Downside risk management and VaR-based optimal portfolios for precious metals,oil and stocks

Value-at-Risk (VaR) is used to analyze the market downside risk associated with investments in six key individual assets including four precious metals, oil and the S&P 500 index, and three diversified portfolios. Using combinations of these assets, three optimal portfolios and their efficient frontiers within a VaR framework are constructed and the returns and downside risks for these portfolios are also analyzed. One-day-ahead VaR forecasts are computed with nine risk models including calibrated RiskMetrics, asymmetric GARCH type models, the filtered Historical Simulation approach, methodologies from statistics of extremes and a risk management strategy involving combinations of models. These risk models are evaluated and compared based on the unconditional coverage, independence and conditional coverage criteria. The economic importance of the results is also highlighted by assessing the daily capital charges under the Basel Accord rule. The best approaches for estimating the VaR for the individual assets under study and for the three VaR-based optimal portfolios and efficient frontiers are discussed. The VaR-based performance measure ranks the most diversified optimal portfolio (Portfolio #2) as the most efficient and the pure precious metals (Portfolio #1) as the least efficient.     

Value at risk models for volatile emerging markets equity portfolios

This paper investigates the issue of market risk quantification for emerging and developed market equity portfolios. A very wide spectrum of popular and widely used in practice Value at Risk (VaR) models are evaluated and compared with Extreme Value Theory (EVT) and adaptive filtered models, during normal, crises, and post-crises periods. The results are interesting and indicate that despite the documented differences between emerging and developed markets, the most successful VaR models are common for both asset classes. Furthermore, in the case of the (fatter tailed) emerging market equity portfolios, most VaR models turn out to yield conservative risk forecasts, in contrast to developed market equity portfolios, where most models underestimate the realized VaR. VaR estimation during periods of financial turmoil seems to be a difficult task, particularly in the case of emerging markets and especially for the higher loss quantiles. VaR models seem to be affected less by crises periods in the case of developed markets. The performance of the parametric (non-parametric) VaR models improves (deteriorates) during post-crises periods due to the inclusion of extreme events in the estimation sample.     

Optimal insurance contract under VaR and CVaR constraints

This study endogenously develops an optimal insurance contractual form for maximizing insured expected utility under VaR and CVaR constraints. We find that CVaR constraint does not affect the contractual form, but may increase minimum insurance premium requirement. Additionally, when the VaR constraint is binding, the optimal contract is a double deductible insurance. However, if the contract is restricted to a regular form (both indemnity schedule and retained loss schedule are continuously nondecreasing) for avoiding moral hazard problem, the optimal contract is a piecewise linear deductible insurance. Finally, we provide intuitive comparison between this study result and relevant studies.     

Interpreting Value at Risk (VaR) forecasts

Value at Risk (VaR) forecasts have been increasingly accepted globally by both risk managers and regulators as a tool to identify and control exposure to financial market risk. However, modern portfolios are characterized by a constantly changing composition of security holdings that reflect portfolio managers’ strategies, expected prices, and net cash flows into the portfolio. As a result of these factors, portfolio returns are time-varying mixtures of distributions which are unlikely to be well approximated by conventional methods.     

基于极值分布理论的VaR与ES度量

本文应用极值分布理论对金融收益序列的尾部进行估计,计算收益序列的在险价值VaR和预期不足ES来度量市场风险。通过伪最大似然估计方法估计的GARCH模型对收益数据进行拟合,应用极值理论中的GPD对新息分布的尾部建模,得到了基于尾部估计产生收益序列的VaR和ES值。采用上证指数日对数收益数据为样本,得到了度量条件极值和无条件极值下VaR和ES的结果。实证研究表明:在置信水平很高(如99%)的条件下,采用极值方法度量风险值效果更好。而置信水平在95%下,其他方法和极值方法结合效果会很好。用ES度量风险能够使我们了解不利情况发生时风险的可能情况。     

Has the Basel Accord improved risk management during the global financial crisis?

The Basel II Accord requires that banks and other Authorized Deposit-taking Institutions (ADIs) communicate their daily risk forecasts to the appropriate monetary authorities at the beginning of each trading day, using one or more risk models to measure Value-at-Risk (VaR). The risk estimates of these models are used to determine capital requirements and associated capital costs of ADIs, depending in part on the number of previous violations, whereby realised losses exceed the estimated VaR. In this paper we define risk management in terms of choosing from a variety of risk models, and discuss the selection of optimal risk models. A new approach to model selection for predicting VaR is proposed, consisting of combining alternative risk models, and we compare conservative and aggressive strategies for choosing between VaR models. We then examine how different risk management strategies performed during the 2008–09 global financial crisis. These issues are illustrated using Standard and Poor's 500 Composite Index.     

The Cost Effectiveness of the UK's Sovereign Debt Portfolio*

This paper provides a recursive empirical analysis of the scope for cost minimization in public debt management when the debt manager faces a given short‐term interest rate dictated by monetary policy as well as risk and market impact constraints. It simulates the ‘real‐time’ interest costs of alternative portfolios for UK government debt between April 1985 and March 2000. These portfolios are constructed using forecasts of return spreads based on a recursive modelling procedure. While we find statistically significant evidence of predictability, the interest cost savings are quite small when portfolio shares are constrained to lie within historical bounds.     

Fat tails,VaR and subadditivity

Financial institutions rely heavily on Value-at-Risk (VaR) as a risk measure, even though it is not globally subadditive. First, we theoretically show that the VaR portfolio measure is subadditive in the relevant tail region if asset returns are multivariate regularly varying, thus allowing for dependent returns. Second, we note that VaR estimated from historical simulations may lead to violations of subadditivity. This upset of the theoretical VaR subadditivity in the tail arises because the coarseness of the empirical distribution can affect the apparent fatness of the tails. Finally, we document a dramatic reduction in the frequency of subadditivity violations, by using semi-parametric extreme value techniques for VaR estimation instead of historical simulations.     

Long run peso/dollar exchange rates and extreme value behavior: Value at Risk modeling

We apply an extended VaR integrating a generalized extreme value distribution to estimate potential losses from investing in the peso/dollar exchange market using daily data for the period 1970–2007; the block maxima approach is used to minimize impact from dependency in prices due to the presence of heteroscedasticity. Estimations are presented for short and long positions. Our evidence confirms the potential of the GEVD to explain the extreme behavior from exchange rates. It also supports the hypothesis that EVT is a more precise and conservative approach estimation than conventional VaR. Backtesting is used to gauge robustness of the results.     

Value‐at‐risk for long and short trading positions

In this paper we model Value‐at‐Risk (VaR) for daily asset returns using a collection of parametric univariate and multivariate models of the ARCH class based on the skewed Student distribution. We show that models that rely on a symmetric density distribution for the error term underperform with respect to skewed density models when the left and right tails of the distribution of returns must be modelled. Thus, VaR for traders having both long and short positions is not adequately modelled using usual normal or Student distributions. We suggest using an APARCH model based on the skewed Student distribution (combined with a time‐varying correlation in the multivariate case) to fully take into account the fat left and right tails of the returns distribution. This allows for an adequate modelling of large returns defined on long and short trading positions. The performances of the univariate models are assessed on daily data for three international stock indexes and three US stocks of the Dow Jones index. In a second application, we consider a portfolio of three US stocks and model its long and short VaR using a multivariate skewed Student density. Copyright © 2003 John Wiley & Sons, Ltd.     

Risk dependence and cointegration between pharmaceutical stock markets: The case of China and the USA

This paper analyses risk-integration and the degree of dependence between the Values-at-Risk (VaRs) estimates for the two major pharmaceutical stock markets in the world: USA and China. To do this, we study the dependence and fractional cointegration properties among risks. Using daily returns for an eleven-year period, we estimated the VaRs obtained for pharmaceutical market portfolios in China (Shanghai) and the USA (NYSE) using the market model and considering both long and short trading positions. We conclude that the Shanghai pharmaceutical market is riskier than NYSE, although is predictable and losses in both markets exhibit tail dependence between VaR estimates. Particularly, there is lower tail VaR dependence for long position and upper tail dependence for short positions, both being small and fairly constant. On the other hand, we have not found fractional cointegration between risks, suggesting that China’s pharmaceutical sector is not integrated into the global pharmaceutical market.     

Model choice and value-at-risk estimation

Value at risk (VaR) is a commonly used tool to measure market risk. In this paper, we discuss the problems of model choice and VaR performance. The VaRs of daily returns of the Shanghai and Shenzhen indexes are calculated using equally weighted moving average (EQMA), exponentially weighted moving average (EWMA), GARCH(1,1), empirical density estimation method, and the Pareto-type extreme-value distribution methods. Considering the length of the window and the requirement for adequate capital, back testing indicates that the Pareto-type extreme-value distribution method reflects the real market risk more accurately than the other models.     

一种多资产组合风险度量解决之道：正则藤Copula

为准确地度量包含有多项金融资产的组合的风险,本文提出使用一种新的高维Copula构建方法,正则藤Copula（Canonical Vine Copula）,来对多资产间的非线性相关结构进行建模,该函数呈现为一个以一系列成对Copula函数作为节点的“藤”的层叠结构。本文基于上海、香港和台湾三个股票市场对构建该高维Copula函数时各个节点上成对Copula函数类型的选取进行了讨论,并证实了正则藤Copula函数相比传统的多元Copula函数能够更灵活地描述各市场间尾部相关性的复杂形式。样本外风险预测绩效分析和模拟研究均表明,使用正则藤Copula函数确实能够更为稳健和准确地预测组合VaR。     

基于GARCH类模型的权证时变VaR值估计

由于权证收益率分布具有尖峰厚尾和非对称性的特征，其市场风险的估算运用GARCH类模型比较合适。本文选取包钢JTB1的日收盘价格序列为样本，分别用EGARCH、TGARCH模型估计样本期间内日VaR值，并进行了比较。结果表明，EGARCH模型较好地预测了损失结果，而TGARCH模型则低估了风险。因此，基于EGARCH模型对VaR值的计算能更好地反映权证收益率的波动特征和准确预计损失，可以为权证的风险管理提供较为可靠的风险度量工具。     

Option pricing and replication with transaction costs and dividends

This paper derives optimal perfect hedging portfolios in the presence of transaction costs within the binomial model of stock returns, for a market maker that establishes bid and ask prices for American call options on stocks paying dividends prior to expiration. It is shown that, while the option holder's optimal exercise policy at the ex-dividend date varies according to the stock price, there are intervals of values for such a price where the optimal policy would depend on the holder's preferences. Nonetheless, the perfect hedging assumption still allows the derivation of optimal hedging portfolios for both long and short positions of a market maker on the option.     

Do Power GARCH models really improve value-at-risk forecasts?

Traditional heteroskedastic models either rely on the specification of the conditional variance as in Bollerslev (1986) or on a direct modeling of the conditional standard deviation as in Taylor (1986). With its endogenous estimation of the optimal power transformation, the Power GARCH (PGARCH) of Ding, Granger, and Engle (1993) represents a flexible alternative that also nests the previous competing families. Building on a “dynamic” estimation and out-of-sample tests, the current paper undertakes a comparison of the three models in a value-at-risk setting. Despite existing fluctuations in the optimal power transformation obtained with the Ding, Granger, and Engle model, our empirical investigations suggest that the parameter is rarely found different from one or two. Although the volatility dynamics may switch from Taylor's to Bollerslev's specification during the life of the future contract, the measures of accuracy and efficiency used to assess the performance of VaR forecasts indicate that the additional flexibility brought by the PGARCH model provides little, if any, improvement for risk management. *** DIRECT SUPPORT *** A00DH023 00004     

Forecast combinations for value at risk and expected shortfall

Combining provides a pragmatic way of synthesising the information provided by individual forecasting methods. In the context of forecasting the mean, numerous studies have shown that combining often leads to improvements in accuracy. Despite the importance of the value at risk (VaR), though, few papers have considered quantile forecast combinations. One risk measure that is receiving an increasing amount of attention is the expected shortfall (ES), which is the expectation of the exceedances beyond the VaR. There have been no previous studies on combining ES predictions, presumably due to there being no suitable loss function for ES. However, it has been shown recently that a set of scoring functions exist for the joint estimation or backtesting of VaR and ES forecasts. We use such scoring functions to estimate combining weights for VaR and ES prediction. The results from five stock indices show that combining outperforms the individual methods for the 1% and 5% probability levels.     

Impact of value-at-risk models on market stability

Financial institutions around the world use value-at-risk (VaR) models to manage their market risk and calculate their capital requirements under Basel Accords. VaR models, as any other risk management system, are meant to keep financial institutions out of trouble by, among other things, guiding investment decisions within established risk limits so that the viability of a business is not put unduly at risk in a sharp market downturn. However, some researchers have warned that the widespread use of VaR models creates negative externalities in financial markets, as it can feed market instability and result in what has been called endogenous risk, that is, risk caused and amplified by the system itself, rather than being the result of an exogenous shock. This paper aims at analyzing the potential of VaR systems to amplify market disturbances with an agent-based model of fundamentalist and technical traders which manage their risk with a simple VaR model and must reduce their positions when the risk of their portfolio goes above a given threshold. We analyse the impact of the widespread use of VaR systems on different financial instability indicators and confirm that VaR models may induce a particular price dynamics that rises market volatility. These dynamics, which we have called `VaR cycles’, take place when a sufficient number of traders reach their VaR limit and are forced to simultaneously reduce their portfolio; the reductions cause a sudden price movement, raise volatility and force even more traders to liquidate part of their positions. The model shows that market is more prone to suffer VaR cycles when investors use a short-term horizon to calculate asset volatility or a not-too-extreme value for their risk threshold.     

Nonparametric expected shortfall forecasting incorporating weighted quantiles

A new semi-parametric expected shortfall (ES) estimation and forecasting framework is proposed. The proposed approach is based on a two-step estimation procedure. The first step involves the estimation of value at risk (VaR) at different quantile levels through a set of quantile time series regressions. Then, the ES is computed as a weighted average of the estimated quantiles. The quantile weighting structure is parsimoniously parameterized by means of a beta weight function whose coefficients are optimized by minimizing a joint VaR and ES loss function of the Fissler–Ziegel class. The properties of the proposed approach are first evaluated with an extensive simulation study using two data generating processes. Two forecasting studies with different out-of-sample sizes are then conducted, one of which focuses on the 2008 Global Financial Crisis period. The proposed models are applied to seven stock market indices, and their forecasting performances are compared to those of a range of parametric, non-parametric, and semi-parametric models, including GARCH, conditional autoregressive expectile (CARE), joint VaR and ES quantile regression models, and a simple average of quantiles. The results of the forecasting experiments provide clear evidence in support of the proposed models.