On the Efficiency of Conditional Heteroskedasticity Models

This paper discusses how conditional heteroskedasticity models can be estimated efficiently without imposing strong distributional assumptions such as normality. Using the generalized method of moments (GMM) principle, we show that for a class of models with a symmetric conditional distribution, the GMM estimates obtained from the joint estimating equations corresponding to the conditional mean and variance of the model are efficient when the instruments are chosen optimally. A simple ARCH(1) model is used to illustrate the feasibility of the proposed estimation procedure.     

Evaluating the Forecast Accuracy of Emerging Market Stock Returns

This paper analyzes the forecast performance of emerging market stock returns using standard autoregressive moving average (ARMA) and more elaborated autoregressive conditional heteroskedasticity (ARCH) models. Our results indicate that the ARMA and ARCH specifications generally outperform random walk models. Models that allow for asymmetric shocks to volatility are better for in-sample estimation (threshold autoregressive conditional heteroskedasticity for daily returns and exponential generalized autoregressive conditional heteroskedasticity for longer periods), and ARMA models are better for out-of-sample forecasts. The results are valid using both U. S. dollar and domestic currencies. Overall, the forecast errors of each Latin American market can be explained by the forecasts of other Latin American markets and Asian markets. The forecast errors of each Asian market can be explained by the forecasts of other Asian markets, but not by Latin American markets. Our predictability results are economically significant and may be useful for portfolio managers to enter or leave the market.     

Refining the Degree of Earnings Surprise: A Comparison of Statistical and Analysts' Forecasts

This paper compares the relative predictive ability of several statistical models with analysts' forecasts. It is one of the first attempts to forecast quarterly earnings using an autoregressive conditional heteroskedasticity (ARCH) model. ARCH and autoregressive integrated moving average models are found to be superior statistical forecasting alternatives. The most accurate forecasts overall are provided by analysts. Analysts have both a contemporaneous and timing advantage over statistical models. When the sample is screened on those firms that have the largest structural change in the earnings process, the forecast accuracy of the best statistical models is similar to analysts' predictions.     

VOLATILITY FORECASTS,TRADING VOLUME,AND THE ARCH VERSUS OPTION‐IMPLIED VOLATILITY TRADE‐OFF

We investigate empirically the role of trading volume (1) in predicting the relative informativeness of volatility forecasts produced by autoregressive conditional heteroskedasticity (ARCH) models versus the volatility forecasts derived from option prices, and (2) in improving volatility forecasts produced by ARCH and option models and combinations of models. Daily and monthly data are explored. We find that if trading volume was low during period t?1 relative to the recent past, ARCH is at least as important as options for forecasting future stock market volatility. Conversely, if volume was high during period t?1 relative to the recent past, option‐implied volatility is much more important than ARCH for forecasting future volatility. Considering relative trading volume as a proxy for changes in the set of information available to investors, our findings reveal an important switching role for trading volume between a volatility forecast that reflects relatively stale information (the historical ARCH estimate) and the option‐implied forward‐looking estimate.     

Smooth Transition ARCH Models: Estimation and Testing

In this paper, we suggest an extension of the ARCH model, the smooth-transition autoregressive conditional heteroskedasticity (STARCH) model. STARCH models endogenously allow for time-varying shifts in the parameters of the conditional variance equation. The most general form of the model that we consider is a double smooth-transition model, the STAR-STARCH model, which permits not only the conditional variance, but also the mean, to be a function of a smooth-transition term. The threshold ARCH model, the Markov-ARCH model and the standard ARCH model are special cases of our STARCH model. We also develop Lagrange multiplier tests of the hypothesis that the smooth-transition term in the conditional variance is zero. We apply our STARCH model to excess Treasury bill returns. We find some evidence of a smooth transition in excess returns, but in contrast to previous studies, we find almost no evidence of volatility persistence once we allow for smooth transitions in the conditional variance. Thus, the apparent persistence in the conditional variance reported by many researchers could be a mere statistical artifact. We conduct in-sample tests comparing STARCH models to nested competitors; these suggest that STARCH models hold promise for improved predictions. Finally, we describe further extensions of the STARCH model and suggest issues in finance to which they might profitably be applied.     

Conditional Heteroskedasticity and Global Stock Return Distributions

This paper investigates conditional return distribution characteristics for seven developed markets (DMs) and eight emerging markets (EMs). With the exception of Germany and Japan, the behavior of monthly returns of DM sample countries is similar to that of the U.S. In contrast, EM returns exhibit a substantially greater degree of serial correlation and a higher incidence of autoregressive conditional heteroskedasticity (ARCH) in monthly data. Aggregation of returns into two- and three-month holding periods decreases the significance of the ARCH effects. However, there are cross-sectional differences in the rate at which ARCH effects become insignificant. The findings of ARCH in monthly returns sample data is attributed to differences in the rate at which information arrives and is transmitted into prices in each market.     

Good News,Bad News,Volatility, and Betas

We investigate the conditional covariances of stock returns using bivariate exponential ARCH (EGARCH) models. These models allow market volatility, portfolio-specific volatility, and beta to respond asymmetrically to positive and negative market and portfolio returns, i.e., “leverage” effects. Using monthly data, we find strong evidence of conditional heteroskedasticity in both market and non-market components of returns, and weaker evidence of time-varying conditional betas. Surprisingly while leverage effects appear strong in the market component of volatility, they are absent in conditional betas and weak and/or inconsistent in nonmarket sources of risk.     

Is long memory necessary? An empirical investigation of nonnegative interest rate processes

This paper analyzes a class of nonnegative processes for the short-term interest rate. The dynamics of interest rates and yields are driven by the dynamics of the conditional volatility of the pricing kernel. We study Markovian interest rate processes as well as more general non-Markovian processes that display “short” and “long” memory. These processes also display heteroskedasticity patterns that are more general than those of existing models. We find that deviations from the Markovian structure significantly improve the empirical performance of the model. Certain aspects of the long memory effect can be captured with a (less parsimonious) short memory parameterization, but a simulation experiment suggests that the implied term structures corresponding to the estimated long- and short-memory specifications are very different. We also find that the choice of proxy for the short rate affects the estimates of heteroskedasticity patterns.     

Volatility and information flows in emerging equity market: A case of the Korean Stock Exchange

Applying the generalized autoregressive conditional heteroskedasticity (GARCH) model to the Korean Stock Exchange, this study examines: (1) the statistical property of time-varying volatility in returns and trading volume data found in an emerging capital market, and (2) the property of the conditional variances of returns in predicting the flow patterns of information across the firms of different sizes. The results find that current trading volume as a proxy of information arrival dramatically reduces the persistence of the conditional variance, meaning that the arrival of information is a source of the ARCH effect in the emerging market just as it is in the U.S. The results also show that just as the volatility of larger firms can be predicted by shocks to smaller firms, the volatility of smaller firms can be predicted by shocks to larger firms. However, the volatility spillover effect from larger to smaller firms is more significant than that from smaller to larger firms.     

Fractionally Integrated Models With ARCH Errors: With an Application to the Swiss 1-Month Euromarket Interest Rate

We introduce ARFIMA-ARCH models, which simultaneously incorporate fractional differencing and conditional heteroskedasticity. We develop the likelihood function and we use it to construct the bias-corrected maximum (modified profile) likelihood estimator. Finite-sample properties of the estimation procedure are explored by Monte Carlo simulation. Backus and Zin (1993) have motivated the existence of fractional integration in interest rates by the persistence of the short rate and the variability of the long end of the yield curve. An empirical investigation of a daily one-month Swiss Euromarket interest rate finds a difference parameter of 0.72. This indicates non-stationary behavior. In contrast to first-order integrated models, the long-run cumulative response of shocks to the series is zero.     

Testing for constant hedge ratios in commodity markets: a multivariate GARCH approach

We develop a new multivariate generalized ARCH (GARCH) parameterization suitable for testing the hypothesis that the optimal futures hedge ratio is constant over time, given that the joint distribution of cash and futures prices is characterized by autoregressive conditional heteroskedasticity (ARCH). The advantage of the new parameterization is that it allows for a flexible form of time-varying volatility, even under the null of a constant hedge ratio. The model is estimated using weekly corn prices. Statistical tests reject the null hypothesis of a constant hedge ratio and also reject the null that time variation in optimal hedge ratios can be explained solely by deterministic seasonality and time to maturity effects.     

The Dynamics of Short-Term Interest Rate Volatility Reconsidered

In this paper we present and estimate a model of short-term interest rate volatility that encompasses both the level effect of Chan, Karolyi, Longstaff and Sanders (1992) and the conditional heteroskedasticity effect of the GARCH class of models. This flexible specification allows different effects to dominate as the level of the interest rate varies. We also investigate implications for the pricing of bond options. Our findings indicate that the inclusion of a volatility effect reduces the estimate of the level effect, and has option implications that differ significantly from the Chan, Karolyi, Longstaff and Sanders (1992) model.     

Multivariate term structure models with level and heteroskedasticity effects

The paper introduces and estimates a multivariate level-GARCH model for the long rate and the term-structure spread where the conditional volatility is proportional to the γth power of the variable itself (level effects) and the conditional covariance matrix evolves according to a multivariate GARCH process (heteroskedasticity effects). The long-rate variance exhibits heteroskedasticity effects and level effects in accordance with the square-root model. The spread variance exhibits heteroskedasticity effects but no level effects. The level-GARCH model is preferred above the GARCH model and the level model. GARCH effects are more important than level effects. The results are robust to the maturity of the interest rates.     

Currency futures market in India: an empirical analysis of market efficiency and volatility

As the Indian currency futures market has been in existence for over 7 years, this paper analyses the effectiveness of the 1-month USD/INR currency futures rates in predicting the expected spot rate. The volatility of the USD/INR spot returns was also analysed. Modelling volatility of the USD/INR spot rate using a generalized autoregressive conditional heteroskedasticity (GARCH) and exponential generalized autoregressive conditional heteroskedasticity (EGARCH) model indicated the presence of volatility clustering. Using multivariate GARCH models such as the constant conditional correlation and dynamic conditional correlation, signs of a volatility spillover between the USD/INR spot and currency futures market were also observed.     

MUTUAL FUND DAILY CONDITIONAL PERFORMANCE

The empirical finance literature reveals that conditional models estimated with monthly data generally improve fund performance. Furthermore, it has been shown that using daily instead of monthly returns in an unconditional framework increases the proportion of abnormal performances relative to timing. In this article, we study conditional performance estimated with daily data in a bivariate generalized autoregressive conditional heteroskedasticity (GARCH) framework. Our daily conditional alphas and global performances with GARCH are significantly better than those estimated with other parametrizations and they persist over time. Finally, the proportion of abnormal timing performances diminishes significantly when conditional parametrizations are used.     

Interest-risk sensitive deposit insurance premia: Stable ACH estimates

The parameters of interest rate uncertainty are estimated by maximum likelihood for the period 1952–1982, and used to evaluate bank or thrift deposit insurance as a function of duration mismatching, capital/asset ratio, and the recent history of interest rate forecasting errors. Homoskedasticity is overwhelmingly rejected in favor of adaptive conditional heteroskedasticity (ACH). Even after removing this heteroskedasticity, normality gives much lower likelihood than Paretian stable distributions with characteristic exponent in the range 1.614 to 1.714. The conditional deposit insurance values fluctuate by factors in excess of 300 for some duration gaps over the past three decades.     

International Asset Pricing and Portfolio Diversification with Time-Varying Risk

We test the conditional capital asset pricing model (CAPM) for the world's eight largest equity markets using a parsimonious generalized autoregressive conditional heteroskedasticity (GARCH) parameterization. Our methodology can be applied simultaneously to many assets and, at the same time, accommodate general dynamics of the conditional moments. The evidence supports most of the pricing restrictions of the model, but some of the variation in risk-adjusted excess returns remains predictable during periods of high interest rates. Our estimates indicate that, although severe market declines are contagious, the expected gains from international diversification for a U.S. investor average 2.11 percent per year and have not significantly declined over the last two decades.     

Emerging Markets and Stock Market Bubbles: Nonlinear Speculation?

Daily returns of stock markets in emerging markets in Asia, Africa, South America, and Eastern Europe from the early 1990s through 2006 are analyzed for the possible presence of nonlinear speculative bubbles. The absence of these is tested for by studying residuals of vector autoregressive-based fundamentals, using the Hamilton regimeswitching model and the rescaled range analysis of Hurst. For the first test, absence of bubbles is rejected for twenty-four countries (except Mexico, Sri Lanka, and Taiwan); for the second test, it is rejected for twenty-six countries (except Malaysia). BDS testing on these residuals after autoregressive conditional heteroskedasticity (ARCH) effects are removed fails to reject further nonlinearity (except for Israel). Policy issues are discussed, noting that what is appropriate varies from country to country and time period to time period.     

The incremental volatility information in one million foreign exchange quotations

The volatility information found in high-frequency exchange rate quotations and in implied volatilities is compared by estimating ARCH models for DM/$ returns. Reuters quotations are used to calculate five-minute returns and hence hourly and daily estimates of realised volatility that can be included in equations for the conditional variances of hourly and daily returns. The ARCH results show that there is a significant amount of information in five-minute returns that is incremental to options information when estimating hourly variances. The same conclusion is obtained by an out-of-sample comparison of forecasts of hourly realised volatility.     

Hedging the black swan: Conditional heteroskedasticity and tail dependence in S&P500 and VIX

The recent financial crisis has accentuated the fact that extreme outcomes have been overlooked and not dealt with adequately. While extreme value theories have existed for a long time, the multivariate variant is difficult to handle in the financial markets due to the prevalent heteroskedasticity embedded in most financial time series, and the complex extremal dependence that cannot be conveniently captured by a single structure. Moreover, most of the existing approaches are based on a limiting argument in which all variables become large at the same rate. In this paper, we show how the conditional approach of Heffernan and Tawn (2004) can be implemented to model extremal dependence between financial time series. We use a hedging example based on VIX futures to demonstrate the flexibility and superiority of the conditional approach against the conventional OLS regression approach.