Higher Moments and Exchange Rate Behavior

This paper uses 15‐minute exchange rate returns data for the six most liquid currencies (i.e., the Australian dollar, British pound, Canadian dollar, Euro, Japanese yen, and Swiss franc) vis‐à‐vis the United States dollar to examine whether a GARCH model augmented with higher moments (HM‐GARCH) performs better than a traditional GARCH (TG) model. Two findings are unraveled. First, the inclusion of odd/even moments in modeling the return/variance improves the statistical performance of the HM‐GARCH model. Second, trading strategies that extract buy and sell trading signals based on exchange rate forecasts from HM‐GARCH models are more profitable than those that depend on TG models.     

EXTENSIONS OF THE STANDARDIZED CROSS‐SECTIONAL APPROACH TO SHORT‐HORIZON EVENT STUDIES

Strong evidence indicates that short‐horizon event‐induced abnormal returns and volatility vary significantly over event days. Event‐study methods that assume constant event‐induced abnormal returns and volatility over event days have potentially inflated Type I error rates and poor test power. Our simple extensions of the Boehmer, Musumeci, and Poulsen (1991) approach scale abnormal returns with conditional variance, which is estimated with GARCH(1,1) and an indicator of the event in a two‐stage estimation. Our method improves the Boehmer, Musumeci, and Poulsen approach on model specification and test power, even under challenging event‐induced mean and volatility structures, and could standardize short‐horizon event studies.     

ON STOCK RETURN SEASONALITY AND CONDITIONAL HETEROSKEDASTICITY

We model the seasonal volatility of stock returns using GARCH specifications and size-sorted portfolios. Estimation results indicate that there are volatility differences between months and that these seasonal volatility patterns are conditional on firm size. Additionally, we find that seasonal volatility does not explain seasonal returns when the reward for risk is held constant over the sample period. Specifically, our results indicate that much of the abnormal return in January for small firms cannot be entirely attributed to either higher systematic risk or a higher risk premium in January.     

Modeling and forecasting stock return volatility using a random level shift model

We consider the estimation of a random level shift model for which the series of interest is the sum of a short-memory process and a jump or level shift component. For the latter component, we specify the commonly used simple mixture model such that the component is the cumulative sum of a process which is 0 with some probability (1 ? α) and is a random variable with probability α. Our estimation method transforms such a model into a linear state space with mixture of normal innovations, so that an extension of Kalman filter algorithm can be applied. We apply this random level shift model to the logarithm of daily absolute returns for the S&P 500, AMEX, Dow Jones and NASDAQ stock market return indices. Our point estimates imply few level shifts for all series. But once these are taken into account, there is little evidence of serial correlation in the remaining noise and, hence, no evidence of long-memory. Once the estimated shifts are introduced to a standard GARCH model applied to the returns series, any evidence of GARCH effects disappears. We also produce rolling out-of-sample forecasts of squared returns. In most cases, our simple random level shift model clearly outperforms a standard GARCH(1,1) model and, in many cases, it also provides better forecasts than a fractionally integrated GARCH model.     

Aggregation of exponential smoothing processes with an application to portfolio risk evaluation

In this paper we propose a unified framework to analyse contemporaneous and temporal aggregation of a widely employed class of integrated moving average (IMA) models. We obtain a closed-form representation for the parameters of the contemporaneously and temporally aggregated process as a function of the parameters of the original one. These results are useful due to the close analogy between the integrated GARCH (1, 1) model for conditional volatility and the IMA (1, 1) model for squared returns, which share the same autocorrelation function. In this framework, we present an application dealing with Value-at-Risk (VaR) prediction at different sampling frequencies for an equally weighted portfolio composed of multiple indices. We apply the aggregation results by inferring the aggregate parameter in the portfolio volatility equation from the estimated vector IMA (1, 1) model of squared returns. Empirical results show that VaR predictions delivered using this suggested approach are at least as accurate as those obtained by applying standard univariate methodologies, such as RiskMetrics.     

Stock market dynamics in a regime-switching asymmetric power GARCH model

This paper analyzes the dynamics of Asian stock index returns through a Regime-Switching Asymmetric Power GARCH model (RS-APGARCH). The model confirms some stylized facts already discussed in former studies but also highlights interesting new characteristics of stock market returns and volatilities. Mainly, it improves the traditional regime-switching GARCH models by including an asymmetric response to news and, above all, by allowing the power transformations of the heteroskedasticity equations to be estimated directly from the data. Several mixture models are compared where a first-order Markov process governs the switching between regimes.     

Identifying common dynamic features in stock returns

This paper proposes volatility and spectral based methods for the cluster analysis of stock returns. Using the information about both the estimated parameters in the threshold GARCH (or TGARCH) equation and the periodogram of the squared returns, we compute a distance matrix for the stock returns. Clusters are formed by looking to the hierarchical structure tree (or dendrogram) and the computed principal coordinates. We employ these techniques to investigate the similarities and dissimilarities between the ‘blue-chip’ stocks used to compute the Dow Jones Industrial Average (DJIA) index.     

Intraday Return Volatility Process: Evidence from NASDAQ Stocks

This paper presents a comprehensive analysis of the distributional and time-series properties of intraday returns. The purpose is to determine whether a GARCH model that allows for time varying variance in a process can adequately represent intraday return volatility. Our primary data set consists of 5-minute returns, trading volumes, and bid-ask spreads during the period January 1, 1999 through March 31, 1999, for a subset of thirty stocks from the NASDAQ 100 Index. Our results indicate that the GARCH(1,1) model best describes the volatility of intraday returns. Current volatility can be explained by past volatility that tends to persist over time. These results are consistent with those of Akgiray (1989) who estimates volatility using the various ARCH and GARCH specifications and finds the GARCH(1,1) model performs the best. We add volume as an additional explanatory variable in the GARCH model to examine if volume can capture the GARCH effects. Consistent with results of Najand and Yung (1991) and Foster (1995) and contrary to those of Lamoureux and Lastrapes (1990), our results show that the persistence in volatility remains in intraday return series even after volume is included in the model as an explanatory variable. We then substitute bid-ask spread for volume in the conditional volatility equation to examine if the latter can capture the GARCH effects. The results show that the GARCH effects remain strongly significant for many of the securities after the introduction of bid-ask spread. Consistent with results of Antoniou, Homes and Priestley (1998), intraday returns also exhibit significant asymmetric responses of volatility to flow of information into the market.     

Forecasting the return distribution using high-frequency volatility measures

The aim of this paper is to forecast (out-of-sample) the distribution of financial returns based on realized volatility measures constructed from high-frequency returns. We adopt a semi-parametric model for the distribution by assuming that the return quantiles depend on the realized measures and evaluate the distribution, quantile and interval forecasts of the quantile model in comparison to a benchmark GARCH model. The results suggest that the model outperforms an asymmetric GARCH specification when applied to the S&P 500 futures returns, in particular on the right tail of the distribution. However, the model provides similar accuracy to a GARCH (1, 1) model when the 30-year Treasury bond futures return is considered.     

Forecasting hedge fund volatility: a Markov regime-switching approach

The article addresses forecasting volatility of hedge fund (HF) returns by using a non-linear Markov-Switching GARCH (MS-GARCH) framework. The in- and out-of-sample, multi-step ahead volatility forecasting performance of GARCH(1,1) and MS-GARCH(1,1) models is compared when applied to 12 global HF indices over the period of January 1990 to October 2010. The results identify different regimes with periods of high and low volatility for most HF indices. In-sample estimation results reveal a superior performance of the MS-GARCH model. The findings show that regime switching is related to structural changes in the market factor for most strategies. Out-of-sample forecasting shows that the MS-GARCH formulation provides more accurate volatility forecasts for most forecast horizons and for most HF strategies. Inclusion of MS dynamics in the GARCH specification highly improves the volatility forecasts for those strategies that are particularly sensitive to general macroeconomic conditions, such as Distressed Restructuring and Merger Arbitrage.     

Forecasting VaR using analytic higher moments for GARCH processes

It is widely accepted that some of the most accurate Value-at-Risk (VaR) estimates are based on an appropriately specified GARCH process. But when the forecast horizon is greater than the frequency of the GARCH model, such predictions have typically required time-consuming simulations of the aggregated returns distributions. This paper shows that fast, quasi-analytic GARCH VaR calculations can be based on new formulae for the first four moments of aggregated GARCH returns. Our extensive empirical study compares the Cornish–Fisher expansion with the Johnson SU distribution for fitting distributions to analytic moments of normal and Student t, symmetric and asymmetric (GJR) GARCH processes to returns data on different financial assets, for the purpose of deriving accurate GARCH VaR forecasts over multiple horizons and significance levels.     

Model-free versus Model-based Volatility Prediction

The well-known ARCH/GARCH models for financial time series havebeen criticized of late for their poor performance in volatilityprediction, that is, prediction of squared returns.¹ Focusingon three representative data series, namely a foreign exchangeseries (Yen vs. Dollar), a stock index series (the S&P500index), and a stock price series (IBM), the case is made thatfinancial returns may not possess a finite fourth moment. Takingthis into account, we show how and why ARCH/GARCH models—whenproperly applied and evaluated—actually do have nontrivialpredictive validity for volatility. Furthermore, we show howa simple model-free variation on the ARCH theme can performeven better in that respect. The model-free approach is basedon a novel normalizing and variance–stabilizing transformation(NoVaS, for short) that can be seen as an alternative to parametricmodeling. Properties of this transformation are discussed, andpractical algorithms for optimizing it are given.     

Does Idiosyncratic Risk Matter for Individual Securities?

This paper investigates the relationship between idiosyncratic risk and returns for individual securities within a generalized autoregressive conditional heteroskedascticity (GARCH)‐in‐mean framework. We demonstrate that, on average, 15% of stocks exhibit a significant relationship between returns and risk, of which 9% are positive. These proportions vary over time and with model specifications. Some characteristics influence the probability of a positive and a negative relationship, while others appear to affect only one, but not the other. This evidence implies that the factors that explain a positive connection between idiosyncratic risk and returns are different from the factors that explain a negative connection.     

On the persistence and volatility in European,American and Asian stocks bull and bear markets

In this paper we examine the statistical properties of several stock market indices in Europe, the US and Asia by means of determining the degree of dependence in both the level and the volatility of the processes. In the latter case, we use the squared returns as a proxy for the volatility. We also investigate the cyclical pattern observed in the data and in particular, if the degree of dependence changes depending on whether there is a bull or a bear period. We use fractional integration and GARCH specifications. The results indicate that the indices are all nonstationary I(1) processes with the squared returns displaying a degree of long memory behaviour. With respect to the bull and bear periods, we do not observe a systematic pattern in terms of the degree of persistence though for some of the indices (FTSE, Dax, Hang Seng and STI) there is a higher degree of dependence in both the level and the volatility during the bull periods.     

STOCK RETURNS AND VOLATILITY ON CHINA'S STOCK MARKETS

We examine time‐series features of stock returns and volatility, as well as the relation between return and volatility in four of China's stock exchanges. Variance ratio tests reject the hypothesis that stock returns follow a random walk. We find evidence of long memory of returns. Application of GARCH and EGARCH models provides strong evidence of time‐varying volatility and shows volatility is highly persistent and predictable. The results of GARCH‐M do not show any relation between expected returns and expected risk. Daily trading volume used as a proxy for information arrival time has no significant explanatory power for the conditional volatility of daily returns. JEL classification: G15     

Market Reaction to Regulatory Action in the Insurance Industry: The Case of Contingent Commission

We examine the market's reaction to New York Attorney General Eliot Spitzer's civil suit against mega‐broker Marsh for bid rigging and inappropriate use of contingent commissions within a generalized autoregressive conditionally heteroskedastic (GARCH) framework. Effects on the stock returns of insurance brokers and insurers are tested. The findings are: (1) GARCH effects are significant in modeling broker/insurer returns; (2) the suit generated negative effects on the brokerage industry and individual brokers, suggesting that contagion dominates competitive effects; (3) spillover effects from the brokerage sector to insurance business are significant and mostly negative, demonstrating industry integration; and (4) information‐based contagion is supported, as opposed to the pure‐panic contagion.     

Robust outlier detection for Asia–Pacific stock index returns

Outliers can lead to model misspecifications, poor forecasts and invalid inferences. Their identification and correction is therefore an important objective of financial modeling.This paper introduces a simple method to detect outliers in a financial series. It uses an AR(1)–GARCH(1,1) model to calculate interval forecasts for one-step ahead returns that are then compared to realized returns to determine whether or not we are in the presence of an aberrant observation. The GARCH model, however, is only used as a filter and the identification algorithm remains robust to model misspecifications.The efficiency of this outlier-correction technique is first tested with a simulation study, before being applied to five Asian stock market returns to identify the outlying observations. After an analysis of these extreme fluctuations, the out-of-sample forecasting performance of our outlier-corrected model is then compared to the classical forecasts of a GARCH model in which no account is taken of outliers.     

Forecasting value-at-risk and expected shortfall using fractionally integrated models of conditional volatility: International evidence

The present study compares the performance of the long memory FIGARCH model, with that of the short memory GARCH specification, in the forecasting of multi-period value-at-risk (VaR) and expected shortfall (ES) across 20 stock indices worldwide. The dataset is composed of daily data covering the period from 1989 to 2009. The research addresses the question of whether or not accounting for long memory in the conditional variance specification improves the accuracy of the VaR and ES forecasts produced, particularly for longer time horizons. Accounting for fractional integration in the conditional variance model does not appear to improve the accuracy of the VaR forecasts for the 1-day-ahead, 10-day-ahead and 20-day-ahead forecasting horizons relative to the short memory GARCH specification. Additionally, the results suggest that underestimation of the true VaR figure becomes less prevalent as the forecasting horizon increases. Furthermore, the GARCH model has a lower quadratic loss between actual returns and ES forecasts, for the majority of the indices considered for the 10-day and 20-day forecasting horizons. Therefore, a long memory volatility model compared to a short memory GARCH model does not appear to improve the VaR and ES forecasting accuracy, even for longer forecasting horizons. Finally, the rolling-sampled estimated FIGARCH parameters change less smoothly over time compared to the GARCH models. Hence, the parameters' time-variant characteristic cannot be entirely due to the news information arrival process of the market; a portion must be due to the FIGARCH modelling process itself.     

A regime-switching real-time copula GARCH model for optimal futures hedging

A regime-switching real-time copula GARCH (RSRTCG) model is suggested for optimal futures hedging. The specification of RSRTCG is to model the margins of asset returns with state-dependent real-time GARCH and the dependence structure of asset returns with regime switching copula functions. RSRTCG is faster in adjusting to the new level of volatility under different market regimes which is a regime-switching multivariate generalization of the state-independent univariate real-time GARCH. RSRTCG is applied to cross hedge the price risk of S&P 500 sector indices with crude oil futures. The empirical results show that RSRTCG possesses superior hedging performance compared to its nested non-real-time or state-independent copula GARCH models based on the criterion of percentage variance reduction, utility gain, model confidence set, model combination strategy, risk-adjusted return and reward-to-semivariance ratio.     

An economic evaluation of stock–bond return comovements with copula-based GARCH models

Owing to their importance in asset allocation strategies, the comovements between the stock and bond markets have become an increasingly popular issue in financial economics. Moreover, the copula theory can be utilized to construct a flexible joint distribution that allows for skewness in the distribution of asset returns as well as asymmetry in the dependence structure between asset returns. Therefore, this paper proposes three classes of copula-based GARCH models to describe the time-varying dependence structure of stock–bond returns, and then examines the economic value of copula-based GARCH models in the asset allocation strategy. We compare their out-of-sample performance with other models, including the passive, the constant conditional correlation (CCC) GARCH and the dynamic conditional correlation (DCC) GARCH models. From the empirical results, we find that a dynamic strategy based on the GJR-GARCH model with Student-t copula yields larger economic gains than passive and other dynamic strategies. Moreover, a less risk-averse investor will pay higher performance fees to switch from a passive strategy to a dynamic strategy based on copula-based GARCH models.