基于VaR的开放式股票型基金市场风险的测量与评价

通过采用半参数法计算投资组合VaR,得到相应VaR的近似置信区间,并结合成分VaR、边际VaR对投资组合vaR进行分解,结果发现,VaR作为风险管理工具同样可以有效应用于开放式股票型基金市场风险的测量与评价.     

Value-at-risk-based risk management: optimal policies and asset prices

This article analyzes optimal, dynamic portfolio and wealth/consumptionpolicies of utility maximizing investors who must also managemarket-risk exposure using Value-at-Risk (VaR). We find thatVaR risk managers often optimally choose a larger exposure torisky assets than non-risk managers and consequently incur largerlosses when losses occur. We suggest an alternative risk-managementmodel, based on the expectation of a loss, to remedy the shortcomingsof VaR. A general-equilibrium analysis reveals that the presenceof VaR risk managers amplifies the stock-market volatility attimes of down markets and attenuates the volatility at timesof up markets.     

Portfolio Diversification Effects of Downside Risk

Risk managers use portfolios to diversify away the unpricedrisk of individual securities. In this article we compare thebenefits of portfolio diversification for downside risk in casereturns are normally distributed with the case of fat-taileddistributed returns. The downside risk of a security is decomposedinto a part which is attributable to the market risk, an idiosyncraticpart, and a second independent factor. We show that the fat-tailed-baseddownside risk, measured as value-at-risk (VaR), should declinemore rapidly than the normal-based VaR. This result is confirmedempirically.     

Active portfolio management with benchmarking: A frontier based on alpha

Active portfolio management often involves the objective of selecting a portfolio with minimum tracking error variance (TEV) for some expected gain in return over a benchmark. However, Roll (1992) shows that such portfolios are generally suboptimal because they do not belong to the mean-variance frontier and are thus overly risky. Our paper proposes an appealing method to lessen this suboptimality that involves the objective of selecting a portfolio from the set of portfolios that have minimum TEV for various levels of ex-ante alpha, which we refer to as the alpha-TEV frontier. Since practitioners commonly use ex-post alpha to assess the performance of managers, the use of this frontier aligns the objectives of managers with how their performance is evaluated. Furthermore, sensible choices of ex-ante alpha lead to the selection of portfolios that are less risky (in variance terms) than the portfolios that active managers would otherwise select.     

Portfolio selection based on the mean–VaR efficient frontier

Value-at-Risk (VaR) has become one of the standard measures for assessing risk not only in the financial industry but also for asset allocations of individual investors. The traditional mean–variance framework for portfolio selection should, however, be revised when the investor's concern is the VaR instead of the standard deviation. This is especially true when asset returns are not normal. In this paper, we incorporate VaR in portfolio selection, and we propose a mean–VaR efficient frontier. Due to the two-objective optimization problem that is associated with the mean–VaR framework, an evolutionary multi-objective approach is required to construct the mean–VaR efficient frontier. Specifically, we consider the elitist non-dominated sorting Genetic Algorithm (NSGA-II). From our empirical analysis, we conclude that the risk-averse investor might inefficiently allocate his/her wealth if his/her decision is based on the mean–variance framework.     

Nonlinear portfolio selection using approximate parametric Value-at-Risk

As the skewed return distribution is a prominent feature in nonlinear portfolio selection problems which involve derivative assets with nonlinear payoff structures, Value-at-Risk (VaR) is particularly suitable to serve as a risk measure in nonlinear portfolio selection. Unfortunately, the nonlinear portfolio selection formulation using VaR risk measure is in general a computationally intractable optimization problem. We investigate in this paper nonlinear portfolio selection models using approximate parametric Value-at-Risk. More specifically, we use first-order and second-order approximations of VaR for constructing portfolio selection models, and show that the portfolio selection models based on Delta-only, Delta–Gamma-normal and worst-case Delta–Gamma VaR approximations can be reformulated as second-order cone programs, which are polynomially solvable using interior-point methods. Our simulation and empirical results suggest that the model using Delta–Gamma-normal VaR approximation performs the best in terms of a balance between approximation accuracy and computational efficiency.     

Dynamic mean–VaR portfolio selection in continuous time

The value-at-risk (VaR) is one of the most well-known downside risk measures due to its intuitive meaning and wide spectra of applications in practice. In this paper, we investigate the dynamic mean–VaR portfolio selection formulation in continuous time, while the majority of the current literature on mean–VaR portfolio selection mainly focuses on its static versions. Our contributions are twofold, in both building up a tractable formulation and deriving the corresponding optimal portfolio policy. By imposing a limit funding level on the terminal wealth, we conquer the ill-posedness exhibited in the original dynamic mean–VaR portfolio formulation. To overcome the difficulties arising from the VaR constraint and no bankruptcy constraint, we have combined the martingale approach with the quantile optimization technique in our solution framework to derive the optimal portfolio policy. In particular, we have characterized the condition for the existence of the Lagrange multiplier. When the opportunity set of the market setting is deterministic, the portfolio policy becomes analytical. Furthermore, the limit funding level not only enables us to solve the dynamic mean–VaR portfolio selection problem, but also offers a flexibility to tame the aggressiveness of the portfolio policy.     

How does the choice of Value-at-Risk estimator influence asset allocation decisions?

Considering the growing need for managing financial risk, Value-at-Risk (VaR) prediction and portfolio optimisation with a focus on VaR have taken up an important role in banking and finance. Motivated by recent results showing that the choice of VaR estimator does not crucially influence decision-making in certain practical applications (e.g. in investment rankings), this study analyses the important question of how asset allocation decisions are affected when alternative VaR estimation methodologies are used. Focusing on the most popular, successful and conceptually different conditional VaR estimation techniques (i.e. historical simulation, peak over threshold method and quantile regression) and the flexible portfolio model of Campbell et al. [J. Banking Finance. 2001, 25(9), 1789–1804], we show in an empirical example and in a simulation study that these methods tend to deliver similar asset weights. In other words, optimal portfolio allocations appear to be not very sensitive to the choice of VaR estimator. This finding, which is robust in a variety of distributional environments and pre-whitening settings, supports the notion that, depending on the specific application, simple standard methods (i.e. historical simulation) used by many commercial banks do not necessarily have to be replaced by more complex approaches (based on, e.g. extreme value theory).     

Emerging markets and portfolio foreign exchange risk: An empirical investigation using a value-at-risk decomposition technique

The correlation between a portfolio's equity and foreign exchange components plays a role in reducing foreign exchange exposure. Investors must account for this correlation when determining the extent of foreign exchange risk in emerging market equity portfolio investments. This study employs a VaR risk factor mapping technique, under the variance–covariance VaR approach, to decompose portfolio risk in Argentina, Brazil, China, India, Mexico and Russia. For comparison purposes, the same technique is used to decompose portfolio risk in the US. The study is conducted from the perspective of a European equity investor with a portfolio of equities in each country. By employing the VaR decomposition technique, the correlation between a portfolio's equity and foreign exchange components is taken into account and portfolio foreign exchange risk is extracted from portfolio systematic risk. Our results uniquely demonstrate significant variation in foreign exchange risk in emerging markets.     

The Effect of VaR Based Risk Management on Asset Prices and the Volatility Smile

Value-at-risk (VaR) has become the standard criterion for assessing risk in the financial industry. Given the widespread usage of VaR, it becomes increasingly important to study the effects of VaR based risk management on the prices of stocks and options. We solve a continuous-time asset pricing model, based on Lucas (1978) and Basak and Shapiro (2001), to investigate these effects. We find that the presence of risk managers tends to reduce market volatility, as intended. However, in some cases VaR risk management undesirably raises the probability of extreme losses. Finally, we demonstrate that option prices in an economy with VaR risk managers display a volatility smile.     

The Impact of Downward Rating Momentum

Rating downgrades are known to make subsequent downgrades more likely. We analyze the impact of this “downward momentum” on credit portfolio risk and bond portfolio management. Using Standard&Poor’s ratings from 1996 to 2005, we apply a novel approach to estimate a transition matrix that is sensitive to previous downgrades and contrast it with an insensitive benchmark matrix. First, we find that, under representative economic conditions, investors who rely on insensitive transition matrices underestimate the momentum-sensitive Value-at-Risk (VaR), on average, by 107 basis points. Second, we show that bond portfolio managers should use our downgrade-sensitive probabilities of default as they seem to be better calibrated than momentum-insensitive estimates.     

Model uncertainty and VaR aggregation

Despite well-known shortcomings as a risk measure, Value-at-Risk (VaR) is still the industry and regulatory standard for the calculation of risk capital in banking and insurance. This paper is concerned with the numerical estimation of the VaR for a portfolio position as a function of different dependence scenarios on the factors of the portfolio. Besides summarizing the most relevant analytical bounds, including a discussion of their sharpness, we introduce a numerical algorithm which allows for the computation of reliable (sharp) bounds for the VaR of high-dimensional portfolios with dimensions d possibly in the several hundreds. We show that additional positive dependence information will typically not improve the upper bound substantially. In contrast higher order marginal information on the model, when available, may lead to strongly improved bounds. Several examples of practical relevance show how explicit VaR bounds can be obtained. These bounds can be interpreted as a measure of model uncertainty induced by possible dependence scenarios.     

Capital allocation for credit portfolios with kernel estimators

Determining the contributions of sub-portfolios or single exposures to portfolio-wide economic capital for credit risk is an important risk measurement task. Often, economic capital is measured as the Value-at-Risk (VaR) of the portfolio loss distribution. For many of the credit portfolio risk models used in practice, the VaR contributions then have to be estimated from Monte Carlo samples. In the context of a partly continuous loss distribution (i.e. continuous except for a positive point mass on zero), we investigate how to combine kernel estimation methods with importance sampling to achieve more efficient (i.e. less volatile) estimation of VaR contributions.     

Portfolio credit-risk optimization

This paper evaluates several alternative formulations for minimizing the credit risk of a portfolio of financial contracts with different counterparties. Credit risk optimization is challenging because the portfolio loss distribution is typically unavailable in closed form. This makes it difficult to accurately compute Value-at-Risk (VaR) and expected shortfall (ES) at the extreme quantiles that are of practical interest to financial institutions. Our formulations all exploit the conditional independence of counterparties under a structural credit risk model. We consider various approximations to the conditional portfolio loss distribution and formulate VaR and ES minimization problems for each case. We use two realistic credit portfolios to assess the in- and out-of-sample performance for the resulting VaR- and ES-optimized portfolios, as well as for those which we obtain by minimizing the variance or the second moment of the portfolio losses. We find that a Normal approximation to the conditional loss distribution performs best from a practical standpoint.     

Value-at-risk capital requirement regulation,risk taking and asset allocation: a mean–variance analysis

In this study, the mean–variance framework is employed to analyze the impact of the Basel value-at-risk (VaR) market risk regulation on the institution's optimal investment policy, the stockholders’ welfare, as well as the tendency of the institution to change the risk profile of the held portfolio. It is shown that with the VaR regulation, the institution faces a new regulated capital market line, which induces resource allocation distortion in the economy. Surprisingly, only when a riskless asset is available does VaR regulation induce the institution to reduce risk. Otherwise, the regulation may induce higher risk, accompanied by asset allocation distortion. On the positive side, the regulation implies an upper bound on the risk the institution takes and it never induces the firm to select an inefficient portfolio. Moreover, when the riskless asset is available, tightening the regulation always increases the amount of maintained eligible capital and decreases risk.     

Optimal Insurance Under the Insurer's VaR Constraint

In this paper, we impose the insurer's Value at Risk (VaR) constraint on Arrow's optimal insurance model. The insured aims to maximize his expected utility of terminal wealth, under the constraint that the insurer wishes to control the VaR of his terminal wealth to be maintained below a prespecified level. It is shown that when the insurer's VaR constraint is binding, the solution to the problem is not linear, but piecewise linear deductible, and the insured's optimal expected utility will increase as the insurer becomes more risk-tolerant. Basak and Shapiro (2001) showed that VaR risk managers often choose larger risk exposures to risky assets. We draw a similar conclusion in this paper. It is shown that when the insured has an exponential utility function, optimal insurance based on VaR constraint causes the insurer to suffer larger losses than optimal insurance without insurer's risk constraint.     

VaR and ES for linear portfolios with mixture of generalized Laplace distributions risk factors

In this paper, we propose an explicit estimation of Value-at-Risk (VaR) and Expected Shortfall (ES) for linear portfolios when the risk factors change with a convex mixture of generalized Laplace distributions (M-GLD). We introduce the dynamics Delta-GLD-VaR, Delta-GLD-ES, Delta-MGLD-VaR and Delta-MGLD-ES, by using conditional correlation multivariate GARCH. The generalized Laplace distribution impose less restrictive assumptions during estimation that should improve the precision of the VaR and ES through the varying shape and fat tails of the risk factors in relation with the historical sample data. We also suggested some areas of application to measure price risk in agriculture, risk management and financial portfolio optimization.     

The effect of downside risk reduction on UK equity portfolios included with Managed Futures Funds

The concept of asymmetric risk estimation has become more widely applied in risk management in recent years with the increased use of Value-at-risk (VaR) methodologies. This paper uses the n-degree lower partial moment (LPM) models, of which VaR is a special case, to empirically analyse the effect of downside risk reduction on UK portfolio diversification and returns. Data on Managed Futures Funds are used to replicate the increasingly popular preference of investors for including hedge funds and fund-of-funds type investments in the UK equity portfolios. The result indicates, however that the potential benefits of fund diversification may deteriorate following reductions in downside risk tolerance levels. These results appear to reinforce the importance of risk (tolerance) perception, particularly downside risk, when making decisions to include Managed Futures Funds in UK equity portfolios as the empirical analysis suggests that this could negatively affect portfolio returns.     

Risk Measurement Performance of Alternative Distribution Functions

This paper evaluates the performance of three extreme value distributions, i.e., generalized Pareto distribution (GPD), generalized extreme value distribution (GEV), and Box‐Cox‐GEV, and four skewed fat‐tailed distributions, i.e., skewed generalized error distribution (SGED), skewed generalized t (SGT), exponential generalized beta of the second kind (EGB2), and inverse hyperbolic sign (IHS) in estimating conditional and unconditional value at risk (VaR) thresholds. The results provide strong evidence that the SGT, EGB2, and IHS distributions perform as well as the more specialized extreme value distributions in modeling the tail behavior of portfolio returns. All three distributions produce similar VaR thresholds and perform better than the SGED and the normal distribution in approximating the extreme tails of the return distribution. The conditional coverage and the out‐of‐sample performance tests show that the actual VaR thresholds are time varying to a degree not captured by unconditional VaR measures. In light of the fact that VaR type measures are employed in many different types of financial and insurance applications including the determination of capital requirements, capital reserves, the setting of insurance deductibles, the setting of reinsurance cedance levels, as well as the estimation of expected claims and expected losses, these results are important to financial managers, actuaries, and insurance practitioners.