Market Risk Measures Research Articles

Forward-Looking Tail Risk Measures

We present an analytical framework for the forward-looking measurement of extreme market risk. In contrast to standard techniques relying on past return data, we propose to extract Value-at-Risk and Expected Shortfall under the physical measure from current option prices. Our empirical evidence suggests that the resulting estimates accurately capture the tail risk of the S&P 500 and that they quickly react to changing market conditions. Compared to dynamic tail risk forecasts driven by past returns, our forward-looking estimates are relatively higher during good times and lower during adverse economic conditions, which could reduce the amplification effects of conventional dynamic risk management policies.

Value-at-Risk and Expected Shortfall When There Is Long Range Dependence

Empirical studies have shown that a large number of financial asset returns exhibit fat tails and are often characterized by volatility clustering and asymmetry. Also revealed as a stylized fact is Long memory or long range dependence in market volatility, with significant impact on pricing and forecasting of market volatility. The implication is that models that accomodate long memory hold the promise of improved long-run volatility forecast as well as accurate pricing of long-term contracts. On the other hand, recent focus is on whether long memory can affect the measurement of market risk in the context of Value-at-Risk (V aR). In this paper, we evaluate the Value-at-Risk (VaR) and Expected Shortfall (ESF) in financial markets under such conditions. We examine one equity portfolio, the British FTSE100 and three stocks of the German DAX index portfolio (Bayer, Siemens and Volkswagen). Classical VaR estimation methodology such as exponential moving average (EMA) as well as extension to cases where long memory is an inherent characteristics of the system are investigated. In particular, we estimate two long memory models, the Fractional Integrated Asymmetric Power-ARCH and the Hyperbolic-GARCH with different error distribution assumptions. Our results show that models that account for asymmetries in the volatility specifications as well as fractional integrated parametrization of the volatility process, perform better in predicting the one-step as well as five-step ahead VaR and ESF for short and long positions than short memory models. This suggests that for proper risk valuation of options, the degree of persistence should be investigated and appropriate models that incorporate the existence of such characteristic be taken into account.

Current volatility as a measure of market risk

The article offers the author's approach to the definition of market risk and specifies its differences from the economic and financial risks. The necessity of taking into account the social component in the analysis of market risk is shown. Two different types of market risk are identified. Convincingly, the article shows the inconsistency of the use of the existing methods for measuring volatility as a measure of market risk, as defined in the article. The article puts forward a new kind of market volatility, which is qualitatively different from the types of volatility considered in the article. By means of the Grassberger-Procaccia entropy, we prove that the measure of current volatility proposed by the author can be adequately used as a measure of market risk. The algorithms of the current volatility measure's use as a quantitative measure of market risk of both types are offered.

Current volatility as a measure of market risk

Current volatility as a measure of market risk

Mixture Of Probabilistic Factor Analyzers For Market Risk Measurement: Empirical Evidence From The Tunisian Foreign Exchange Market

In this paper, we propose a new approach for Basel-Compliant Value-at-Risk (VaR) estimation in financial portfolio risk management, which combines Gaussian Mixture Models with probabilistic factor analysis models. This new mixed specification provides an alternative, compact, model to handle co-movements, heterogeneity and intra-frame correlations in financial data. This results in a model which concurrently performs clustering and dimensionality reduction, and can be considered as a reduced dimension mixture of probabilistic factor analyzers. For maximum likelihood estimation we have used an iterative approach based on the Alternating Expectation Conditional Maximization (AECM) algorithm. Using a set of historical data in a rolling time window, from the Tunisian foreign exchange market, the model structure as well as its parameters are determined and estimated. Then, the fitted model combined with a modified Monte-Carlo simulation algorithm was used to predict the VaR. Through a Backtesting analysis, we found that this new specification exhibits a good fit to the data compared to other competing approaches, improves the accuracy of VaR prediction, possesses more flexibility, and can avoid serious violations when a financial crisis occurs.

Conditional Equity Premium and Aggregate Investment: Is the Stock Market a Sideshow?

We document a strong negative relation between aggregate corporate investment and conditional equity premium estimated from direct stock market risk measures. Consistent with the investment-based asset pricing model, the comovement with conditional equity premium fully accounts for aggregate investment’s market return predictive power. Similarly, conditional equity premium is a significant determinant of classic Tobin’s q measure, although q has much weaker explanatory power for aggregate investment possibly because of its measurement errors. Moreover, the positive relation between aggregate investment and investor sentiment documented in previous studies reflects the fact that both variables correlate closely with conditional equity premium.

Automatic Portmanteau Tests with Applications to Market Risk Management

This article reviews some recent advances in testing for serial correlation, provides Stata code for implementation and illustrates its application to market risk forecast evaluation. The classical and widely used Portamenteau tests and their data-driven versions are the focus of this article. These tests are simple to implement for two reasons: First, the researcher does not need to specify the order of the autocorrelation tested, since the test automatically chooses this number; second, its asymptotic null distribution is chi-square with one degree of freedom, so there is no need of using a bootstrap procedure to estimate the critical values. We illustrate the wide applicability of the methodology with applications to forecast evaluation for market risk measures, such as Value-at-Risk and Expected Shortfall.

The development of downside accounting beta as a measure of risk

This paper develops a new method for measuring market risk called downside accounting beta (DAB). To test the validity of DAB the method is applied to the financial data for 14 food companies listed on the Warsaw Stock Exchange during a 6-year period. DAB calculates how changes in the profitability of the whole sector affects the profitability of a given company. The paper concludes that when calculating DAB using Return on Assets (ROA) and Return on Equity (ROE) there is a positive correlation with market betas. The practical implication of this research is that investors, owners and managers can use DAB to calculate the systematic risk of companies not listed on stock markets and consequently to identify the levels of risk associated with companies within the sector.

Computation of Market Risk Measures with Stochastic Liquidity Horizon

The Basel Committee of Banking Supervision has recently set out the revised standards for minimum capital requirements for market risk. The Committee has focused, among others, on the two key areas of moving from Value-at-Risk (VaR) to Expected Shortfall (ES) and considering a comprehensive incorporation of the risk of market illiquidity by extending the risk measurement horizon. The estimation of the ES for several trading desks and taking into account different liquidity horizons is computationally very involved. We present a novel numerical method to compute the VaR and ES of a given portfolio within the stochastic holding period framework. Two approaches are considered, the delta-gamma approximation, for modelling the change in value of the portfolio as a quadratic approximation of the change in value of the risk factors, and some of the state-of-the-art stochastic processes for driving the dynamics of the log-value change of the portfolio like the Merton jump-diffusion model and the the Kou model. Central to this procedure is the application of the SWIFT method developed for option pricing, that appears to be a very efficient and robust Fourier inversion method for risk management purposes.

The impact of the IRB approach on the risk weights of European banks

We use European Banking Authority (EBA) 2014 stress test data to study the use of the internal ratings based approach (IRB) and the risk weights of European banks. A simple inspection of data at country level reveals significant differences in the use of the IRB approach by banks and in risk weighted asset (RWA) densities. Empirical analysis of these differences is conducted at both the level of bank group and country of exposure. A clearly negative relation is found between use of the IRB approach and RWA densities, even after controlling for portfolio and bank characteristics. The jurisdiction in which a credit exposure is located affects both the use of IRB and risk density. Portfolio variables (default rate, weight of corporate exposures), and bank characteristics (book equity ratio, liquidity measures) are also significantly related to risk weights. The analysis of the dataset also provides some evidence of a relation between RWA density and IRB utilization, and portfolio composition, bank size, and market risk measures (stock return volatility, CDS spreads).

Modeling systemic risk and dependence structure between oil and stock markets using a variational mode decomposition-based copula method

Abstract This study combines the variational mode decomposition (VMD) method and static and time-varying symmetric and asymmetric copula functions to examine the dependence structure between crude oil prices and major regional developed stock markets (S&P500, stoxx600, DJPI and TSX indexes) during bear, normal and bull markets under different investment horizons. Furthermore, it analyzes the upside and downside short- and long-run risk spillovers between oil and stock markets by quantifying three market risk measures, namely the value at risk (VaR), conditional VaR (CoVaR) and the delta CoVaR (∆CoVaR). The results show that there is a tail dependence between oil and all stock markets for the raw return series. By considering time horizons, we show that there is an average dependence between the considered markets for the short-run horizons. However, the tail dependence is also found for the long-run horizons between the oil and stock markets, with the exception of the S&P500 index which exhibits average dependence with the oil market. Moreover, we find strong evidence of up and down risk asymmetric spillovers from oil to stock markets and vice versa in the short-and long run horizons. Finally, the market risk spillovers are asymmetric over the time and investment horizons.

Introducing cybernomics: A unifying economic framework for measuring cyber risk

This is the first in a series of papers on the risk measures and unifying economic framework encompassing the cross-disciplinary field of “Cybernomics”. This is also the first academic paper to formally propose measurement units for cyber risk. In this paper, multidisciplinary methodologies are used to apply proven risk measurement methods in finance and medicine to define novel risk units central to cybernomics. Leveraging established risk units – MicroMort (MM) for measuring medical risk and Value-at-Risk (VaR) for measuring market risk – BitMort (BM) and hekla (named after an Icelandic volcano) are defined as cyber risk units. Risk calculation methods and examples are introduced in this paper to measure cost-effectiveness of control factors, articulate an entity's “willingness-to-pay” (risk pricing) for cyber risk reduction, cyber risk limit, and cyber risk appetite. Built around BM and hekla, cybernomics integrates cyber risk management and economics to study the requirements of a databank in order to improve risk analytics solutions for: 1) the valuation of digital assets; 2) the measurement of risk exposure of digital assets; and 3) the capital optimization for managing residual cyber risk. Establishing adequate, holistic and statistically robust data points on the entity, portfolio and global levels for the development of a cybernomics databank are essential for the resilience of our shared digital future. This paper explains the need to establish data schemes such as International Digital Asset Classification (IDAC) and International Classification of Cyber Incidents (ICCI).

Sufficiency Economy Philosophy and Firm Risks

Using data from Thailand, we designed and created our Sufficiency Economy Philosophy score (SEP score) that measures the extent to which a firm is aligned with Sufficiency Economy Philosophy. We find that our SEP score has a negative relationship with firm-specific risk measured by the standard deviation of residuals from the market model. However we find no relationship between SEP score with neither market risk nor other measures of firms’ performance. The findings support the notion that alignment with Sufficiency Economy Philosophy could reduce risk without sacrificing performance, it leads to sustainability, and that Sufficiency Economy Philosophy practices are well aligned with shareholders’ interests.

To debt or not to debt: Are Islamic banks less risky than conventional banks?

We empirically analyze the market risk profiles of Islamic banks with two sets of conventional banks taken from the same geographical locations as Islamic banks and from a random global sample respectively for the period 2000–2013. Moreover, we divided our sample period into pre-financial crisis, during financial and post financial crisis. Estimates of Value-at-Risk (VaR) and Expected Shortfall (ES) which incorporates losses beyond VaR are used as market risk measures for both univariate and multivariate portfolios. Our key input is the share price by market capitalization of publicly traded banks of similar size in Islamic and non-Islamic countries. Univariate analysis finds no discernible differences between Islamic and conventional banks. However, dynamic correlations obtained via a multivariate setting shows Islamic banks to be less riskier for both sets of conventional banks; and especially so during the recent global financial crisis. The policy implications are: (i) that the inclusion of Islamic banks within asset portfolios may mitigate potential risk; (ii) that the Basel committee should consider the ES measure of risk for Islamic banks in preference to the current VaR methodology, which over-estimates the market risk of Islamic banks.

Multiscale dependence analysis and portfolio risk modeling for precious metal markets

In this paper, we propose a new Bivariate EMD copula based approach to analyze and model the multiscale dependence structure in the precious metal markets. The proposed model constructs the Copula based dependence structure formulation in the Bivariate Empirical Mode Decomposition (BEMD) transformed multiscale domain. We further propose the BEMD Copula based Portfolio Value at Risk (PVaR) model to estimate the precious metal market risk measure. Empirical studies in the typical precious metal markets have been conducted. We found the evidence of multiscale structure of the time varying dependence structure among precious metal markets. We show that significantly improved portfolio risk forecasting performance could be achieved with the proposed model when the multiscale dependence structure is taken into account during the modeling process.

Comparison of methods for estimating the uncertainty of value at risk

Purpose Value at risk (VaR) is a market risk measure widely used by risk managers and market regulatory authorities, and various methods are proposed in the literature for its estimation. However, limited studies discuss its distribution or its confidence intervals. The purpose of this paper is to compare different techniques for computing such intervals to identify the scenarios under which such confidence interval techniques perform properly. Design/methodology/approach The methods that are included in the comparison are based on asymptotic normality, extreme value theory and subsample bootstrap. The evaluation is done by computing the coverage rates for each method through Monte Carlo simulations under certain scenarios. The scenarios consider different persistence degrees in mean and variance, sample sizes, VaR probability levels, confidence levels of the intervals and distributions of the standardized errors. Additionally, an empirical application for the stock market index returns of G7 countries is presented. Findings The simulation exercises show that the methods that were considered in the study are only valid for high quantiles. In particular, in terms of coverage rates, there is a good performance for VaR(99 per cent) and bad performance for VaR(95 per cent) and VaR(90 per cent). The results are confirmed by an empirical application for the stock market index returns of G7 countries. Practical implications The findings of the study suggest that the methods that were considered to estimate VaR confidence interval are appropriated when considering high quantiles such as VaR(99 per cent). However, using these methods for smaller quantiles, such as VaR(95 per cent) and VaR(90 per cent), is not recommended. Originality/value This study is the first one, as far as it is known, to identify the scenarios under which the methods for estimating the VaR confidence intervals perform properly. The findings are supported by simulation and empirical exercises.

Stock Market Risk Measurement Method Based on Improved Genetic Algorithm

Stock Market Risk Measurement Method Based on Improved Genetic Algorithm

Practical Applications of VIX versus Size

What explains the cross-section of returns in the US equity market? <b>Maggie Copeland</b> and <b>Thomas Copeland</b>, Co-Founders of <b>Copeland Valuation Consultants</b>, say that changes in VIX can explain stock returns. Their research shows that forward implied volatility, as measured by the VIX Index, is a key determinant,statistically more important than market cap. The VIX—the “fear gauge”—is a commonly used measure of market risk, a contrarian indicator that spikes when the stock market declines. Using a data sample from the period 2000–2011, the authors find that when the VIX has a positive move, large-cap stocks outperform small-cap stocks, and viceversa. Their finding debunks the commonly held assumption that the size effect always holds true.

LIQUIDITY RISK AND INSTABILITIES IN PORTFOLIO OPTIMIZATION

We show that including a term which accounts for finite liquidity in portfolio optimization naturally mitigates the instabilities that arise in the estimation of coherent risk measures on finite samples. This is because taking into account the impact of trading in the market is mathematically equivalent to introducing a regularization on the risk measure. We show here that the impact function determines which regularizer is to be used. We also show that any regularizer based on the norm [Formula: see text] with [Formula: see text] makes the sensitivity of coherent risk measures to estimation error disappear, while regularizers with [Formula: see text] do not. The [Formula: see text] norm represents a border case: its “soft” implementation does not remove the instability, but rather shifts its locus, whereas its “hard” implementation (including hard limits or a ban on short selling) eliminates it. We demonstrate these effects on the important special case of expected shortfall (ES) which has recently become the global regulatory market risk measure.

Effects of derivatives usage and financial statement items on capital market risk measures of Bank stocks: evidence from India

This paper examines the impact of off-balance sheet derivatives usage by banks combined with financial statement items on their capital market risk measures. Financial markets liberalization policies in the 1990s, led to a surge in investment in Indian banks’ stocks, and therefore, understanding capital market risk is of critical interest to domestic and foreign investors in bank stocks, as well as to bank managers. Using panel data analysis of publicly listed private and public sector banks, our findings indicate that bank size, core capital-to-risk adjusted asset ratio, and interest spread of banks are significantly related to the total return risk of bank stocks. The market risk of bank stocks is significantly positively related to the amount of derivatives usage and to the return on asset ratio of banks. Also, the firm-specific risk component of bank stocks is significantly affected by the volume of total assets, interest spread, and their core capital-to-asset ratio. The interest rate risk exposure of bank stocks is significantly related to the core capital-to-asset ratio, and the interest spread. The off-balance sheet derivatives exposure, bank size, and the core capital to risk adjusted asset ratios are seen to have a significant effect on the overall systematic risk component of the bank stocks. The bank ownership structure, i.e., private versus public sector banks do not have any significant effect on the capital market risk measures.