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 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 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 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.

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.

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.

A Theory for Measures of Tail Risk

2021 ◽  
Author(s):  
Fangda Liu ◽  
Ruodu Wang
Keyword(s):  
Value At Risk ◽  
Financial Regulation ◽  
Risk Measures ◽  
Risk Measure ◽  
Continuity Condition ◽  
Tail Risk ◽  
Dual Representations ◽  
Joint Properties ◽  
Risk Aggregation ◽  
Popular Classes

The notion of “tail risk” has been a crucial consideration in modern risk management and financial regulation, as very well documented in the recent regulatory documents. To achieve a comprehensive understanding of the tail risk, we carry out an axiomatic study for risk measures that quantify the tail risk, that is, the behaviour of a risk beyond a certain quantile. Such risk measures are referred to as tail risk measures in this paper. The two popular classes of regulatory risk measures in banking and insurance, value at risk (VaR) and expected shortfall, are prominent, yet elementary, examples of tail risk measures. We establish a connection between a tail risk measure and a corresponding law-invariant risk measure, called its generator, and investigate their joint properties. A tail risk measure inherits many properties from its generator, but not subadditivity or convexity; nevertheless, a tail risk measure is coherent if and only if its generator is coherent. We explore further relevant issues on tail risk measures, such as bounds, distortion risk measures, risk aggregation, elicitability, and dual representations. In particular, there is no elicitable tail convex risk measure other than the essential supremum, and under a continuity condition, the only elicitable and positively homogeneous monetary tail risk measures are the VaRs.

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 Measurement of Commodity Price Risk: an overview of Brazilian agricultural markets

2017 ◽  
Vol 55 (3) ◽  
pp. 515-532
Author(s):  
Daniel Henrique Dario Capitani ◽  
Fabio Mattos
Keyword(s):  
At Risk ◽  
Value At Risk ◽  
Risk Measures ◽  
Commodity Price ◽  
Downside Risk ◽  
Conditional Value At Risk ◽  
Price Risk ◽  
Agricultural Markets ◽  
Price Variability ◽  
Agricultural Industry

Abstract: This study explores different procedures to estimate price risk in commodity markets. Focusing on Brazilian agricultural markets, the paper proposes to assess both dispersion and downside risk measures using five different approaches (volatility, coefficient of variation, lower partial moments, value at risk and conditional value at risk). Results suggest that some commodities have large price variability but small downside risk, while other commodities show small price variability and large downside risk. Thus, there is no single answer to the question of which commodity exhibits more price risk, but rather distinct answers depending on how risk is perceived by different individuals. These findings are relevant for agents in the agricultural industry as they affect marketing and risk management decisions and for policy makers involved in support programs to agriculture.

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.

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