Assessing dependence between financial market indexes using conditional time-varying copulas: applications to Value at Risk (VaR)

We analyse the dynamic dependence structure between broad stock market indexes from the United States (S&P500), Britain (FTSE100), Brazil (BOVESPA) and Mexico (PCMX). We employ Patton’s [Int. Econ. Rev., 2006, 2, 527–556] conditional copula setting and additionally observe the impact of different copula functions on Value at Risk (VaR) estimation. We conclude that the dependence between BOVESPA and the other indexes has intensified since the beginning of 2007. In our case the particular copula form is not crucial for VaR estimation. A goodness-of-fit test based on the parametric bootstrap is also applied. The best fits are obtained via time constant Student-t and time-varying Normal copulas.     

A smooth non-parametric estimation framework for safety-first portfolio optimization

In this paper, we adopt a smooth non-parametric estimation to explore the safety-first portfolio optimization problem. We obtain a non-parametric estimation calculation formula for loss (truncated) probability using the kernel estimator of the portfolio returns’ cumulative distribution function, and embed it into two types of safety-first portfolio selection models. We numerically and empirically test our non-parametric method to demonstrate its accuracy and efficiency. Cross-validation results show that our non-parametric kernel estimation method outperforms the empirical distribution method. As an empirical application, we simulate optimal portfolios and display return-risk characteristics using China National Social Security Fund strategic stocks and Shanghai Stock Exchange 50 Index components.     

Factor investing and currency portfolio management

Currency-specific pricing factors are pervasive in international asset pricing. However, portfolio and risk management based on forex factors, instead of individual currencies, are rarely discussed. This paper tries to fill this gap by modelling dynamic correlations and non-normality among forex factors. By considering the four most popular forex factors: the dollar risk factor, the carry trade factor, the currency momentum factor, and the currency value factor, we find that a dynamic conditional correlation copula (DCC-copula) model with skewed-t kernel fits the joint distribution well. We show that, for risk-averse investors who focus on factor investing or employ the forex factors to resize the specific risk exposure, ignoring the tail dependence structure of forex factors brings significant costs.     

Long-term U.S. infrastructure returns and portfolio selection

Our understanding of the long-term return behavior and portfolio characteristics of public infrastructure investments is limited by a relatively short history of empirical data. We re-construct U.S. listed infrastructure index returns by mapping their monthly performance to received systematic and industry risk factors from 1927 through 2010. Our findings reveal that the infrastructure returns in recent years may understate the tail-risk that investors could experience over the long-term, however, this tail-risk is commensurate with holding a broad portfolio of U.S. stocks. For mean-variance and mean-CVaR investors, we report the benefits of holding public infrastructure assets in investment portfolios.     

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.     

Applying VaR to REITs: A comparison of alternative methods

This study employs five methods to calculate the VaR of twelve REITs portfolios and evaluates the accuracy of these methods. Firstly, we find that the VaR varies among individual portfolios. The Hotel REITs has consistently the largest VaR. The low-leveraging portfolio tends to have the largest VaR measured by the parametric methods, while the high leveraging portfolio has the largest VaR calculated by the non-parametric methods. Secondly, each method performs differently at different confidence levels, and no method dominates the others. At the 95% confidence level, the EWMA method performs relatively well. The EQWMA and the two non-parametric methods perform equivalently and slightly overestimate VaRs. The EQWMA_T method ranks the bottom and significantly overestimates VaRs for all portfolios. At the 99% confidence level, the EQWMA method performs the best. The EQWMA_T and the two non-parametric methods perform equivalently and may overestimate VaR for all portfolios. The EWMA method turns out to be the worst and tends to underestimate the VaR. These findings may provide more insights for institutional real estate investors.     

基于VaR模型的商业银行体系系统性风险研究

本文以中国2016年之前上市商业银行作为中国银行业的代表,测算银行业系统性 风险VaR。整体来讲,我国银行业系统性风险较低,但VaR在2015年较高。虽如此,我国银行业资本持有量能够抵御银行体系的系统性风险。在系统性风险VaR贡献度方面,本文实证分析表明,在样本期间内,浦发银行、中国银行、农业银行、交通银行贡献度较高。银行体系系统 性风险VaR受GDP增长率和沪深300指数收益率的显著影响。     

A synthetic factor approach to the estimation of value-at-risk of a portfolio of interest rate swaps

In this paper we decompose the interest rate swap yield curves of 10 major currencies into their common factors and find that the first two factors, interpreted as parallel shift and rotation, explain between 97.1% and 98.6% of the variation in the interest rate swap rates across all 10 currencies. The main contribution of the paper however is that we then model these two factors as simplified synthetic factors so that they may be used to develop an innovative approach to the computation of Value-at-Risk (VaR) for a portfolio of interest rate swaps.     

A mean/variance approach to long-term fixed-income portfolio allocation

Abstract

Long-term investments in bonds offer known returns, but with risks corresponding to defaults of the underwriters. The excess return for a risky bond is measured by the spread between the expected yield and the risk-free rate. Similarly, the risk can be expressed in the form of a default spread, measuring the difference between the yield when no default occurs and the expected yield. For zero-coupon bonds and for actual market data, the default spread is proportional to the probability of default per year. The analysis of market data shows that the yield spread scales as the square root of the default spread. This relation expresses the risk premium over the risk-free rate that the bond market offers, similarly to the risk premium for equities. With these measures for risk and return, an optimal bond allocation scheme can be built following a mean/variance utility function. Straightforward computations allow us to obtain the optimal portfolio, depending on a pre-set risk-aversion level. As for equities, the optimal portfolio is a linear combination of one risk-free bond and a risky portfolio. Using the scaling law for the default spread allows us to obtain simple expressions for the value, yield and risk of the optimal portfolio.     

Optimal portfolio allocation under the probabilistic VaR constraint and incentives for financial innovation

We characterize the investor’s optimal portfolio allocation subject to a budget constraint and a probabilistic VaR constraint in complete markets environments with a finite number of states. The set of feasible portfolios might no longer be connected or convex, while the number of local optima increases exponentially with the number of states, implying computational complexity. The optimal constrained portfolio allocation may therefore not be monotonic in the state–price density. We propose a type of financial innovation, which splits states of nature, that is shown to weakly enhance welfare, restore monotonicity of the optimal portfolio allocation in the state-price density, and reduce computational complexity. We are grateful to Ken Kavajecz and seminar participants at Harvard Business School, London School of Economics, Maastrict University, ZEI Bonn, and Danske Bank Symposium on Asset allocation and Value-at-Risk: Where Theory Meets Practice for comments on an earlier version of this paper. We also benefitted from the suggestions of two anonymous referees. Our papers can be downloaded from www.RiskResearch.org.     

Semiparametric estimation of multi-asset portfolio tail risk

When correlations between assets turn positive, multi-asset portfolios can become riskier than single assets. This article presents the estimation of tail risk at very high quantiles using a semiparametric estimator which is particularly suitable for portfolios with a large number of assets. The estimator captures simultaneously the information contained in each individual asset return that composes the portfolio, and the interrelation between assets. Noticeably, the accuracy of the estimates does not deteriorate when the number of assets in the portfolio increases. The implementation is as easy for a large number of assets as it is for a small number. We estimate the probability distribution of large losses for the American stock market considering portfolios with ten, fifty and one hundred assets of stocks with different market capitalization. In either case, the approximation for the portfolio tail risk is very accurate. We compare our results with well known benchmark models.     

Reduction of estimation risk in optimal portfolio choice using redundant constraints

It is well known that when the moments of the distribution governing returns are estimated from sample data, the out-of-sample performance of the optimal solution of a mean–variance (MV) portfolio problem deteriorates as a consequence of the so-called “estimation risk”. In this document we provide a theoretical analysis of the effects caused by redundant constraints on the out-of-sample performance of optimal MV portfolios. In particular, we show that the out-of-sample performance of the plug-in estimator of the optimal MV portfolio can be improved by adding any set of redundant linear constraints. We also illustrate our findings when risky assets are equally correlated and identically distributed. In this specific case, we report an emerging trade-off between diversification and estimation risk and that the allocation of estimation risk across portfolios forming the optimal solution changes dramatically in terms of number of assets and correlations.     

The selection of multinational equity portfolios: forecasting models and estimation risk

The problem considered is the selection of a portfolio of international assets, particularly the forecasting of the inputs to a selection algorithm. Four models of the asset return generating process are considered, two of which ignore the international nature of the universe of assets, two which exploit it in different ways. Several estimation methods are considered for each component: expected return, variance and covariance of returns. The combinations of model and estimation method are first evaluated in terms of their forecasting performance for the components mentioned for the individual assets. The universe used is the components of the Financial Times Eurotrack 100 Index. Significant differences were found between the forecasting accuracy of the methods considered for each component. In the final stage of the analysis, a comparison of the returns on portfolios chosen using each combination showed a significant difference. The analysis suggests that the choice of estimation method is more critical than the choice of pricing model.     

基于ARCH类模型的VaR方法在外汇风险计量中的应用

本文将残差项服从t分布的ARCH类模型应用于我国外汇风险的计量。通过美元/人民币汇率日波动率VaR值的实证分析发现:(1)ARCH类模型预测得到的VaR值都能很好地拟合美元/人民币汇率日波动率的实际情况,美元/人民币汇率存在明显的ARCH效应;(2)基于ARCH类模型预测的VaR值其计算精度基本上都超过了J.P.Morgan公司RiskMetrics所采用的EWMA模型,这验证了本文选取ARCH类模型以及考虑残差项服从t分布的合理性;(3)ARCH类模型中以TARCH-M(1,1)模型计算结果最为理想。本研究可为金融机构、监管部门以及外汇投资者规避外汇风险提供决策依据和理论参考。     

Haar wavelets-based approach for quantifying credit portfolio losses

This paper proposes a new methodology to compute Value at Risk (VaR) for quantifying losses in credit portfolios. We approximate the cumulative distribution of the loss function by a finite combination of Haar wavelet basis functions and calculate the coefficients of the approximation by inverting its Laplace transform. The Wavelet Approximation (WA) method is particularly suitable for non-smooth distributions, often arising in small or concentrated portfolios, when the hypothesis of the Basel II formulas are violated. To test the methodology we consider the Vasicek one-factor portfolio credit loss model as our model framework. WA is an accurate, robust and fast method, allowing the estimation of the VaR much more quickly than with a Monte Carlo (MC) method at the same level of accuracy and reliability.     

Credit portfolios: What defines risk horizons and risk measurement?

The strong autocorrelation between economic cycles demands that we analyze credit portfolio risk in a multiperiod setup. We embed a standard one-factor model in such a setup. We discuss the calibration of the model to Standard & Poor’s ratings data in detail. But because single-period risk measures cannot capture the cumulative effects of systematic shocks over several periods, we define an alternative risk measure, which we call the time-conditional expected shortfall (TES), to quantify credit portfolio risk over a multiperiod horizon.     

A subjective assessment of approximate probabilities with a portfolio application

This paper extends the assessment of approximate probabilities in two important directions. The first is to investigate some mathematical relations between the probability ranges and derives the most unbiased probability for the case when the limits are subjectively defined. The second is to suggest a simple method to determine the optimal solution which represents the optimal portfolio proportions of securities that possess the minimum risk measured by the maximum entropy measure. The paper considers the derivation of portfolio modeling under a fuzzy situation using probability theory, and provides various other (non-probabilistic) scenarios with their utility in risk modeling. A simple method for identification of mean-entropic frontier is proposed. Then, a comparison of mean-variance procedure with the discrete mean-entropic method is implemented by an example.     

VaR模型及其在寿险公司风险管理中的应用

随着保险产品的创新、竞争的加剧及金融市场的发展,我国寿险公司面临的风险将更为复杂和多样,如何对这些风险进行有效管理是寿险公司面临的重要难题,而VaR模型作为当前国际金融风险管理和金融监管的主流方法,含有丰富的风险管理思想,故对VaR模型进行研究并探讨其在我国寿险公司风险管理中的应用具有一定的现实意义。本文分析了寿险公司应用VaR模型时需注意的问题,并指出我国寿险公司建立基于VaR的风险管理体系需在公司治理结构、风险管理组织架构、风险管理技术、风险数据库等方面加以完善。     

VaR与CVaR在商业银行风险度量中的比较分析及应用

本文系统地阐述了时下银行流行的VaR(ValueatRisk)风险度量技术,并分析了该理论存在的缺陷和使用上的局限性,从而提出以CVaR(ConditionalValueatRisk)模型作为风险度量的替代方法,详细分析了CVaR的原理、特长以及在银行业应用前景,包括风险度量、绩效分析和行为指引等方面的突出作用。最后研究了CVaR在我国商业银行的具体应用。