scenario Generation ◽  
Tail Risk ◽  
Stochastic Programs

AbstractScenario generation is the construction of a discrete random vector to represent parameters of uncertain values in a stochastic program. Most approaches to scenario generation are distribution-driven, that is, they attempt to construct a random vector which captures well in a probabilistic sense the uncertainty. On the other hand, a problem-driven approach may be able to exploit the structure of a problem to provide a more concise representation of the uncertainty. In this paper we propose an analytic approach to problem-driven scenario generation. This approach applies to stochastic programs where a tail risk measure, such as conditional value-at-risk, is applied to a loss function. Since tail risk measures only depend on the upper tail of a distribution, standard methods of scenario generation, which typically spread their scenarios evenly across the support of the random vector, struggle to adequately represent tail risk. Our scenario generation approach works by targeting the construction of scenarios in areas of the distribution corresponding to the tails of the loss distributions. We provide conditions under which our approach is consistent with sampling, and as proof-of-concept demonstrate how our approach could be applied to two classes of problem, namely network design and portfolio selection. Numerical tests on the portfolio selection problem demonstrate that our approach yields better and more stable solutions compared to standard Monte Carlo sampling.

scholarly journals Estimation of the Portfolio Risk from Conditional Value at Risk Using Monte Carlo Simulation

2021 ◽  
Vol 17 (3) ◽  
pp. 370-380
Author(s):  
Ervin Indarwati ◽  
Rosita Kusumawati
Keyword(s):  
At Risk ◽  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Value At Risk ◽  
Risk Measures ◽  
Risk Measure ◽  
Risk Estimation ◽  
Conditional Value At Risk ◽  
Portfolio Risk ◽  
Portfolio Returns

Portfolio risk shows the large deviations in portfolio returns from expected portfolio returns. Value at Risk (VaR) is one method for determining the maximum risk of loss of a portfolio or an asset based on a certain probability and time. There are three methods to estimate VaR, namely variance-covariance, historical, and Monte Carlo simulations. One disadvantage of VaR is that it is incoherent because it does not have sub-additive properties. Conditional Value at Risk (CVaR) is a coherent or related risk measure and has a sub-additive nature which indicates that the loss on the portfolio is smaller or equal to the amount of loss of each asset. CVaR can provide loss information above the maximum loss. Estimating portfolio risk from the CVaR value using Monte Carlo simulation and its application to PT. Bank Negara Indonesia (Persero) Tbk (BBNI.JK) and PT. Bank Tabungan Negara (Persero) Tbk (BBTN.JK) will be discussed in this study.  The  daily  closing  price  of  each  BBNI  and BBTN share from 6 January 2019 to 30 December 2019 is used to measure the CVaR of the two banks' stock portfolios with this Monte Carlo simulation. The steps taken are determining the return value of assets, testing the normality of return of assets, looking for risk measures of returning assets that form a normally distributed portfolio, simulate the return of assets with monte carlo, calculate portfolio weights, looking for returns portfolio, calculate the quartile of portfolio return as a VaR value, and calculate the average loss above the VaR value as a CVaR value. The results of portfolio risk estimation of the value of CVaR using Monte Carlo simulation on PT. Bank Negara Indonesia (Persero) Tbk and PT. Bank Tabungan Negara (Persero) Tbk at a confidence level of 90%, 95%, and 99% is 5.82%, 6.39%, and 7.1% with a standard error of 0.58%, 0.59%, and 0.59%. If the initial funds that will be invested in this portfolio are illustrated at Rp 100,000,000, it can be interpreted that the maximum possible risk that investors will receive in the future will not exceed Rp 5,820,000, Rp 6,390,000 and Rp 7,100,000 at the significant level 90%, 95%, and 99%

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.

scholarly journals RM-CVaR: Regularized Multiple β-CVaR Portfolio

2020 ◽  
Author(s):  
Kei Nakagawa ◽  
Shuhei Noma ◽  
Masaya Abe
Keyword(s):  
Portfolio Optimization ◽  
Value At Risk ◽  
Optimization Problems ◽  
Risk Measures ◽  
Risk Measure ◽  
Superior Performance ◽  
Conditional Value At Risk ◽  
Related Risk ◽  
Mean And Variance ◽  
Portfolio Optimization Problem

The problem of finding the optimal portfolio for investors is called the portfolio optimization problem. Such problem mainly concerns the expectation and variability of return (i.e., mean and variance). Although the variance would be the most fundamental risk measure to be minimized, it has several drawbacks. Conditional Value-at-Risk (CVaR) is a relatively new risk measure that addresses some of the shortcomings of well-known variance-related risk measures, and because of its computational efficiencies, it has gained popularity. CVaR is defined as the expected value of the loss that occurs beyond a certain probability level (β). However, portfolio optimization problems that use CVaR as a risk measure are formulated with a single β and may output significantly different portfolios depending on how the β is selected. We confirm even small changes in β can result in huge changes in the whole portfolio structure. In order to improve this problem, we propose RM-CVaR: Regularized Multiple β-CVaR Portfolio. We perform experiments on well-known benchmarks to evaluate the proposed portfolio. Compared with various portfolios, RM-CVaR demonstrates a superior performance of having both higher risk-adjusted returns and lower maximum drawdown.

scholarly journals Scenario aggregation method for portfolio expectile optimization

2016 ◽  
Vol 33 (1-2) ◽  
Author(s):  
Edgars Jakobsons
Keyword(s):  
Portfolio Optimization ◽  
Value At Risk ◽  
Optimization Problem ◽  
Optimization Problems ◽  
Risk Measures ◽  
Risk Measure ◽  
Conditional Value At Risk ◽  
Aggregation Method ◽  
Portfolio Optimization Problem ◽  
Scenario Aggregation

AbstractThe statistical functional expectile has recently attracted the attention of researchers in the area of risk management, because it is the only risk measure that is both coherent and elicitable. In this article, we consider the portfolio optimization problem with an expectile objective. Portfolio optimization problems corresponding to other risk measures are often solved by formulating a linear program (LP) that is based on a sample of asset returns. We derive three different LP formulations for the portfolio expectile optimization problem, which can be considered as counterparts to the LP formulations for the Conditional Value-at-Risk (CVaR) objective in the works of Rockafellar and Uryasev [

scholarly journals Backtesting Marginal Expected Shortfall and Related Systemic Risk Measures

2020 ◽  
Author(s):  
Denisa Banulescu-Radu ◽  
Christophe Hurlin ◽  
Jérémy Leymarie ◽  
Olivier Scaillet
Keyword(s):  
At Risk ◽  
Financial Institutions ◽  
Systemic Risk ◽  
Value At Risk ◽  
Risk Measures ◽  
Risk Measure ◽  
Expected Shortfall ◽  
Conditional Value At Risk ◽  
Finite Sample ◽  
Marginal Expected Shortfall

This paper proposes an original approach for backtesting systemic risk measures. This backtesting approach makes it possible to assess the systemic risk measure forecasts used to identify the financial institutions that contribute the most to the overall risk in the financial system. Our procedure is based on simple tests similar to those generally used to backtest the standard market risk measures such as value-at-risk or expected shortfall. We introduce a concept of violation associated with the marginal expected shortfall (MES), and we define unconditional coverage and independence tests for these violations. We can generalize these tests to any MES-based systemic risk measures such as the systemic expected shortfall (SES), the systemic risk measure (SRISK), or the delta conditional value-at-risk ([Formula: see text]CoVaR). We study their asymptotic properties in the presence of estimation risk and investigate their finite sample performance via Monte Carlo simulations. An empirical application to a panel of U.S. financial institutions is conducted to assess the validity of MES, SRISK, and [Formula: see text]CoVaR forecasts issued from a bivariate GARCH model with a dynamic conditional correlation structure. Our results show that this model provides valid forecasts for MES and SRISK when considering a medium-term horizon. Finally, we propose an early warning system indicator for future systemic crises deduced from these backtests. Our indicator quantifies how much is the measurement error issued by a systemic risk forecast at a given point in time which can serve for the early detection of global market reversals. This paper was accepted by Kay Giesecke, finance.

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 On quantile based co-risk measures and their estimation

2020 ◽  
Vol 8 (1) ◽  
pp. 396-416
Author(s):  
Sebastian Fuchs ◽  
Wolfgang Trutschnig
Keyword(s):  
At Risk ◽  
Value At Risk ◽  
Risk Measures ◽  
Risk Measure ◽  
Conditional Value At Risk ◽  
Regularity Conditions ◽  
Related Risk ◽  
Consistent Estimators ◽  
Strongly Consistent ◽  
Different Levels

AbstractConditional Value-at-Risk (CoVaR) is defined as the Value-at-Risk of a certain risk given that the related risk equals a given threshold (CoVaR=) or is smaller/larger than a given threshold (CoVaR</CoVaR≥). We extend the notion of Conditional Value-at-Risk to quantile based co-risk measures that are weighted mixtures of CoVaR at different levels and hence involve the stochastic dependence that occurs among the risks and that is captured by copulas. We show that every quantile based co-risk measure is a quantile based risk measure and hence fulfills all related properties. We further discuss continuity results of quantile based co-risk measures from which consistent estimators for CoVaR< and CoVaR≥ based risk measures immediately follow when plugging in empirical copulas. Although estimating co-risk measures based on CoVaR= is a nontrivial endeavour since conditioning on events with zero probability is necessary we show that working with so-called empirical checkerboard copulas allows to construct strongly consistent estimators for CoVaR= and related co-risk measures under very mild regularity conditions. A small simulation study illustrates the performance of the obtained estimators for special classes of copulas.

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.

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