Robust asset allocation with conditional value at risk using the forward search

The well‐known Markowitz approach to portfolio allocation, based on expected returns and their covariance, seems to provide questionable results in financial management. One motivation for the pitfall is that financial returns have heavier than Gaussian tails, so the covariance of returns, used in the Markowitz model as a measure of portfolio risk, is likely to provide a loose quantification of the effective risk. Additionally, the Markowitz approach is very sensitive to small changes in either the expected returns or their correlation, often leading to irrelevant portfolio allocations. More recent allocation techniques are based on alternative risk measures, such as value at risk (VaR) and conditional VaR (CVaR), which are believed to be more accurate measures of risk for fat‐tailed distributions. Nevertheless, both VaR and CVaR estimates can be influenced by the presence of extreme returns. In this paper, we discuss sensitivity to the presence of extreme returns and outliers when optimizing the allocation, under the constraint of keeping CVaR to a minimum. A robust and efficient approach, based on the forward search, is suggested. A Monte Carlo simulation study shows the advantages of the proposed approach, which outperforms both robust and nonrobust alternatives under a variety of specifications. The performance of the method is also thoroughly evaluated with an application to a set of US stocks.     

Value-at-Risk via mixture distributions reconsidered

Value-at-Risk (VaR) has evolved as one of the most prominent measures of downside risk in financial markets. Zhang and Cheng [M.-H. Zhang, Q.-S. Cheng, An Approach to VaR for capital markets with Gaussian mixture, Applied Mathematics and Computation 168 (2005) 1079–1085] proposed an approach to VaR for daily returns based on Gaussian mixtures, which have become rather popular in empirical economics and finance since the seminal paper of Hamilton [J.D. Hamilton, A new approach to the economic analysis of nonstationary time series and the business cycle, Econometrica 57 (2) (1989) 357–384]. However, they do not conduct tests to assess the accuracy of the mixture-implied VaR measures. Recently, Guidolin and Timmermann [M. Guidolin, A. Timmermann, Term structure of risk under alternative econometric specifications, Journal of Econometrics, 131 (2006) 285–308] showed that Markov mixture models do well in measuring VaR at a monthly frequency, but the results may not hold for daily returns due to their more pronounced non-Gaussian features. This paper provides an extensive application of various Markov mixture models to VaR for daily returns of major European stock markets, including out-of-sample backtesting. To accommodate the properties of daily returns, we consider both Gaussian and Student’s t mixtures, and we compare the performance of both uni- and multivariate models under different parameter updating schemes. We find that a univariate mixture of two Student’s t distributions performs best overall. However, by the example of the recent turmoil in financial markets, we also highlight a weak point of the approach.     

Estimating Value-at-Risk and Expected Shortfall using the intraday low and range data

Value-at-Risk (VaR) is a popular measure of market risk. To convey information regarding potential exceedances beyond the VaR, Expected Shortfall (ES) has become the risk measure for trading book bank regulation. However, the estimation of VaR and ES is challenging, as it requires the estimation of the tail behaviour of daily returns. In this paper, we take advantage of recent research that develops joint scoring functions for VaR and ES. Using these functions, we present a novel approach to estimating the two risk measures based on intraday data. We focus on the intraday range, which is the difference between the highest and lowest intraday log prices. In contrast to intraday observations, the intraday low and high are widely available for many financial assets. To alleviate the challenge of modelling extreme risk measures, we propose the use of the intraday low series. We draw on a theoretical result for Brownian motion to show that a quantile of the daily returns can be estimated as the product of a constant term and a less extreme quantile of the intraday low returns, which we define as the difference between the lowest log price of the day and the log closing price of the previous day. In view of this, we use estimates of the VaR and ES of the intraday low returns to estimate the VaR and ES of the daily returns. We provide empirical support for the new proposals using data for five stock indices and five individual stocks.     

Heston随机波动率市场中带VaR约束的最优投资策略

本文研究了Heston随机波动率市场下, 基于VaR约束下的动态最优投资组合问题。
假设Heston随机波动率市场由一个无风险资产和一个风险资产构成,投资者的目标为最大化其终端的期望效用。与此同时, 投资者将动态地评估其待选的投资组合的VaR风险,并将其控制在一个可接受的范围之内。本文在合理的假设下,使用动态规划的方法,来求解该问题的最优投资策略。在特定的参数范围内,利用数值方法计算出近似的最优投资策略和相应值函数, 并对结果进行了分析。     

市场风险值VaR的算法与应用

进行金融风险管理时可以将风险划分为四类，即信用风险、经营风险、流动性风险和市场风险。其中市场风险是指金融市场价格（包括股票价格、利率、汇率和大宗可交易商品的价格）波动而引起的未来收益的不确定性。市场风险值VaR(Value at Risk）就是用来评价给定资产所面临的市场风险大小。本文介绍了VaR的定义、相关的计算方法和在证券投资决策中的应用实例。     

Estimating value at risk with semiparametric support vector quantile regression

Value at Risk (VaR) has been used as an important tool to measure the market risk under normal market. Usually the VaR of log returns is calculated by assuming a normal distribution. However, log returns are frequently found not normally distributed. This paper proposes the estimation approach of VaR using semiparametric support vector quantile regression (SSVQR) models which are functions of the one-step-ahead volatility forecast and the length of the holding period, and can be used regardless of the distribution. We find that the proposed models perform better overall than the variance-covariance and linear quantile regression approaches for return data on S&P 500, NIKEI 225 and KOSPI 200 indices.     

Mean–variance analysis of a single supplier and retailer supply chain under a returns policy

In the literature, most of the supply chain coordinating policies target at improving the supply chain’s efficiency in terms of expected cost reduction or expected profit improvement. However, optimizing the expected performance alone cannot guarantee that the realized performance measure will fall within a small neighborhood of its expected value when the corresponding variance is high. Moreover, it ignores the risk aversion of supply chain members which may affect the achievability of channel coordination. As a result, we carry out in this paper a mean–variance (MV) analysis of supply chains under a returns policy. We first propose an MV formulation for a single supplier single retailer supply chain with a newsvendor type of product. The objective of each supply chain decision maker is to maximize the expected profit such that the standard deviation of profit is under the decision maker’s control. We study both the cases with centralized and decentralized supply chains. We illustrate how a returns policy can be applied for managing the supply chains to address the issues such as channel coordination and risk control. Extensive numerical studies are conducted and managerial findings are proposed.     

基于回收期的科技创新项目决策模型分析

回收期方法是一种常用的评价方法.本文通过实物期权思想,对在不确定性下的科技创新项目,论证了回收期方法是合理的,通过本文的计算分析可知,较短的回收期隐含着较少的等待价值,也隐含着较高的单位资本回报.因此,利用回收期方法评价科技创新项目,不仅能得出与NPV方法评价的同样结论,而且还给投资者更多的信息,如几年之内可望收回投资.这对于资本不太雄厚的投资者来说更具有实际的意义,而对于资本雄厚的投资者也提供了能获得更多回报的投资决策评价方法.     

需求可变性降低对均值CVaR约束销售努力决策库存系统的影响

本文运用Levy提出的变换研究需求可变性降低对风险偏好零售商的库存决策、销售努力决策和期望效用的影响,用均值CVaR刻画零售商的风险偏好特性,它包括风险厌恶、风险追求,也具有损失规避的特性。首先,运用该变换定量刻画需求可变性的降低,证明该变换蕴含经典随机占优中的割准则序和二阶随机占优等。其次,给出系统的最优订货量、最优期望效用和最优销售努力水平,得到它们关于风险偏好系数的单调性,并给出降低需求可变性对期望效用的影响。第三,针对风险中性、风险厌恶(最大化CVaR)和风险追求(最小化CVaR)这三种特殊情况得到相应的结果,并给出企业在库存决策和促销决策的管理启示。最后,通过数值例子验证了得到的研究结果并给出相应的管理启示。     

A matrix-based VaR model for risk identification in power supply networks

This paper presents a value-at-risk (VaR) model based on the singular value decomposition (SVD) of a sparsity matrix for voltage risk identification in power supply networks. The matrix-based model provides a more computationally efficient risk assessment method than conventional models such as probability analysis and sensitivity analysis, for example, and provides decision makers in the power supply industry with sufficient information to minimize the risk of network collapse or blackouts. The VaR model is incorporated into a risk identification system (RIS) programmed in the MATLAB environment. The feasibility of the proposed approach is confirmed by performing a series of risk assessment simulations using the standard American Electric Power (AEP) test models (i.e. 14-, 30- and 57-node networks) and a real-world power network (Taiwan power network), respectively. In general, the simulated results confirm the ability of the matrix-based model VaR model to efficient identify risk of power supply networks.     

A conditional-SGT-VaR approach with alternative GARCH models

This paper proposes a conditional technique for the estimation of VaR and expected shortfall measures based on the skewed generalized t (SGT) distribution. The estimation of the conditional mean and conditional variance of returns is based on ten popular variations of the GARCH model. The results indicate that the TS-GARCH and EGARCH models have the best overall performance. The remaining GARCH specifications, except in a few cases, produce acceptable results. An unconditional SGT-VaR performs well on an in-sample evaluation and fails the tests on an out-of-sample evaluation. The latter indicates the need to incorporate time-varying mean and volatility estimates in the computation of VaR and expected shortfall measures.     

A TUTORIAL ON EVALUATING EXPECTED RETURNS FROM RESEARCH FOR FISHERY MANAGEMENT USING BAYES' THEOREM

Traditional methods for evaluating potential or actual returns from research and development include scoring methods, cost-benefit analysis and production-function approaches. The research reported in the present paper complements these traditional methods with the use of statistical decision analysis and Bayesian methods to account explicitly for risk and uncertainty and to capture some of the effects of information evolution. Measurement of the expected returns from research for fishery management is detailed. Both ex post and ex ante evaluation of expected returns are illustrated by deliberately simplified example.     

GlueVaR risk measures in capital allocation applications

GlueVaR risk measures defined by Belles-Sampera et al. (2014) generalize the traditional quantile-based approach to risk measurement, while a subfamily of these risk measures has been shown to satisfy the tail-subadditivity property. In this paper we show how GlueVaR risk measures can be implemented to solve problems of proportional capital allocation. In addition, the classical capital allocation framework suggested by Dhaene et al. (2012) is generalized to allow the application of the Value-at-Risk (VaR) measure in combination with a stand-alone proportional allocation criterion (i.e., to accommodate the Haircut allocation principle). Two new proportional capital allocation principles based on GlueVaR risk measures are defined. An example based on insurance claims data is presented, in which allocation solutions with tail-subadditive risk measures are discussed.     

Stable modeling in energy risk management

High price volatility in energy markets compels the companies to adopt and implement policies for measurement and management of the energy risk. A popular measure of risk exposure is the Value at Risk (VaR). Traditional methods of estimation of VaR used by major energy companies fail to capture the heavy tails and asymmetry of energy returns distributions. We suggest the use of stable distributions for modeling energy return distributions. The results of our study demonstrate that stable modeling captures asymmetry and heavy-tails of returns, and, therefore, provides more accurate estimates of energy VaR.     

Efficient versus inefficient hedging strategies in the presence of financial and longevity (value at) risk

This paper provides a closed-form Value-at-Risk (VaR) for the net exposure of an annuity provider, taking into account both mortality and interest-rate risk, on both assets and liabilities. It builds a classical risk-return frontier and shows that hedging strategies–such as the transfer of longevity risk–may increase the overall risk while decreasing expected returns, thus resulting in inefficient outcomes. Once calibrated to the 2010 UK longevity and bond market, the model gives conditions under which hedging policies become inefficient.     

GARCH模型在股票市场风险计量中的应用

本文以上证综指的日收益率为研究对象,运用GARCH模型簇分析上海股市日收益率波动的条件异方差性,计算每天的V aR值.实证研究表明,GARCH模型的V aR计算方法对我国股市风险的管理有较好的效果.     

均值-VaR模型的一种新解法：鞍点近似、遗传算法

以均值度量收益,方差度量风险的均值.方差模型,广泛应用于资产组合优化.随着对金融风险度量方法研究的不断深入,VaR作为一种简便、易于理解的风险度量方法,在金融企业中得到日益广泛的应用.本文用VaR代替均值-方差模型中的方差,构建了均值-VaR模型应用干投资组合优化.均值-VaR模型是非线性规划,仅当VaR满足凸性和可微性的前提下,满足库恩-塔克条件的解才是全局最优解.本文在CreditRisk+框架下,提出一个在不允许卖空条件下,不需对VaR的性质做出前提假定的新解法:将鞍点近似法用于计算VaR,在资产头寸与VaR之间建立起函数关系,采用遗传算法寻找模型的近似最优解.并用一个债券组合说明该方法的有效性。     

Modeling international investment decisions for financial holding companies

This research analyzes the internationalization process model developed by Johanson and Vahlne and derives two integer programming investment decision models that consider the risk attitudes of investment firms. Johanson and Vahlne’s model provides a starting point for building a model that suits the investment approach and decision making process of financial holding companies. In practice, when firms make an international investment decision, there is a need for a model that can generate outputs based on financial measures such as profit, investment returns, and tolerable levels of risk. Thus, in this paper, Johanson and Vahlne’s concepts are studied and financial managers are interviewed to derive models that match the investment decision procedures of the firms. The model helps firms manage the risks of their investments and derive accurate investment strategies based on investment objectives and constraints.     

t-分布与不同风险度量下有效投资组合及其边缘的相互关系研究

In order to study the effect of different risk measures on the efficient portfolios (frontier) while properly describing the characteristic of return distributions in the stock market, it is assumed in this paper that the joint return distribution of risky assets obeys the multivariate t-distribution. Under the mean-risk analysis framework, the interrelationship of efficient portfolios (frontier) based on risk measures such as variance, value at risk (VaR), and expected shortfall (ES) is analyzed and compared. It is proved that, when there is no riskless asset in the market, the efficient frontier under VaR or ES is a subset of the mean-variance (MV) efficient frontier, and the efficient portfolios under VaR or ES are also MV efficient; when there exists a riskless asset in the market, a portfolio is MV efficient if and only if it is a VaR or ES efficient portfolio. The obtained results generalize relevant conclusions about investment theory, and can better guide investors to make their investment decision.     

STUDY ON THE INTERRELATION OF EFFICIENT PORTFOLIOS AND THEIR FRONTIER UNDER t DISTRIBUTION AND VARIOUS RISK MEASURES

In order to study the effect of different risk measures on the efficient portfolios (frontier) while properly describing the characteristic of return distributions in the stock market, it is assumed in this paper that the joint return distribution of risky assets obeys the multivari-ate t-distribution. Under the mean-risk analysis framework, the interrelationship of efficient portfolios (frontier) based on risk measures such as variance, value at risk (VaR), and expected shortfall (ES) is analyzed and compared. It is proved that, when there is no riskless asset in the market, the efficient frontier under VaR or ES is a subset of the mean-variance (MV) efficient frontier, and the efficient portfolios under VaR or ES are also MV efficient; when there exists a riskless asset in the market, a portfolio is MV efficient if and only if it is a VaR or ES efficient portfolio. The obtained results generalize relevant conclusions about investment theory, and can better guide investors to make their investment decision.