Portfolio Risk Measures Research Articles

Tail risk in energy portfolios

This article analyzes the tail behavior of energy price risk using a multivariate approach, in which the exposure to energy markets is given by a portfolio of oil, gas, coal, and electricity. To accommodate various dependence and tail decay patterns, this study models energy returns using different generalized hyperbolic conditional distributions and time-varying conditional mean and covariance. Employing daily energy futures data from August 2005 to March 2012, the authors recursively estimate the models and evaluate tail risk measures for the portfolio's profit-and-loss distribution for long and short positions at various horizons and confidence levels. Both in-sample and out-of-sample analyses applied to different energy portfolios show the importance of heavy tails and positive asymmetry in the distribution of energy risk factors. Thus, tail risk measures for energy portfolios based on standard methods (e.g. normality, constant covariance matrix) and on models with exponential tail decay underestimate actual tail risk, especially for short positions and short time horizons.

Estimation of risk measures for large credit portfolios

In this paper saddlepoint techniques are used in the computation of risk measures for large market - to - market credit portfolios with stochastic recovery and correlation between obligors depending on the state of the economy. We compare the efficiency of the saddlepoint approach with existing methods such as plain Monte Carlo simulation and large deviation theory. By measuring run time and accuracy of calculations of the Value at Risk and the conditional Value at Risk for different significance levels we analyze the quality of these approximation approaches. Furthermore the approximation quality over the whole portfolio loss distribution function is analyzed. The results show that the saddlepoint approximation performs not only very fast but also very accurate over the whole loss distribution function. This result is not limited to large portfolios but can also be achieved for small portfolios.

Thinly Traded Securities and Risk Management

Thinly traded securities exist in both emerging and well developed markets. However, plausible estimations of market risk measures for portfolios with infrequently traded securities have not been explored in the literature. We propose a methodology to calculate market risk measures based on the Kalman filter which can be used on incomplete datasets. We implement our approach in a fixed-income portfolio within a thin trading environment. However, a similar approach may be also applied to other markets with thinly traded securities. Our methodology provides reliable market risk measures in portfolios with infrequent trading.

Thinly traded securities and risk management

Thinly traded securities exist in both emerging and well developed markets. However, plausible estimations of market risk measures for portfolios with infrequently traded securities have not been explored in the literature. We propose a methodology to calculate market risk measures based on the Kalman filter which can be used on incomplete datasets. We implement our approach in a fixed-income portfolio within a thin trading environment. However, a similar approach may be also applied to other markets with thinly traded securities. Our methodology provides reliable market risk measures in portfolios with infrequent trading.

Coherent and convex risk measures for portfolios with applications

Abstract In this paper, we propose a framework of risk measures for portfolio vectors, which is an extension of the ones introduced by Burgert and Ruschendorf (2006) and Ruschendorf (2013). Representation results for coherent and convex risk measures for portfolio vectors are provided. Applications to the multi-period risk measures are also given.

Bank Credit Risk Management and Migration Analysis; Conditioning Transition Matrices on the Stage of the Business Cycle

Credit risk has been one of the most active areas of recent financial research. It is driven by advances in portfolio risk measurement and management techniques, growth in credit derivatives trading, the Basel II implementation, and regulatory concerns stemming from the commercial credit crunch that initially took place in 2001 and 2002 in the USA. Within this broader literature, a growing body of research analyzes the meaning, role, and influence of credit ratings that quantify credit risk. This paper examines the two-way links between credit risk measurement and the macroeconomic conditions, interpreted through phases of business cycles. We propose a methodology applied on bank internal rating data, which estimates ratings migration probabilities while integrating the state of the economy. We first discuss the issue of whether credit risk is low or high in different economic scenarios. In order to evaluate this prospect, we examine each year in four quarters that represent different scenarios throughout the year. We then review how macroeconomic considerations are incorporated into credit risk models and the risk measurement approach that underlies Basel II and Basel III.

평균/VaR 최적화 모형에 의한 전환사채 주식전환 비중 결정

In this study we suggested two optimization models to determine conversion weight of convertible bonds. The problem of this study is same as that of Park and Shim [1]. But this study used Value-at-Risk (VaR) for risk measurement instead of CVaR, Conditional-Value-at-Risk. In comparison with conventional Markowitz portfolio models, which use the variance of return, our models used VaR. In 1996, Basel Committee on Banking Supervision recommended VaR for portfolio risk measurement. But there are difficulties in solving optimization models including VaR. Benati and Rizzi [5] proved NP-hardness of general portfolio optimization problems including VaR. We adopted their approach. But we developed efficient algorithms with time complexity O(nlogn) or less for our models. We applied examples of our models to the convertible bond issued by a semiconductor company Hynix.

Robust risk measurement and model risk

Financial risk measurement relies on models of prices and other market variables, but models inevitably rely on imperfect assumptions and estimates, creating model risk. Moreover, optimization decisions, such as portfolio selection, amplify the effect of model error. In this work, we develop a framework for quantifying the impact of model error and for measuring and minimizing risk in a way that is robust to model error. This robust approach starts from a baseline model and finds the worst-case error in risk measurement that would be incurred through a deviation from the baseline model, given a precise constraint on the plausibility of the deviation. Using relative entropy to constrain model distance leads to an explicit characterization of worst-case model errors; this characterization lends itself to Monte Carlo simulation, allowing straightforward calculation of bounds on model error with very little computational effort beyond that required to evaluate performance under the baseline nominal model. This approach goes well beyond the effect of errors in parameter estimates to consider errors in the underlying stochastic assumptions of the model and to characterize the greatest vulnerabilities to error in a model. We apply this approach to problems of portfolio risk measurement, credit risk, delta hedging and counterparty risk measured through credit valuation adjustment.

Contagion effect on bond portfolio risk measures in a hybrid credit risk model

This paper illustrates how modelling the contagion effect among assets of a given bond portfolio changes the risk perception associated to it. This empirical work is developed in a hybrid credit risk framework that incorporates recovery rate risk. Dependence structures among firms and between external shocks affecting firms together are considered. The presence of correlations among firm leverage ratios and the interrelation between default probabilities and recovery rates produces clusters of defaults with low recovery rates. This has a major impact on standard risk measures such as Value-at-Risk and conditional tail expectation. Consequently, an appropriate measurement of the contagion has a tremendous effect on the capital requirement of many financial institutions.

Based on Monte Carlo Simulation Investment Portfolio VaR Risk Analysis

This paper introduces VaR（Value at Risk） principle and uses the Monte Carlo simulation in investment portfolio risk analysis. Monte Carlo simulation may be used to calculate VaR even when a portfolio is strongly non-linear. The procedure of the method is simple and it can provide a great deal of information because it produces the actual distribution of results in the calculation process. One of the main advantages of the Monte Carlo methodology is that it generates a large number of scenarios as a proxy of a wide range of possible future events. The Monte Carlo simulation provides a forward looking approach to compute the risk of a portfolio. This method enhanced investment portfolio risk measure precision and could help mangers to make good decisions. Monte Carlo simulation has the broad prospect in the financial risk management.

Research on Assessment Method for Credit Risk in Commercial Banks of China Based on Data Mining

Due to the huge loss to the bank caused by credit risk in the financial debt crisis of the international Banking industry in 1980s, the research on Credit Assessment Methods is becoming the central issue of the study of financial theory in China and abroad. This paper builded the assets financial evaluation system of credit risk level based on the association rules-Apriori algorithm of data mining technology, which aimed the problems and the serious shortage of risk quantification study in domestic banks credit risk management. At the same time, taking into account the actual situation of our country, this paper analyzed that there are certain difficulties to use modern credit risk measurement models to evaluation the credit risk of commercial banks. And it suggests building a credit portfolio risk measurement model suitable for China's commercial banks with using logistic regression model of data mining technology.

Are Basel II Risk Weights Aligned with Risk?

Using supervisory data for US banks, we evaluate the alignment of Basel II/III AIRB (Advanced Internal Ratings Based) risk estimates with portfolio risk. We use loan performance as a direct measure of portfolio risk as well as less direct market-based measures. Our results document that loan performance is highly correlated with AIRB risk weights and that, in contrast, Basel I risk weights are not reflective of loan performance. We find that capital requirements under the AIRB approach are higher than those under Basel I especially for portfolios recently under stress such as mortgages and some sovereign exposures. The alignment of Basel risk estimates with market-based risk indicators is less robust although, the association is nevertheless stronger for AIRB risk weights relative to Basel I. Our results support the view that internally generated risk weights are determined mostly by portfolio risk and are, as a result, substantially more risk sensitive then the fixed asset type based risk weights of Basel I.

Tail Risk in Energy Portfolios

This article analyzes the tail behavior of energy price risk using a multivariate approach, in which the exposure to energy markets is given by a portfolio of oil, gas, coal, and electricity. To accommodate various dependence and tail decay patterns, this study models energy returns using different generalized hyperbolic conditional distributions and time-varying conditional mean and covariance.Employing daily energy futures data from August 2005 to March 2012, the authors recursively estimate the models and evaluate tail risk measures for the portfolio's profit-and-loss distribution for long and short positions at various horizons and confidence levels. Both in-sample and out-of-sample analysis applied to different energy portfolios show the importance of heavy tails and positive asymmetry in the distribution of energy risk factors. Thus, tail risk measures for energy portfolios based on standard methods (e.g. normality, constant covariance matrix) and on models with exponential tail decay underestimate actual tail risk, especially for short positions and short time horizons.

The Risk Sensitivity of Capital Requirements: Evidence from an International Sample of Large Banks*

Using an international sample of large banks between 2000 and 2010, we evaluate the risk sensitivity of minimum capital requirements. Our results show that risk-weighted assets (the regulatory measure of portfolio risk, which determines minimum capital requirements) are ill-calibrated to a market measure of bank portfolio risk. We show that this low-risk sensitivity of capital requirements permits banks to build up capital buffers by underreporting their portfolio risk and undermines banks’ ability to withstand adverse shocks. While the risk sensitivity of capital requirements is higher for banks that have adopted Basel II, it remains low across banks and countries.

Measuring financial risk and portfolio optimization with a non-Gaussian multivariate model

In this paper, we propose a multivariate market model with returns assumed to follow a multivariate normal tempered stable distribution. This distribution, defined by a mixture of the multivariate normal distribution and the tempered stable subordinator, is consistent with two stylized facts that have been observed for asset distributions: fat-tails and an asymmetric dependence structure. Assuming infinitely divisible distributions, we derive closed-form solutions for two important measures used by portfolio managers in portfolio construction: the marginal VaR and the marginal AVaR. We illustrate the proposed model using stocks comprising the Dow Jones Industrial Average, first statistically validating the model based on goodness-of-fit tests and then demonstrating how the marginal VaR and marginal AVaR can be used for portfolio optimization using the model. Based on the empirical evidence presented in this paper, our framework offers more realistic portfolio risk measures and a more tractable method for portfolio optimization.

Robust Risk Measurement and Model Risk

Financial risk measurement relies on models of prices and other market variables, but models inevitably rely on imperfect assumptions and estimates, creating model risk. Moreover, optimization decisions, such as portfolio selection, amplify the effect of model error. In this work, we develop a framework for quantifying the impact of model error and for measuring and minimizing risk in a way that is robust to model error. This robust approach starts from a baseline model and finds the worst-case error in risk measurement that would be incurred through a deviation from the baseline model, given a precise constraint on the plausibility of the deviation. Using relative entropy to constrain model distance leads to an explicit characterization of worst-case model errors; this characterization lends itself to Monte Carlo simulation, allowing straightforward calculation of bounds on model error with very little computational effort beyond that required to evaluate performance under the baseline nominal model. This approach goes well beyond the effect of errors in parameter estimates to consider errors in the underlying stochastic assumptions of the model and to characterize the greatest vulnerabilities to error in a model. We apply this approach to problems of portfolio risk measurement, credit risk, delta hedging, and counterparty risk measured through credit valuation adjustment.

Conditional Value-at-Risk: An Alternative Measure for Low-Risk Strategies?

In contrast with existing literature that focuses on conditional Value-At-Risk (CVaR) as a portfolio risk measure, we examine here the properties of portfolios built to minimize CVaR. We look into the stability and performance potential of CVaR-optimal portfolios and compare our results with Minimum Variance portfolios. Finally, we run realistic simulations of risk-minimizing strategies using CVaR as risk measure and compare their performances to otherwise identical variance minimizing strategies.

Credit Spreads, Recovery Rates and Bond Portfolio Risk Measures in a Hybrid Credit Risk Model

This paper presents a framework in which many structural credit risk models can be made hybrid by randomizing the default trigger, while keeping the capital structure intact. This produces random recovery rates negatively correlated with the default probability. The approach is implemented on a firm-by-firm basis using maximum likelihood and the unscented Kalman filter (UKF) on each of the 225 companies of the CDX NA IG and HY indices using weekly CDS data from December 2007 to January 2012. Adding the surprise element and the time-varying distribution of recovery rates has a large impact on credit spreads as it modifies both the level and shape of the curves. When a bond portfolio is considered, the presence of dependence among firm leverage ratios and between default probabilities and recovery rates produces clusters of defaults with low recovery rates. It has a major impact on standard risk measures such as Value- at-Risk and conditional tail expectation.

Measuring large comovements in financial markets

A general, copula-based framework for measuring the dependence among financial time series is presented. Particular emphasis is placed on multivariate conditional Spearman's rho (MCS), a new measure of multivariate conditional dependence that describes the association between large or extreme negative returns—so-called tail dependence. We demonstrate that MCS has a number of advantages over conventional measures of tail dependence, both in theory and in practical applications. In the analysis of univariate financial series, data are filtered to remove temporal dependence as a matter of routine. We show that standard filtering procedures may strongly influence the conclusions drawn concerning tail dependence. We give empirical applications to two large data sets of high-frequency asset returns. Our results have immediate implications for portfolio risk management, derivative pricing and portfolio selection. In this context we address portfolio tail diversification and tail hedging. Amongst other aspects, it is shown that the proposed modeling framework improves the estimation of portfolio risk measures such as the value at risk.

Impact of factor models on portfolio risk measures: a structural approach

This paperanalyzes the impact of several popular factor models on the calculation of value-at-risk (VaR) for the loss of a credit portfolio with many obligors. The study covers linear and nonlinear factor models focusing on the importance of tail dependence. The financial crisis, which was an example of an extreme tail event, showed the need for models other than the Gaussian model. We show that, even when controlling for correlation and fat marginal tails among models, the tail dependence has an important impact on VaR and asset allocation. We use the central limit theorem to approximate the loss distribution conditional on the common factors. The efficient frontier and portfolio allocation are provided by optimizing a portfolio of corporate loans. We give evidence that the Gaussian factor model can lead to portfolios with a misleading optimal risk–return trade- off because it does not capture extreme events adequately.