Risk quantification for commodity ETFs: Backtesting value-at-risk and expected shortfall

This paper calibrates risk assessment of alternative methods for modeling commodity ETFs. We implement recently proposed backtesting techniques for both value-at-risk (VaR) and expected shortfall (ES) under parametric and semi-nonparametric techniques. Our results indicate that skewed-t and Gram-Charlier distributional assumptions present the best relative performance for individual Commodity ETFs for those confidence levels recommended by Basel Accords. In view of these results, we recommend the application of leptokurtic distributions and semi-nonparametric techniques to mitigate regulation concerns about global financial stability of commodity business.     

Backtesting extreme value theory models of expected shortfall

We use stock market data to analyze the quality of alternative models and procedures for forecasting expected shortfall (ES) at different significance levels. We compute ES forecasts from conditional models applied to the full distribution of returns as well as from models that focus on tail events using extreme value theory (EVT). We also apply the semiparametric filtered historical simulation (FHS) approach to ES forecasting to obtain 10-day ES forecasts. At the 10-day horizon we combine FHS with EVT. The performance of the different models is assessed using six different ES backtests recently proposed in the literature. Our results suggest that conditional EVT-based models produce more accurate 1-day and 10-day ES forecasts than do non-EVT based models. Under either approach, asymmetric probability distributions for return innovations tend to produce better forecasts. Incorporating EVT in parametric or semiparametric approaches also improves ES forecasting performance. These qualitative results are also valid for the recent crisis period, even though all models then underestimate the level of risk. FHS narrows the range of numerical forecasts obtained from alternative models, thereby reducing model risk. Combining EVT and FHS seems to be best approach for obtaining accurate ES forecasts.     

Forecasting realised volatility using ARFIMA and HAR models

Recent literature provides mixed empirical evidence with respect to the forecasting performance of ARFIMA and HAR models. This paper compares the forecasting performance of both models using high frequency data of 100 stocks representing 10 business sectors for the period 2000-2010. We allow for different sectors, changing market conditions, variation in the sampling frequency and forecasting horizons. For the overall sample and using the 300 sec sampling frequency, the forecasting performance of both models is indistinguishable. However, differences arise under different market regimes, forecasting horizons and sampling frequencies. ARFIMA models are superior for the crisis and pre-crisis sub-samples. HAR forecasts are less sensitive to regime change and to longer forecasting horizons. Variations in forecasting performance could also be explained using differences in the levels of persistence underlying each model.     

Multiple-days-ahead value-at-risk and expected shortfall forecasting for stock indices,commodities and exchange rates: Inter-day versus intra-day data

In order to provide reliable Value-at-Risk (VaR) and Expected Shortfall (ES) forecasts, this paper attempts to investigate whether an inter-day or an intra-day model provides accurate predictions. We investigate the performance of inter-day and intra-day volatility models by estimating the AR(1)-GARCH(1,1)-skT and the AR(1)-HAR-RV-skT frameworks, respectively. This paper is based on the recommendations of the Basel Committee on Banking Supervision. Regarding the forecasting performances, the exploitation of intra-day information does not appear to improve the accuracy of the VaR and ES forecasts for the 10-steps-ahead and 20-steps-ahead for the 95%, 97.5% and 99% significance levels. On the contrary, the GARCH specification, based on the inter-day information set, is the superior model for forecasting the multiple-days-ahead VaR and ES measurements. The intra-day volatility model is not as appropriate as it was expected to be for each of the different asset classes; stock indices, commodities and exchange rates.The multi-period VaR and ES forecasts are estimated for a range of datasets (stock indices, commodities, foreign exchange rates) in order to provide risk managers and financial institutions with information relating the performance of the inter-day and intra-day volatility models across various markets. The inter-day specification predicts VaR and ES measures adequately at a 95% confidence level. Regarding the 97.5% confidence level that has been recently proposed in the revised 2013 version of Basel III, the GARCH-skT specification provides accurate forecasts of the risk measures for stock indices and exchange rates, but not for commodities (that is Silver and Gold). In the case of the 99% confidence level, we do not achieve sufficiently accurate VaR and ES forecasts for all the assets.     

Multivariate fractionally integrated APARCH modeling of stock market volatility: A multi-country study

Tse (1998) proposes a model which combines the fractionally integrated GARCH formulation of Baillie, Bollerslev and Mikkelsen (1996) with the asymmetric power ARCH specification of Ding, Granger and Engle (1993). This paper analyzes the applicability of a multivariate constant conditional correlation version of the model to national stock market returns for eight countries. We find this multivariate specification to be generally applicable once power, leverage and long-memory effects are taken into consideration. In addition, we find that both the optimal fractional differencing parameter and power transformation are remarkably similar across countries. Out-of-sample evidence for the superior forecasting ability of the multivariate FIAPARCH framework is provided in terms of forecast error statistics and tests for equal forecast accuracy of the various models.     

Backtesting trading risk of commercial banks using expected shortfall

This paper uses saddlepoint technique to backtest the trading risk of commercial banks using expected shortfall. It is found that four out of six US commercial banks have excessive trading risks. Monte Carlo simulation studies show that the proposed backtest is very accurate and powerful even for small test samples. More importantly, risk managers can carry out the proposed backtest based on any number of exceptions, so that incorrect risk models can be promptly detected before any further huge losses are realized.     

Estimating stochastic volatility models using integrated nested Laplace approximations

Volatility in financial time series is mainly analysed through two classes of models; the generalized autoregressive conditional heteroscedasticity (GARCH) models and the stochastic volatility (SV) ones. GARCH models are straightforward to estimate using maximum-likelihood techniques, while SV models require more complex inferential and computational tools, such as Markov Chain Monte Carlo (MCMC). Hence, although provided with a series of theoretical advantages, SV models are in practice much less popular than GARCH ones. In this paper, we solve the problem of inference for some SV models by applying a new inferential tool, integrated nested Laplace approximations (INLAs). INLA substitutes MCMC simulations with accurate deterministic approximations, making a full Bayesian analysis of many kinds of SV models extremely fast and accurate. Our hope is that the use of INLA will help SV models to become more appealing to the financial industry, where, due to their complexity, they are rarely used in practice.     

Aggregate volatility risk: International evidence

Using a procedure analogous to that of Ang et al. (2006), this paper documents that aggregate volatility risk does not appear to be priced in European equity markets. Specifically, based on the 2002–2016 period (for which European stock return data is available), the price of aggregate volatility risk is not statistically different from zero. Analysis based on GARCH-class and high-frequency intraday data models support these results. Consequently, contrary to what has been reported in some studies that examine U.S. data, whether aggregate volatility risk is priced in equity markets is an open question.     

Multiday expected shortfall under generalized t distributions: evidence from global stock market

Review of Quantitative Finance and Accounting - Earnings management research often uses discretionary accruals from Jones-type models. These models assume a linear relation between sales changes...     

Forecasting stock market volatility: Further international evidence

Abstract

This paper evaluates the out-of-sample forecasting accuracy of eleven models for monthly volatility in fifteen stock markets. Volatility is defined as within-month standard deviation of continuously compounded daily returns on the stock market index of each country for the ten-year period 1988 to 1997. The first half of the sample is retained for the estimation of parameters while the second half is for the forecast period. The following models are employed: a random walk model, a historical mean model, moving average models, weighted moving average models, exponentially weighted moving average models, an exponential smoothing model, a regression model, an ARCH model, a GARCH model, a GJR-GARCH model, and an EGARCH model. First, standard (symmetric) loss functions are used to evaluate the performance of the competing models: mean absolute error, root mean squared error, and mean absolute percentage error. According to all of these standard loss functions, the exponential smoothing model provides superior forecasts of volatility. On the other hand, ARCH-based models generally prove to be the worst forecasting models. Asymmetric loss functions are employed to penalize under-/over-prediction. When under-predictions are penalized more heavily, ARCH-type models provide the best forecasts while the random walk is worst. However, when over-predictions of volatility are penalized more heavily, the exponential smoothing model performs best while the ARCH-type models are now universally found to be inferior forecasters.     

Estimation of multiple period expected shortfall and median shortfall for risk management

With the regulatory requirements for risk management, Value at Risk (VaR) has become an essential tool in determining capital reserves to protect the risk induced by adverse market movements. The fact that VaR is not coherent has motivated the industry to explore alternative risk measures such as expected shortfall. The first objective of this paper is to propose statistical methods for estimating multiple-period expected shortfall under GARCH models. In addition to the expected shortfall, we investigate a new tool called median shortfall to measure risk. The second objective of this paper is to develop backtesting methods for assessing the performance of expected shortfall and median shortfall estimators from statistical and financial perspectives. By applying our expected shortfall estimators and other existing approaches to seven international markets, we demonstrate the superiority of our methods with respect to statistical and practical evaluations. Our expected shortfall estimators likely provide an unbiased reference for setting the minimum capital required for safeguarding against expected loss.     

Forecasting stock market volatility with various geopolitical risks categories: New evidence from machine learning models

This paper investigates how geopolitical risks influence the prediction performance on the US stock market volatility with machine learning models. Further, it compares the predictive performance of individual and combination forecast methods. With SHAP algorithm, it could identify which factor has a great impact and fully extract the information of geopolitical risks in predicting. Empirical results show that military build-ups and escalation of war have great importance on predicting realized volatility among various geopolitical risks. The research further emphasizes the superior performance of machine learning and forecast combination methods, especially SVR method and trimmed mean combination. In addition, by allocating portfolio according to the machine learning-based volatility forecasts, particularly elastic net and random forest, a mean-variance investor can achieve sizeable financial benefits. Our paper provides substantial implications for political risk management and volatility forecasting.     

Forecasting variance using stochastic volatility and GARCH

This paper estimates the conditional variance of daily Swedish OMX-index returns with stochastic volatility (SV) models and GARCH models and evaluates the in-sample performance as well as the out-of-sample forecasting ability of the models. Asymmetric as well as weekend/holiday effects are allowed for in the variance, and the assumption that errors are Gaussian is released. Evidence is found of a leverage effect and of higher variance during weekends. In both in-sample and out-of-sample comparisons SV models outperform GARCH models. However, while asymmetry, weekend/holiday effects and non-Gaussian errors are important for the in-sample fit, it is found that these factors do not contribute to enhancing the forecasting ability of the SV models.     

VaR and expected shortfall: a non-normal regime switching framework

We have developed a regime switching framework to compute the Value at Risk and Expected Shortfall measures. Although Value at Risk as a risk measure has been criticized by some researchers for lack of subadditivity, it is still a central tool in banking regulations and internal risk management in the finance industry. In contrast, Expected Shortfall is coherent and convex, so it is a better measure of risk than Value at Risk. Expected Shortfall is widely used in the insurance industry and has the potential to replace Value at Risk as a standard risk measure in the near future. We have proposed regime switching models to measure value at risk and expected shortfall for a single financial asset as well as financial portfolios. Our models capture the volatility clustering phenomenon and variance-independent variation in the higher moments by assuming the returns follow Student-t distributions.     

Relative forecasting performance of volatility models: Monte Carlo evidence

Abstract

A Monte Carlo (MC) experiment is conducted to study the forecasting performance of a variety of volatility models under alternative data-generating processes (DGPs). The models included in the MC study are the (Fractionally Integrated) Generalized Autoregressive Conditional Heteroskedasticity models ((FI)GARCH), the Stochastic Volatility model (SV), the Long Memory Stochastic Volatility model (LMSV) and the Markov-switching Multifractal model (MSM). The MC study enables us to compare the relative forecasting performance of the models accounting for different characterizations of the latent volatility process: specifications that incorporate short/long memory, autoregressive components, stochastic shocks, Markov-switching and multifractality. Forecasts are evaluated by means of mean squared errors (MSE), mean absolute errors (MAE) and value-at-risk (VaR) diagnostics. Furthermore, complementarities between models are explored via forecast combinations. The results show that (i) the MSM model best forecasts volatility under any other alternative characterization of the latent volatility process and (ii) forecast combinations provide systematic improvements upon most single misspecified models, but are typically inferior to the MSM model even if the latter is applied to data governed by other processes.     

Consumption-based CAPM models: International evidence

We examine the performance of several types of the consumption-based CAPM (C-CAPM) models to explore if consumption factors matter for determining excess returns across 17 MSCI country indexes. While the classic world C-CAPM does exhibit some power in explaining cross-sectional variations of expected excess returns, the model seems to require an implausibly large coefficient of risk aversion. The more sophisticated models including the heterogeneous C-CAPM, the world surplus consumption and the habit-formation models provide more reasonable estimates and add substantial explanatory power for the variation in the cross section of excess stock returns. Our results suggest that country-specific consumption risk is not fully diversified thus implying that stock returns are related to idiosyncratic consumption risk.     

Large returns,conditional correlation and portfolio diversification: a value-at-risk approach

This paper, using daily returns on 30 Dow Jones Industrial stocks for the period 1991-1999, investigates the possibility of portfolio diversification when there are negative large movements in the stock returns (i.e. when the market is bearish). We estimate the quantiles of stock return distributions using non-parametric and parametric methods that are widely being used in measuring value-at-risk (VaR). We find that the average conditional correlation of 30 stocks is much higher when the large movements are negative than that when the market is 'usual'. Further, we find that, contrary to the results of previous studies, there is no notable difference between the average conditional correlations when the large movements are positive and when the market is 'usual'. Moreover, it is evident from the results of the conditional CAPM that the portfolio's diversifiable and non-diversifiable risks, as measured by the error variance of the CAPM and beta respectively, are highly unstable when the market is bearish than that when it is 'usual' or bullish. The overall results suggest that the possibility of portfolio diversification would be eroded when the stock market is bearish. These findings have implications for portfolio diversification and risk management in particular and for finance in general. The ideas presented in this paper can be utilized for testing contagion in the international financial markets, a much-researched topic in international finance.     

Forecasting exchange rate volatility: The superior performance of conditional combinations of time series and option implied forecasts

This paper provides empirical evidence that combinations of option implied and time series volatility forecasts that are conditional on current information are statistically superior to individual models, unconditional combinations, and hybrid forecasts. Superior forecasting performance is achieved by both, taking into account the conditional expected performance of each model given current information, and combining individual forecasts. The method used in this paper to produce conditional combinations extends the application of conditional predictive ability tests to select forecast combinations. The application is for volatility forecasts of the Mexican peso–US dollar exchange rate, where realized volatility calculated using intraday data is used as a proxy for the (latent) daily volatility.     

Oil futures volatility predictability: New evidence based on machine learning models

This paper comprehensively examines the connection between oil futures volatility and the financial market based on a model-rich environment, which contains traditional predicting models, machine learning models, and combination models. The results highlight the efficiency of machine learning models for oil futures volatility forecasting, particularly the ensemble models and neural network models. Most interestingly, we consider the “forecast combination puzzle” in machine learning models, and find that combination models continue to have more satisfactory performances in all types of situations. We also discuss the model interpretability and each indicator's contribution to the prediction. Our paper provides new insights for machine learning methods' applications in futures market volatility prediction, which is helpful for academics, policy-makers, and investors.     

Target zones and conditional volatility: The role of realignments

This paper examines the relationship between the conditional volatility of target zone exchange rates and realignments of the system. To investigate this question, modified jump-diffusion Generalized Autoregressive Conditional Heteroskedasticity (GARCH) and absolute value GARCH models are fit to six exchange rates of the Exchange Rate Mechanism (ERM) of the European Monetary System (EMS). Time-varying jump probability and absolute value GARCH models are effective in improving the fit of jump-diffusion models on target zone data. There is some evidence that conditional volatility is higher around the periods of realignments.