Single‐index and portfolio models for forecasting value‐at‐risk thresholds

The variance of a portfolio can be forecast using a single index model or the covariance matrix of the portfolio. Using univariate and multivariate conditional volatility models, this paper evaluates the performance of the single index and portfolio models in forecasting value‐at‐risk (VaR) thresholds of a portfolio. Likelihood ratio tests of unconditional coverage, independence and conditional coverage of the VaR forecasts suggest that the single‐index model leads to excessive and often serially dependent violations, while the portfolio model leads to too few violations. The single‐index model also leads to lower daily Basel Accord capital charges. The univariate models which display correct conditional coverage lead to higher capital charges than models which lead to too many violations. Overall, the Basel Accord penalties appear to be too lenient and favour models which have too many violations. Copyright © 2008 John Wiley & Sons, Ltd.     

Forecasting value‐at‐risk with a parsimonious portfolio spillover GARCH (PS‐GARCH) model

Accurate modelling of volatility (or risk) is important in finance, particularly as it relates to the modelling and forecasting of value‐at‐risk (VaR) thresholds. As financial applications typically deal with a portfolio of assets and risk, there are several multivariate GARCH models which specify the risk of one asset as depending on its own past as well as the past behaviour of other assets. Multivariate effects, whereby the risk of a given asset depends on the previous risk of any other asset, are termed spillover effects. In this paper we analyse the importance of considering spillover effects when forecasting financial volatility. The forecasting performance of the VARMA‐GARCH model of Ling and McAleer (2003), which includes spillover effects from all assets, the CCC model of Bollerslev (1990), which includes no spillovers, and a new Portfolio Spillover GARCH (PS‐GARCH) model, which accommodates aggregate spillovers parsimoniously and hence avoids the so‐called curse of dimensionality, are compared using a VaR example for a portfolio containing four international stock market indices. The empirical results suggest that spillover effects are statistically significant. However, the VaR threshold forecasts are generally found to be insensitive to the inclusion of spillover effects in any of the multivariate models considered. Copyright © 2008 John Wiley & Sons, Ltd.     

Strategic asset allocation by mixing shrinkage,vine copula and market equilibrium

We propose a new portfolio optimization method combining the merits of the shrinkage estimation, vine copula structure, and Black–Litterman model. It is useful for many investors to satisfy simultaneously the three investment objectives: estimation sensitivity, asymmetric risks appreciation, and portfolio stability. A typical investor with such objectives is a sovereign wealth fund (SWF). We use China's SWF as an example to empirically test the method based on a 15‐asset strategic asset allocation problem. Robustness tests using subsamples not only show the method's overall effectiveness but also manifest that the function of each component is as expected.     

Evaluating predictive performance of value‐at‐risk models in emerging markets: a reality check

We investigate the predictive performance of various classes of value‐at‐risk (VaR) models in several dimensions—unfiltered versus filtered VaR models, parametric versus nonparametric distributions, conventional versus extreme value distributions, and quantile regression versus inverting the conditional distribution function. By using the reality check test of White (2000), we compare the predictive power of alternative VaR models in terms of the empirical coverage probability and the predictive quantile loss for the stock markets of five Asian economies that suffered from the 1997–1998 financial crisis. The results based on these two criteria are largely compatible and indicate some empirical regularities of risk forecasts. The Riskmetrics model behaves reasonably well in tranquil periods, while some extreme value theory (EVT)‐based models do better in the crisis period. Filtering often appears to be useful for some models, particularly for the EVT models, though it could be harmful for some other models. The CaViaR quantile regression models of Engle and Manganelli (2004) have shown some success in predicting the VaR risk measure for various periods, generally more stable than those that invert a distribution function. Overall, the forecasting performance of the VaR models considered varies over the three periods before, during and after the crisis. Copyright © 2006 John Wiley & Sons, Ltd.     

Bayesian Forecasting for Financial Risk Management,Pre and Post the Global Financial Crisis

Value‐at‐risk (VaR) forecasting via a computational Bayesian framework is considered. A range of parametric models is compared, including standard, threshold nonlinear and Markov switching generalized autoregressive conditional heteroskedasticity (GARCH) specifications, plus standard and nonlinear stochastic volatility models, most considering four error probability distributions: Gaussian, Student‐t, skewed‐t and generalized error distribution. Adaptive Markov chain Monte Carlo methods are employed in estimation and forecasting. A portfolio of four Asia–Pacific stock markets is considered. Two forecasting periods are evaluated in light of the recent global financial crisis. Results reveal that: (i) GARCH models outperformed stochastic volatility models in almost all cases; (ii) asymmetric volatility models were clearly favoured pre crisis, while at the 1% level during and post crisis, for a 1‐day horizon, models with skewed‐t errors ranked best, while integrated GARCH models were favoured at the 5% level; (iii) all models forecast VaR less accurately and anti‐conservatively post crisis. Copyright © 2011 John Wiley & Sons, Ltd.     

Nonlinearities in the CAPM: Evidence from Developed and Emerging Markets

This paper examines the forecasting ability of the nonlinear specifications of the market model. We propose a conditional two‐moment market model with a time‐varying systematic covariance (beta) risk in the form of a mean reverting process of the state‐space model via the Kalman filter algorithm. In addition, we account for the systematic component of co‐skewness and co‐kurtosis by considering higher moments. The analysis is implemented using data from the stock indices of several developed and emerging stock markets. The empirical findings favour the time‐varying market model approaches, which outperform linear model specifications both in terms of model fit and predictability. Precisely, higher moments are necessary for datasets that involve structural changes and/or market inefficiencies which are common in most of the emerging stock markets. Copyright © 2016 John Wiley & Sons, Ltd.     

Short-run wavelet-based covariance regimes for applied portfolio management

Decisions on ass et allocations are often determined by covariance estimates from historical market data. In this paper, we introduce a wavelet-based portfolio algorithm, distinguishing between newly embedded news and long-run information that has already been fully absorbed by the market. Exploiting the wavelet decomposition into short- and long-run covariance regimes, we introduce an approach to focus on particular covariance components. Using generated data, we demonstrate that short-run covariance regimes comprise the relevant information for periodical portfolio management. In an empirical application to US stocks and other international markets for weekly, monthly, quarterly, and yearly holding periods (and rebalancing), we present evidence that the application of wavelet-based covariance estimates from short-run information outperforms portfolio allocations that are based on covariance estimates from historical data.     

Forecasting High‐Frequency Risk Measures

This article proposes intraday high‐frequency risk (HFR) measures for market risk in the case of irregularly spaced high‐frequency data. In this context, we distinguish three concepts of value‐at‐risk (VaR): the total VaR, the marginal (or per‐time‐unit) VaR and the instantaneous VaR. Since the market risk is obviously related to the duration between two consecutive trades, these measures are completed with a duration risk measure, i.e. the time‐at‐risk (TaR). We propose a forecasting procedure for VaR and TaR for each trade or other market microstructure event. Subsequently, we perform a backtesting procedure specifically designed to assess the validity of the VaR and TaR forecasts on irregularly spaced data. The performance of the HFR measure is illustrated in an empirical application for two stocks (Bank of America and Microsoft) and an exchange‐traded fund based on Standard & Poor's 500 index. We show that the intraday HFR forecasts capture accurately the volatility and duration dynamics for these three assets. Copyright © 2015 John Wiley & Sons, Ltd.     

Direction‐of‐change forecasting using a volatility‐based recurrent neural network

This paper investigates the profitability of a trading strategy, based on recurrent neural networks, that attempts to predict the direction‐of‐change of the market in the case of the NASDAQ composite index. The sample extends over the period 8 February 1971 to 7 April 1998, while the sub‐period 8 April 1998 to 5 February 2002 has been reserved for out‐of‐sample testing purposes. We demonstrate that the incorporation in the trading rule of estimates of the conditional volatility changes strongly enhances its profitability, after the inclusion of transaction costs, during bear market periods. This improvement is being measured with respect to a nested model that does not include the volatility variable as well as to a buy‐and‐hold strategy. We suggest that our findings can be justified by invoking either the ‘volatility feedback’ theory or the existence of portfolio insurance schemes in the equity markets. Our results are also consistent with the view that volatility dependence produces sign dependence. Copyright © 2008 John Wiley & Sons, Ltd.     

Incorporating higher moments into value‐at‐risk forecasting

Value‐at‐risk (VaR) forecasting generally relies on a parametric density function of portfolio returns that ignores higher moments or assumes them constant. In this paper, we propose a simple approach to forecasting of a portfolio VaR. We employ the Gram‐Charlier expansion (GCE) augmenting the standard normal distribution with the first four moments, which are allowed to vary over time. In an extensive empirical study, we compare the GCE approach to other models of VaR forecasting and conclude that it provides accurate and robust estimates of the realized VaR. In spite of its simplicity, on our dataset GCE outperforms other estimates that are generated by both constant and time‐varying higher‐moments models. Copyright © 2009 John Wiley & Sons, Ltd.     

Backtesting Value‐at‐Risk: A Generalized Markov Test

Testing the validity of value‐at‐risk (VaR) forecasts, or backtesting, is an integral part of modern market risk management and regulation. This is often done by applying independence and coverage tests developed by Christoffersen (International Economic Review, 1998; 39(4), 841–862) to so‐called hit‐sequences derived from VaR forecasts and realized losses. However, as pointed out in the literature, these aforementioned tests suffer from low rejection frequencies, or (empirical) power when applied to hit‐sequences derived from simulations matching empirical stylized characteristics of return data. One key observation of the studies is that higher‐order dependence in the hit‐sequences may cause the observed lower power performance. We propose to generalize the backtest framework for VaR forecasts, by extending the original first‐order dependence of Christoffersen to allow for a higher‐ or kth‐order dependence. We provide closed‐form expressions for the tests as well as asymptotic theory. Not only do the generalized tests have power against kth‐order dependence by definition, but also included simulations indicate improved power performance when replicating the aforementioned studies. Further, included simulations show much improved size properties of one of the suggested tests. Copyright © 2017 John Wiley & Sons, Ltd.     

Using CAViaR Models with Implied Volatility for Value‐at‐Risk Estimation

This paper proposes value‐at risk (VaR) estimation methods that are a synthesis of conditional autoregressive value at risk (CAViaR) time series models and implied volatility. The appeal of this proposal is that it merges information from the historical time series and the different information supplied by the market's expectation of risk. Forecast‐combining methods, with weights estimated using quantile regression, are considered. We also investigate plugging implied volatility into the CAViaR models—a procedure that has not been considered in the VaR area so far. Results for daily index returns indicate that the newly proposed methods are comparable or superior to individual methods, such as the standard CAViaR models and quantiles constructed from implied volatility and the empirical distribution of standardised residuals. We find that the implied volatility has more explanatory power as the focus moves further out into the left tail of the conditional distribution of S&P 500 daily returns. Copyright © 2012 John Wiley & Sons, Ltd.     

On the use of power transformations in CAViaR models

Value at risk (VaR) is a risk measure widely used by financial institutions in allocating risk. VaR forecast estimation involves the conditional evaluation of quantiles based on the currently available information. Recent advances in VaR evaluation incorporate a proxy for conditional variance, yielding the conditional autoregressive VaR (CAViaR) models. However, early work in finance literature has shown that the introduction of power transformations has resulted in improvements in volatility forecasting. Having a direct association between volatility and conditional VaR, we adopt power-transformed CAViaR models. We investigate whether the flexible conditional VaR dynamics associated with power-transformed CAViaR models can result in better forecasting results than those assumed by the nontransformed CAViaR models. Estimation in CAViaR models is based on an early-rejection Markov chain Monte Carlo algorithm. We illustrate our forecasting evaluation results using simulated and financial daily return data series. The results demonstrate that there is strong evidence that supports the use of power-transformed CAViaR models when forecasting VaR.     

The predictability of stock market volatility in emerging economies: Relative roles of local,regional, and global business cycles

This paper explores the role of business cycle proxies, measured by the output gap at the global, regional, and local levels, as potential predictors of stock market volatility in the emerging BRICS nations. We observe that the emerging BRICS nations display a rather heterogeneous pattern when it comes to the relative role of idiosyncratic factors as a predictor of stock market volatility. While domestic output gap is found to capture significant predictive information for India and China particularly, the business cycles associated with emerging economies and the world in general are strongly important for the BRIC countries and weakly for South Africa, especially in the postglobal financial crisis era. The findings suggest that despite the increase in the financial integration of world capital markets, emerging economies can still bear significant exposures to idiosyncratic risk factors, an issue of high importance for the profitability of global diversification strategies.     

International Evidence on GFC‐Robust Forecasts for Risk Management under the Basel Accord

A risk management strategy designed to be robust to the global financial crisis (GFC), in the sense of selecting a value‐at‐risk (VaR) forecast that combines the forecasts of different VaR models, was proposed by McAleer and coworkers in 2010. The robust forecast is based on the median of the point VaR forecasts of a set of conditional volatility models. Such a risk management strategy is robust to the GFC in the sense that, while maintaining the same risk management strategy before, during and after a financial crisis, it will lead to comparatively low daily capital charges and violation penalties for the entire period. This paper presents evidence to support the claim that the median point forecast of VaR is generally GFC robust. We investigate the performance of a variety of single and combined VaR forecasts in terms of daily capital requirements and violation penalties under the Basel II Accord, as well as other criteria. In the empirical analysis we choose several major indexes, namely French CAC, German DAX, US Dow Jones, UK FTSE100, Hong Kong Hang Seng, Spanish Ibex 35, Japanese Nikkei, Swiss SMI and US S&P 500. The GARCH, EGARCH, GJR and RiskMetrics models as well as several other strategies, are used in the comparison. Backtesting is performed on each of these indexes using the Basel II Accord regulations for 2008–10 to examine the performance of the median strategy in terms of the number of violations and daily capital charges, among other criteria. The median is shown to be a profitable and safe strategy for risk management, both in calm and turbulent periods, as it provides a reasonable number of violations and daily capital charges. The median also performs well when both total losses and the asymmetric linear tick loss function are considered Copyright © 2012 John Wiley & Sons, Ltd.     

Exponentially Smoothing the Skewed Laplace Distribution for Value‐at‐Risk Forecasting

Value‐at‐risk (VaR) is a standard measure of market risk in financial markets. This paper proposes a novel, adaptive and efficient method to forecast both volatility and VaR. Extending existing exponential smoothing as well as GARCH formulations, the method is motivated from an asymmetric Laplace distribution, where skewness and heavy tails in return distributions, and their potentially time‐varying nature, are taken into account. The proposed volatility equation also involves novel time‐varying dynamics. Back‐testing results illustrate that the proposed method offers a viable, and more accurate, though conservative, improvement in forecasting VaR compared to a range of popular alternatives. Copyright © 2013 John Wiley & Sons, Ltd.     

A Study of Value‐at‐Risk Based on M‐Estimators of the Conditional Heteroscedastic Models

In this paper, we investigate the performance of a class of M‐estimators for both symmetric and asymmetric conditional heteroscedastic models in the prediction of value‐at‐risk. The class of estimators includes the least absolute deviation (LAD), Huber's, Cauchy and B‐estimator, as well as the well‐known quasi maximum likelihood estimator (QMLE). We use a wide range of summary statistics to compare both the in‐sample and out‐of‐sample VaR estimates of three well‐known stock indices. Our empirical study suggests that in general Cauchy, Huber and B‐estimator have better performance in predicting one‐step‐ahead VaR than the commonly used QMLE. Copyright © 2011 John Wiley & Sons, Ltd.     

Using Firm‐Level Leverage as an Investment Strategy

We use an investment strategy based on firm‐level capital structures. Investing in low‐leverage firms yields abnormal returns of 4.43% per annum. If an investor holds a portfolio of low‐leverage and low‐market‐to‐book‐ratio firms, abnormal returns increase to 16.18% per annum. A portfolio of low leverage and low market risk yields abnormal returns of 6.67% and a portfolio of small firms with low leverage earns 5.37% per annum. We use the Fama‐Macbeth (1973) methodology with modifications. We confirm that portfolios based on low leverage earn higher returns in longer investment horizons. Our results are robust to other risk factors and the risk class of the firm. Copyright © 2011 John Wiley & Sons, Ltd.     

Modeling and forecasting commodity market volatility with long-term economic and financial variables

This paper investigates the time-varying volatility patterns of some major commodities as well as the potential factors that drive their long-term volatility component. For this purpose, we make use of a recently proposed generalized autoregressive conditional heteroskedasticity–mixed data sampling approach, which typically allows us to examine the role of economic and financial variables of different frequencies. Using commodity futures for Crude Oil (WTI and Brent), Gold, Silver and Platinum, as well as a commodity index, our results show the necessity for disentangling the short-term and long-term components in modeling and forecasting commodity volatility. They also indicate that the long-term volatility of most commodity futures is significantly driven by the level of global real economic activity as well as changes in consumer sentiment, industrial production, and economic policy uncertainty. However, the forecasting results are not alike across commodity futures as no single model fits all commodities.     

Selection of Value‐at‐Risk models

Value‐at‐Risk (VaR) is widely used as a tool for measuring the market risk of asset portfolios. However, alternative VaR implementations are known to yield fairly different VaR forecasts. Hence, every use of VaR requires choosing among alternative forecasting models. This paper undertakes two case studies in model selection, for the S&P 500 index and India's NSE‐50 index, at the 95% and 99% levels. We employ a two‐stage model selection procedure. In the first stage we test a class of models for statistical accuracy. If multiple models survive rejection with the tests, we perform a second stage filtering of the surviving models using subjective loss functions. This two‐stage model selection procedure does prove to be useful in choosing a VaR model, while only incompletely addressing the problem. These case studies give us some evidence about the strengths and limitations of present knowledge on estimation and testing for VaR. Copyright © 2003 John Wiley & Sons, Ltd.