Evidence of psychological barriers in the conditional moments of major world stock indices

This study investigates the existence of psychological barriers in the Dow Jones Industrial Average, the S&;P 500, and six foreign stock indices. It is believed by many in the investment community that index levels that are multiples of 100 serve as barriers, and that markets may resist crossing these barriers. Although return dynamics in the neighborhood of barrier points are not identical for all series studied, we find aberrations in the conditional means and variances consistent with psychological barriers. In five of the eight indices studied, conditional mean returns are significantly higher after crossing a barrier as part of an upward move, while only two series exhibit significant mean effects after crossing a barrier as part of a downward move. In seven of the eight series studied, we find significant conditional variance effects coincident with a barrier crossing. In addition, most series exhibit evidence of autoregressive conditional heteroskedastic (ARCH), generalized ARCH (GARCH), and leverage effects.     

Labor Income and Predictable Stock Returns

We propose a novel economic mechanism that generates stock returnpredictability in both the time series and the cross-section.Investors’ income has two sources, wages and dividendsthat grow stochastically over time. As a consequence the fractionof total income produced by wages fluctuates depending on economicconditions. We show that the risk premium that investors requireto hold stocks varies with these fluctuations. A regressionof stock returns on lagged values of the labor income to consumptionratio produces statistically significant coefficients and largeadjusted R²s. Tests of the model’s cross-sectional predictionson the set of 25 Fama–French portfolios sorted on sizeand book-to-market are also met with considerable support.     

The information content of implied volatilities and model-free volatility expectations: Evidence from options written on individual stocks

We measure the volatility information content of stock options for individual firms using option prices for 149 US firms and the S&P 100 index. We use ARCH and regression models to compare volatility forecasts defined by historical stock returns, at-the-money implied volatilities and model-free volatility expectations for every firm. For 1-day-ahead estimation, a historical ARCH model outperforms both of the volatility estimates extracted from option prices for 36% of the firms, but the option forecasts are nearly always more informative for those firms that have the more actively traded options. When the prediction horizon extends until the expiry date of the options, the option forecasts are more informative than the historical volatility for 85% of the firms. However, at-the-money implied volatilities generally outperform the model-free volatility expectations.     

Periodic Stochastic Volatility and Fat Tails

This article provides a comprehensive analysis of the size andstatistical significance of the day of the week, month of theyear, and holiday effects in daily stock index returns and volatility.We employ data from the Dow Jones Industrial Average (DJIA),the S&P 500, the S&P MidCap 400, and the S&P SmallCap600 in order to test whether the seasonal patterns of mediumand small firms are similar to those of large firms. Using formalhypothesis tests based on bootstrapping, we demonstrate thatthere are more significant calendar effects in volatility thanin expected returns, especially for the two large cap indices.More importantly, we introduce the periodic stochastic volatility(PSV) model for characterizing the observed seasonal patternsof daily financial market volatility. We analyze the interactionbetween seasonal heteroskedasticity and fat tails by comparingthe performance of Gaussian PSV and fat-tailed PSVt specificationsto the plain vanilla SV and SVt benchmarks. Consistent withour model-free results, we find strong evidence of seasonalperiodicity in volatility, which essentially eliminates theneed for a fat-tailed conditional distribution, and is robustto the exclusion of the crash of 1987 outliers.     

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     

Explaining Returns with Cash-Flow Proxies

Stock returns are correlated with contemporaneous earnings growth,dividend growth, future real activity, and other cash-flow proxies.The correlation between cash-flow proxies and stock returnsmay arise from association of cash-flow proxies with one-periodexpected returns, cash-flow news, and/or expected-return news.We use Campbell’s (1991) return decomposition to measurethe relative importance of these three effects in regressionsof returns on cash-flow proxies. In some of the popular specifications,variables that are motivated as proxies for cash-flow news alsotrack a nontrivial proportion of one-period expected returnsand expected-return news. As a result, the R² from a regressionof returns on cash-flow proxies may overstate or understatethe importance of cash-flow news as a source of return variance.     

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.     

Price Informativeness and Investment Sensitivity to Stock Price

The article shows that two measures of the amount of privateinformation in stock price—price nonsynchronicity andprobability of informed trading (PIN)—have a strong positiveeffect on the sensitivity of corporate investment to stock price.Moreover, the effect is robust to the inclusion of controlsfor managerial information and for other information-relatedvariables. The results suggest that firm managers learn fromthe private information in stock price about their own firms’fundamentals and incorporate this information in the corporateinvestment decisions. We relate our findings to an alternativeexplanation for the investment-to-price sensitivity, namelythat it is generated by capital constraints, and show that boththe learning channel and the alternative channel contributeto this sensitivity. (JEL G14, G31)     

A closed-form GARCH option valuation model

This paper develops a closed-form option valuation formula fora spot asset whose variance follows a GARCH(p, q) process thatcan be correlated with the returns of the spot asset. It providesthe first readily computed option formula for a random volatilitymodel that can be estimated and implemented solely on the basisof observables. The single lag version of this model containsHeston's (1993) stochastic volatility model as a continuous-timelimit. Empirical analysis on S&P500 index options showsthat the out-of-sample valuation errors from the single lagversion of the GARCH model are substantially lower than thead hoc Black-Scholes model of Dumas, Fleming and Whaley (1998)that uses a separate implied volatility for each option to fitto the smirk/smile in implied volatilities. The GARCH modelremains superior even though the parameters of the GARCH modelare held constant and volatility is filtered from the historyof asset prices while the ad hoc Black-Scholes model is updatedevery period. The improvement is largely due to the abilityof the GARCH model to simultaneously capture the correlationof volatility, with spot returns and the path dependence involatility.     

On the distribution and conditional heteroscedasticity in Taiwan stock prices

This paper studies the distribution and conditional heteroscedasticity in stock returns on the Taiwan stock market. Apart from the normal distribution, in order to explain the leptokurtosis and skewness observed in the stock return distribution, we also examine the Student-t, the Poisson–normal, and the mixed-normal distributions, which are essentially a mixture of normal distributions, as conditional distributions in the stock return process. We also use the ARMA (1,1) model to adjust the serial correlation, and adopt the GJR–generalized autoregressive conditional heteroscedasticity (GARCH (1,1)) model to account for the conditional heterscedasticity in the return process. The empirical results show that the mixed–normal–GARCH model is the most probable specification for Taiwan stock returns. The results also show that skewness seems to be diversifiable through portfolio. Thus the normal–GARCH or the Student-t–GARCH model which involves symmetric conditional distribution may be a reasonable model to describe the stock portfolio return process¹.     

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.     

Tempered stable and tempered infinitely divisible GARCH models

In this paper, we introduce a new GARCH model with an infinitely divisible distributed innovation. This model, which we refer to as the rapidly decreasing tempered stable (RDTS) GARCH model, takes into account empirical facts that have been observed for stock and index returns, such as volatility clustering, non-zero skewness, and excess kurtosis for the residual distribution. We review the classical tempered stable (CTS) GARCH model, which has similar statistical properties. By considering a proper density transformation between infinitely divisible random variables, we can find the risk-neutral price process, thereby allowing application to option-pricing. We propose algorithms to generate scenarios based on GARCH models with CTS and RDTS innovations. To investigate the performance of these GARCH models, we report parameter estimates for the Dow Jones Industrial Average index and stocks included in this index. To demonstrate the advantages of the proposed model, we calculate option prices based on the index.     

An Empirical Analysis of the Volatility in the Open-End Fund Market: Evidence from China

This paper applies a set of GARCH models to investigate the three characteristics, including time persistence, leverage effect, and risk premium, of the volatilities of the four China Securities Index (CSI) fund indices. This study made the following four findings: (1) a strong ARCH effect exists in the returns; (2) time persistence is significant in all the CSI fund indices, namely, "stock index," "hybrid index," and "bond index" in descending order of significance; (3) the leverage effect is not statistically significant, yet there may be a positive leverage effect on the bond funds; (4) a risk premium effect exists in the open-end fund market, especially in the bond fund market.     

NONLINEAR DYNAMICS AND THE DISTRIBUTION OF DAILY STOCK INDEX RETURNS

Three alternative models of daily stock index returns are considered: (1) a diffusion-jump process; (2) an extended generalized autoregressive conditional heteroskedasticity (GARCH) process; and (3) a combination of the GARCH and jump processes. Non-nested tests between the diffusion-jump process and a GARCH(1.1) process with t-distributed errors reject the diffusion-jump process, but do not always reject the GARCH process. Kolmogorov-Smirnov tests of fit, however, reject the GARCH(1,1)-t process for all cases. Nonlinear dependence is not removed for the value-weighted index and the S&P 500 stock index; therefore, deterministic chaos cannot be dismissed.     

Estimating GARCH models using support vector machines*

Abstract

Support vector machines (SVMs) are a new nonparametric tool for regression estimation. We will use this tool to estimate the parameters of a GARCH model for predicting the conditional volatility of stock market returns. GARCH models are usually estimated using maximum likelihood (ML) procedures, assuming that the data are normally distributed. In this paper, we will show that GARCH models can be estimated using SVMs and that such estimates have a higher predicting ability than those obtained via common ML methods.     

A nesting framework for Markov-switching GARCH modelling with an application to the German stock market

In this paper, we establish a generalized two-regime Markov-switching GARCH model which enables us to specify complex (symmetric and asymmetric) GARCH equations that may differ considerably in their functional forms across the two Markov regimes. We show how previously proposed collapsing procedures for the Markov-switching GARCH model can be extended to estimate our general specification by means of classical maximum-likelihood methods. We estimate several variants of the generalized Markov-switching GARCH model using daily excess returns of the German stock market index DAX sampled during the last decade. Our empirical study has two major findings. First, our generalized model outperforms all nested specifications in terms of (a) statistical fit (when model selection is based on likelihood ratio tests) and (b) out-of-sample volatility forecasting performance. Second, we find significant Markov-switching structures in German stock market data, with substantially differing volatility equations across the regimes.     

Asymmetric Correlation and Volatility Dynamics among Stock, Bond, and Securitized Real Estate Markets

We apply a multivariate asymmetric generalized dynamic conditional correlation GARCH model to daily index returns of S&P500, US corporate bonds, and their real estate counterparts (REITs and CMBS) from 1999 to 2008. We document, for the first time, evidence for asymmetric volatilities and correlations in CMBS and REITs. Due to their high levels of leverage, REIT returns exhibit stronger asymmetric volatilities. Also, both REIT and stock returns show strong evidence of asymmetries in their conditional correlation, suggesting reduced hedging potential of REITs against the stock market downturn during the sample period. There is also evidence that corporate bonds and CMBS may provide diversification benefits for stocks and REITs. Furthermore, we demonstrate that default spread and stock market volatility play a significant role in driving dynamics of these conditional correlations and that there is a significant structural break in the correlations caused by the recent financial crisis.     

Transmission of Stock Returns and Volatility between the U.S. and Japan: Evidence from the Stock Index Futures Markets

In this paper, we examine the nature of transmission of stock returns and volatility between the U.S. and Japanese stock markets using futures prices on the S&P 500 and Nikkei 225 stock indexes. We use stock index futures prices to mitigate the stale quote problem found in the spot index prices and to obtain more robust results. By employing a two-step GARCH approach, we find that there are unidirectional contemporaneous return and volatility spillovers from the U.S. to Japan. Furthermore, the U.S.'s influence on Japan in returns is approximately four times as large as the other way around. Finally, our results show no significant lagged spillover effects in both returns and volatility from the Osaka market to the Chicago market, while a significant lagged volatility spillover is observed from the U.S. to Japan. This revised version was published online in August 2006 with corrections to the Cover Date.     

Testing for persistence in stock returns with GARCH-stable shocks

We investigate persistence in CRSP monthly excess stock returns, using a state space model with stable disturbances. The non-Gaussian state space model with volatility persistence is estimated by maximum likelihood, using the optimal filtering algorithm given by Sorenson and Alspach (1971 Automatica 7 465–79). The conditional distribution has a stable α of 1.89, and normality is strongly rejected even after accounting for GARCH. However, stock returns do not contain a significant mean-reverting component. The optimal predictor is the unconditional expectation of the series, which we estimate to be 9.8% per annum.     

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.