Long memory in stock market volatility and the volatility-in-mean effect: The FIEGARCH-M Model

We extend the fractionally integrated exponential GARCH (FIEGARCH) model for daily stock return data with long memory in return volatility of Bollerslev and Mikkelsen (1996) by introducing a possible volatility-in-mean effect. To avoid that the long memory property of volatility carries over to returns, we consider a filtered FIEGARCH-in-mean (FIEGARCH-M) effect in the return equation. The filtering of the volatility-in-mean component thus allows the co-existence of long memory in volatility and short memory in returns. We present an application to the daily CRSP value-weighted cum-dividend stock index return series from 1926 through 2006 which documents the empirical relevance of our model. The volatility-in-mean effect is significant, and the FIEGARCH-M model outperforms the original FIEGARCH model and alternative GARCH-type specifications according to standard criteria.     

Ex Ante Stock Market Return Volatility Implied by the OEX Option Premium

Previous empirical evidence suggests that stock return volatility expectations change over time, but the existing models of time-varying variance lack a theoretical structure that is rigorously linked to the efficient markets dividend discount model. This paper develops and tests such a model. The conditional forecast variance of the return on the stock market portfolio is expressed as a linear combination of the adjusted conditional forecast variance of the interest rate and the dividend growth rate. An empirical test using the implied variance of the S&P 100 index option provides evidence that supports the model's predictions.     

Risk and the January effect

We use a time-series GARCH framework with the conditional variance/covariance as proxies for systematic risk to reexamine the proposition by Rozeff and Kinney (1976) and Rogalski and Tinic (1986) that the January effect may be a phenomenon of risk compensation in the month. We find no clear evidence that either conditional volatility or unconditional volatility in January is predominantly higher across the sampling years. Hence, against the proposition, the January effect is not due to risk per se. Rather, we find strong evidence that the January effect is due to higher compensation for risk in the month. This may be possible if investors have an increasing RRA utility function. Although many studies find that volatility tends to be higher in January, we find it to be period-specific and mostly in value-weighted return series, but not in equal-weighted return series. This is true both for the unconditional and conditional return volatility.     

Accurate minimum capital risk requirements: A comparison of several approaches

In this paper we estimate, for several investment horizons, minimum capital risk requirements for short and long positions, using the unconditional distribution of three daily indexes futures returns and a set of short and long memory stochastic volatility and GARCH-type models. We consider the possibility that errors follow a t-Student distribution in order to capture the kurtosis of the returns’ series. The results suggest that accurate modelling of extreme observations obtained for long and short trading investment positions is possible with an autoregressive stochastic volatility model. Moreover, modelling futures returns with a long memory stochastic volatility model produces, in general, excessive volatility persistence, and consequently, leads to large minimum capital risk requirement estimates. Finally, the models’ predictive ability is assessed with the help of out-of-sample conditional tests.     

Asymmetric volatility in the foreign exchange markets

We examine the presence or absence of asymmetric volatility in the exchange rates of Australian dollar (AUD), Euro (EUR), British pound (GBP) and Japanese yen (JPY), all against US dollar. Our investigation is based on a variant of the heterogeneous autoregressive realized volatility model, using daily realized variance and return series from 1996 to 2004. We find that a depreciation against USD leads to significantly greater volatility than an appreciation for AUD and GBP, whereas the opposite is true for JPY. Relative to volatility on days following a positive one-standard-deviation return, volatility on days following a negative one-standard-deviation return is higher by 6.6% for AUD, 6.1% for GBP, and 21.2% for JPY. The realized volatility of EUR appears to be symmetric. These results are robust to the removal of jump component from realized volatility and the sub-samplings defined by structural-changes. The asymmetry in AUD, GBP and JPY appears to be embedded in the continuous component of realized volatility rather than the jump component.     

Forecasting daily variability of the S&P 100 stock index using historical,realised and implied volatility measurements

The increasing availability of financial market data at intraday frequencies has not only led to the development of improved volatility measurements but has also inspired research into their potential value as an information source for volatility forecasting. In this paper, we explore the forecasting value of historical volatility (extracted from daily return series), of implied volatility (extracted from option pricing data) and of realised volatility (computed as the sum of squared high frequency returns within a day). First, we consider unobserved components (UC-RV) and long memory models for realised volatility which is regarded as an accurate estimator of volatility. The predictive abilities of realised volatility models are compared with those of stochastic volatility (SV) models and generalised autoregressive conditional heteroskedasticity (GARCH) models for daily return series. These historical volatility models are extended to include realised and implied volatility measures as explanatory variables for volatility. The main focus is on forecasting the daily variability of the Standard & Poor's 100 (S&P 100) stock index series for which trading data (tick by tick) of almost 7 years is analysed. The forecast assessment is based on the hypothesis of whether a forecast model is outperformed by alternative models. In particular, we will use superior predictive ability tests to investigate the relative forecast performances of some models. Since volatilities are not observed, realised volatility is taken as a proxy for actual volatility and is used for computing the forecast error. A stationary bootstrap procedure is required for computing the test statistic and its p-value. The empirical results show convincingly that realised volatility models produce far more accurate volatility forecasts compared to models based on daily returns. Long memory models seem to provide the most accurate forecasts.     

On the realized volatility of the ECX CO2 emissions 2008 futures contract: distribution, dynamics and forecasting

This article documents the conditional and unconditional distributions of the realized volatility for the 2008 futures contract in the European climate exchange (ECX), which is valid under the EU emissions trading scheme (EU ETS). Realized volatility measures from naive, kernel-based and subsampling estimators are used to obtain inferences about the distributional and dynamic properties of the ECX emissions futures volatility. The distribution of the daily realized volatility in logarithmic form is shown to be close to normal. The mixture-of-normals hypothesis is strongly rejected, as the returns standardized using daily measures of volatility clearly departs from normality. A simplified HAR-RV model (Corsi in J Financ Econ 7:174–196, 2009) with only a weekly component, which reproduces long memory properties of the series, is then used to model the volatility dynamics. Finally, the predictive accuracy of the HAR-RV model is tested against GARCH specifications using one-step-ahead forecasts, which confirms the HAR-RV superior ability.     

Long memory and level shifts in REITs returns and volatility

This paper provides an empirical investigation of the long memory in the returns and volatility of REITs markets of the USA, the UK, Hong Kong, Australia, and Japan. Initially, we subject the series to unit root tests proposed by Saikkonen and Lütkepohl (2002) and Lanne et al. (2002), which allow for a level shift in the data generating process. We confirm the stationarity of the REITs returns in the presence of structural breaks, with the breaks happening during the 2008 and 2009 periods. Second, by employing long memory tests and estimators, a weak long memory is demonstrated in the return series, but a strong evidence is provided in the volatility measures. Then using Smith (2005)'s modified GPH estimator, we find that a short-memory model with a level shift is a viable alternative to a long memory model for the USA, Hong Kong and Japan and not for the UK nor for Australia. Finally, we confirm that the long memory in volatility is real and not caused by shifts in variance for all markets. Our results should be useful to market participants in the REITs markets, whose success depends on the ability to forecast and model REITs price movements.     

Combining long memory and level shifts in modelling and forecasting the volatility of asset returns

We propose a parametric state space model of asset return volatility with an accompanying estimation and forecasting framework that allows for ARFIMA dynamics, random level shifts and measurement errors. The Kalman filter is used to construct the state-augmented likelihood function and subsequently to generate forecasts, which are mean and path-corrected. We apply our model to eight daily volatility series constructed from both high-frequency and daily returns. Full sample parameter estimates reveal that random level shifts are present in all series. Genuine long memory is present in most high-frequency measures of volatility, whereas there is little remaining dynamics in the volatility measures constructed using daily returns. From extensive forecast evaluations, we find that our ARFIMA model with random level shifts consistently belongs to the 10% Model Confidence Set across a variety of forecast horizons, asset classes and volatility measures. The gains in forecast accuracy can be very pronounced, especially at longer horizons.     

Developing a stress testing framework based on market risk models

The Basel 2 Accord requires regulatory capital to cover stress tests, yet no coherent and objective framework for stress testing portfolios exists. We propose a new methodology for stress testing in the context of market risk models that can incorporate both volatility clustering and heavy tails. Empirical results compare the performance of eight risk models with four possible conditional and unconditional return distributions over different rolling estimation periods. When applied to major currency pairs using daily data spanning more than 20 years we find that stress test results should have little impact on current levels of foreign exchange regulatory capital.     

A reexamination of corporate sell-offs of real estate assets

This article reexamines the now generally accepted notion that sell-offs of real estate assets provide positive returns for sellers but not for buyers. Following previous research, we use event study methods, but we modify the conventional market model to permit its residuals (unexpected returns) to be described by a time-varying conditional variance. We also differ from previous work in that our sample contains only sell-offs that can be precisely dated. Although we find substantial evidence of time-varying volatility in the unexpected return series, our economic results confirm the conventional viewpoint.     

上证指数收益率波动的实证分析：基于ARCH族模型

股价指数的收益率序列具有时变波动性、厚尾特征、波动性群集等特点,传统的计量分析无法刻画这些特点。文章利用ARCH族模型,选取2003年1月20日～2013年12月12日上证指数每日收益率共2621个数据对其波动进行定量与定性的分析,结果显示,上证指数日收益率存在高阶的ARCH效应,杠杆效应,波动集聚性特征,条件方差对日收益率有很强的影响,其中EGARCH模型在反映股市波动性方面优于其他模型。     

Dependence and mean reversion in stock prices: The case of the MENA region

This paper provides empirical evidence on the long memory behavior of the stock markets of Egypt, Jordan, Morocco, and Turkey. To test for long memory in the returns and volatility, we employ the modified rescaled range statistic R/S proposed by Lo [Lo, A.W., 1991. Long-term memory in stock market prices. Econometrica 59, 1279–1313] and the recently proposed rescaled variance V/S statistic developed by Giraitis et al. [Giraitis, L., Kokoszka, P.S. Leipus, R., Teyssiere, G., 2003. Rescaled variance and related tests for long memory in volatility and levels. J. Econ. 112, 265–294]. Further analysis is conducted by employing the ARFIMA (p, d, q) model to estimate the long memory parameters. Egypt and Morocco show evidence of long memory in the return series, while Jordan and Turkey display negative persistence. For the volatility series, long memory is conclusively demonstrated for all markets. Then, we compare the forecasting performance of ARMA and ARFIMA models and find that the ARFIMA model outperforms in out-of-sample forecasting of the markets. Our results should be useful to regulators, practitioners and derivative market participants, whose success depends on the ability to forecast stock price movements in these markets.     

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.     

Influence of structural changes in transmission of information between stock markets: A European empirical study

The aim of this study is to analyze the influence of structural changes in volatility on the transmission of information. We present empirical evidence on European stock exchange markets based on information from the principal European stock indexes. In order to include structural changes in variance, we followed the [Sansó, A., Aragó, V., Carrión, J.Ll., 2004. Testing for changes in the unconditional variance of financial time series. Revista de Economía Financiera 4, 32–53] modification of the methodology proposed by [Inclan, C., Tiao, G.C., 1994. Use of cumulative sums of squares for retrospective detection of changes of variance. Journal of the American Statistical Association 89, 913–923.], to take into account the problems of kurtosis and heteroskedasticity in the analyzed series. To study the existence of transmission of volatility we used an asymmetric bivariate GARCH model, specifically, the time-varying covariance asymmetric BEKK model [Engle, R.F., Kroner, K.F., 1995. Multivariate simultaneous generalized ARCH. Econometric Theory 11, 122–150]. The most outstanding result is the significance of the variables that represent these changes. When taken into consideration, they influence the scheme of transmission. Structural changes should therefore be incorporated into this type of study.     

How predictable are precious metal returns?

This paper provides strong evidence of time-varying return predictability of three precious metals from January 1987 to September 2014. We use three variations of the variance ratio test, the nonlinear Brock, Dechert and Schieinkman test as well as the Hurst exponent to evaluate the time-varying return predictability of precious metals to reduce the risk of spurious results. Our full sample results report mixed findings where some tests indicate significant predictability while some suggest no predictability. However through a time-varying procedure, we show that each precious metal market goes through periods of significant predictability as well as periods of unpredictability. Therefore this finding suggests that return predictability does vary over time and is not a static, all-or-nothing condition and therefore is consistent with the adaptive market hypothesis. We also show that platinum is the most predictable of the three precious metals and silver the least predictable, which may be of great to investors who include precious metals in their investment portfolios.     

The time-varying asymmetry of exchange rate returns: A stochastic volatility – stochastic skewness model

While the time-varying volatility of financial returns has been extensively modelled, most existing stochastic volatility models either assume a constant degree of return shock asymmetry or impose symmetric model innovations. However, accounting for time-varying asymmetry as a measure of crash risk is important for both investors and policy makers. This paper extends a standard stochastic volatility model to allow for time-varying skewness of the return innovations. We estimate the model by extensions of traditional Markov Chain Monte Carlo (MCMC) methods for stochastic volatility models. When applying this model to the returns of four major exchange rates, skewness is found to vary substantially over time. In addition, stochastic skewness can help to improve forecasts of risk measures. Finally, the results support a potential link between carry trading and crash risk.     

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     

Optimal hedge ratio and hedging effectiveness of stock index futures: evidence from India

In a free capital mobile world with increased volatility, the need for an optimal hedge ratio and its effectiveness is warranted to design a better hedging strategy with future contracts. This study analyses four competing time series econometric models with daily data on NSE Stock Index Futures and S&P CNX Nifty Index. The effectiveness of the optimal hedge ratios is examined through the mean returns and the average variance reduction between the hedged and the unhedged positions for 1-, 5-, 10- and 20-day horizons. The results clearly show that the time-varying hedge ratio derived from the multivariate GARCH model has higher mean return and higher average variance reduction across hedged and unhedged positions. Even though not outperforming the GARCH model, the simple OLS-based strategy performs well at shorter time horizons. The potential use of this multivariate GARCH model cannot be sublined because of its estimation complexities. However, from a cost of computation point of view, one can equally consider the simple OLS strategy that performs well at the shorter time horizons.     

Semi-parametric Bayesian tail risk forecasting incorporating realized measures of volatility

Realized measures employing intra-day sources of data have proven effective for dynamic volatility and tail-risk estimation and forecasting. Expected shortfall (ES) is a tail risk measure, now recommended by the Basel Committee, involving a conditional expectation that can be semi-parametrically estimated via an asymmetric sum of squares function. The conditional autoregressive expectile class of model, used to implicitly model ES, has been extended to allow the intra-day range, not just the daily return, as an input. This model class is here further extended to incorporate information on realized measures of volatility, including realized variance and realized range (RR), as well as scaled and smoothed versions of these. An asymmetric Gaussian density error formulation allows a likelihood that leads to direct estimation and one-step-ahead forecasts of quantiles and expectiles, and subsequently of ES. A Bayesian adaptive Markov chain Monte Carlo method is developed and employed for estimation and forecasting. In an empirical study forecasting daily tail risk measures in six financial market return series, over a seven-year period, models employing the RR generate the most accurate tail risk forecasts, compared to models employing other realized measures as well as to a range of well-known competitors.