Conditional Return Volatility Research Articles

Equilibrium Stock Return Dynamics Under Alternative Rules of Learning About Hidden States

We examine the properties of equilibrium stock returns in an incomplete information economy in which agents need to learn the hidden state of the endowment process. Both Bayesian and suboptimal learning rules are considered, including near-rational learning, conservatism, representativeness, optimism, and pessimism. We demonstrate that Bayesian learning performs reasonably well in producing realistic variation in the conditional equity risk premium, return volatility, and Sharpe ratio. Alternative learning behaviors alter significantly both the level and time-variation of the conditional moments of returns. However, when we allow the agents to be conscious of their learning mistakes and to price assets accordingly, the properties of equilibrium stock returns under alternative learning are virtually indistinguishable from those under Bayesian learning.

Trading intensity, volatility, and arbitrage activity

The objective of this paper is to uncover the determinants of trading intensity in futures markets. In particular, the time between adjacent transactions (referred to as transaction duration) on the FTSE 100 index futures market is modeled using various augmentations of the basic autoregressive conditional duration (ACD) model introduced by Engle and Russell [Econometrica 66 (1998) 1127]. The definition of transaction duration used in this paper is an important variable as it represents the inverse of instantaneous conditional return volatility. As such, this paper can also be viewed as an investigation into the determinants of (the inverse of) instantaneous conditional return volatility. The estimated parameters from various ACD models form the basis of the hypothesis tests carried out in the paper. As predicted by various market microstructure theories, we find that bid–ask spread and transaction volume have a significant impact upon subsequent trading intensity. However, the major innovation of this paper is the finding that large (small) differences between the market price and the theoretical price of the futures contract (referred to as pricing error) lead to high (low) levels of trading intensity in the subsequent period. Moreover, the functional dependence between pricing error and transaction duration appears to be non-linear in nature. Such dependence is implied by the presence of arbitragers facing non-zero transaction costs. Finally, a comparison of the forecasting ability of the various estimated models shows that a threshold ACD model provides the best out-of-sample performance.

A New Approach to Measuring Financial Contagion

This article proposes a new approach to evaluate contagion in financial markets. Our measure of contagion captures the coincidence of extreme return shocks across countries within a region and across regions. We characterize the extent of contagion, its economic significance, and its determinants using a multinomial logistic regression model. Applying our approach to daily returns of emerging markets during the 1990s, we find that contagion is predictable and depends on regional interest rates, exchange rate changes, and conditional stock return volatility. Evidence that contagion is stronger for extreme negative returns than for extreme positive returns is mixed.

Estimating GARCH models using support vector machines*

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. * Paper presented at Applications of Physics in Financial Analysis (APFA) 3, 5-7 December 2001, Museum of London, UK.

Do Macroeconomic Announcements Cause Asymmetric Volatility?

In this paper we study the impact of macroeconomic news announcements on the conditional volatility of stock and bond returns. Using daily returns on the S&P 500 index, the NASDAQ index, and the 1 and 10 year U.S. Treasury bonds, for January 1982 - August 2001, some interesting results emerge. Announcement shocks appear to have a strong impact on the (dynamics of) bond and stock market volatility. Our results provide empirical evidence thatasymmetric volatility in the Treasury bond market can be largely explained by these macroeconomic announcement shocks. This suggests that the asymmetric volatility found in government bond markets are likely due to misspecification of the volatility model. After including macroeconomic announcements into the model, the asymmetry disappears. Becausefirm-specific news is the most important source of information in the stock market, the asymmetries in stock volatility do not disappear after incorporating macroeconomic announcements into the volatility model.

Risk-return-volume relationship in an emerging stock market

This paper aims to provide empirical evidence for the risk-return-volume relationship in the Ýstanbul Stock Exchange (ISE) for the period 2 January 1992 to 29 May 1998. The Generalized Autoregressive Conditional Heteroscedasticity-in-Mean (GARCH-M) specification reveals that daily return volatility is time-varying and highly persistent. In addition, return is positively associated with risk, i.e. the estimate of the conditional standard deviation. Contemporaneous changes in volume have a positive effect on returns. The previous day's change in volume affects conditional volatility of returns positively.

The Determinants of Asymmetric Volatility

Volatility in equity markets is asymmetric: contemporaneous return and conditional return volatility are negatively correlated. In this article I develop an asymmetric volatility model where dividend growth and dividend volatility are the two state variables of the economy. The model allows both the leverage effect and the volatility feedback effect, the two popular explanations of asymmetry. The model is estimated by the simulated method of moments. I find that both the leverage effect and volatility feedback are important determinants of asymmetric volatility, and volatility feedback is significant both statistically and economically.

The Introduction of Derivatives on the Dow Jones Industrial Average and Their Impact on the Volatility of Component Stocks

AbstractThis article examines the impact of trading in the Dow Jones Industrial Average (DJIA) index futures and futures options on the conditional volatility of component stocks. It investigates the contention that the introduction of futures and futures options on the DJIA could increase volatility in the 30 stocks comprising the DJIA. The conditional volatility of intraday returns for each stock before and after the introduction of derivatives is estimated with the Generalized Autoregressive Conditional Heteroscedasticity (GARCH) model. Estimated parameters of conditional volatility in prefutures and postfutures periods are then compared to determine if the estimated parameters have changed significantly after the introduction of the various derivatives. The results suggest that the introduction of index futures and futures options on the DJIA has produced no structural changes in the conditional volatility of component stocks. © 2001 John Wiley & Sons, Inc. Jrl Fut Mark 21: 633–653, 2001

Robust conditional variance estimation and value-at-risk

The exponentially weighted moving average (EWMA) estimator is widely used to forecast the conditional volatility of short-horizon asset returns. The EWMA estimator is appropriate when returns are drawn from a normal conditional distribution, but when the conditional distribution of returns is fat-tailed – as is commonly found in practice – the EWMA estimator is inefficient in the sense that it attaches too much weight to extreme returns. In this paper we propose a simple generalization of the EWMA estimator that nests both the standard EWMA estimator and other EWMA estimators that are robust to leptokurtosis in the conditional distribution of returns. We illustrate the new estimator by forecasting the value-at-risk (VAR) of aggregate equity portfolios for the US, the UK and Japan using historical simulation. Back-testing results show that a robust EWMA estimator based on the absolute value of returns rather than their squares offers an improvement over the standard EWMA estimator.

Belief-dependent Utilities, Aversion to State-Uncertainty and Asset Prices

This paper reinterprets standard axioms in choice theory to introduce the concepts of belief dependent utility functions and to state-uncertainty, and it shows that this type of preferences helps to explain the various stylized facts of asset returns, including a high equity risk premium, a low risk-free rate, a high return volatility, stock return predictability and volatility clustering. In one particular specification consistent with habit formation preferences, I also argue that aversion to state gives rise to aversion to long run risk, that is, to the uncertainty surrounding the long run average of future consumption. In order to solve for asset prices and returns under general conditions about the hidden state variable, the paper also develops a discretization methodology to obtain approximate analytical solutions. In a parsimonious parametrization, I then show that the model calibrated to real consumption generates unconditional moments for asset returns that closely match the empirical ones. Finally, due to the estimated time-variation in the dispersion of the conditional distribution on the drift rate of consumption, the model also generates a time series of conditional return volatility in line with the ex-post integrated volatility of stock returns.

The Determinants of Asymmetric Volatility

Volatility in equity markets is asymmetric: contemporaneous return and conditional return volatility are negatively correlated. In this paper we develop an asymmetric volatility model where dividend growth and dividend volatility are the two state variables of the economy. The model allows both the leverage effect and the volatility feedback effect, the two popular explanations of the asymmetry. The model is estimated by the simulated method of moments. We find that both the leverage effect and the volatility feedback are important determinants of asymmetric volatility, and volatility feedback is significant both statistically and economically.

A New Approach to Measuring Financial Contagion

This paper proposes a new approach to evaluate contagion in financial markets. Our measure of contagion captures the co-incidence of extreme return shocks across countries within a region and across regions that cannot be explained by linear propagation models of shocks. We characterize the extent of contagion, its economic significance, and its determinants using a multinomial logistic regression model. Applying our approach to daily returns of emerging markets during the 1990s, we find that contagion, when measured by the co-incidence within and across regions of extreme return shocks, is predictable and depends on regional interest rates, exchange rate changes, and conditional stock return volatility. Evidence that contagion is stronger for extreme negative returns than for extreme positive returns is mixed.

Stock Market Risk and Return: An Equilibrium Approach

Empirical evidence that expected stock returns are weakly related to volatility at the market level appears to contradict the intuition that risk and return are positively related. We investigate this issue in a general equilibrium exchange economy characterized by a regime-switching consumption process with time-varying transition probabilities between regimes. When estimated using consumption data, the model generates a complex, nonlinear and time-varying relation between expected returns and volatility, duplicating the salient features of the risk/return trade-off in the data. The results emphasize the importance of time-varying investment opportunities and highlight the perils of relying on intuition from static models. Understanding the risk/return trade-off is fundamental to equilibrium asset pricing. In this context, the stock market is one of the most natural starting points since it serves as a proxy for the wealth portfolio that is studied in finance theory. It is perhaps surprising, therefore, that there is still a good deal of controversy around the issue of how to measure risk at the market level. Recent empirical studies [e.g., Glosten, Jagannathan, and Runkle (1993), Whitelaw (1994), and Boudoukh, Richardson, and Whitelaw (1997)] document two puzzling results with regard to the intertemporal relation between equity risk and return at the market level. 1 First, they provide evidence of a weak, or even negative, relation between conditional expected returns and the conditional volatility of returns. 2 Second, they document significant time variation in this relation. Specifically, in a modified GARCH-M framework using post-World War II monthly data, Glosten, Jagannathan, and Runkle (1993) find that the estimated coefficient on volatility in the expected return regression is negative. In a similar dataset, when both conditional moments are estimated as functions of predetermined financial variables, Whitelaw (1994)

Interdependence of international equity market volatility

This paper investigates whether equity market volatility in one major market is related to volatility elsewhere. This paper models the daily conditional volatility of equity market wide returns as a GARCH-(1,1) process. Such a model will capture the changing nature of the conditional variance through time. It is found that the correlation between the conditional variances of major equity markets has increased substantially over the last two decades. This supports work which has been undertaken on conditional mean returns which indicates there has been an increase in equity market integration.

Asymmetric index stock returns: evidence from the G–7

There is able empirical evidence that the conditional volatility of stock returns is asymmetric in the sense that negative innovations increase volatility more than positive innovations of an equal magnitude. Less attention, however, has been paid to possible asymmetries in the conditional mean. This paper uses time-varying asymmetric distributions to model index stock returns of the Group of Seven (G-7) industrialized nations. In agreement with the extant literature, all index stock returns exhibit asymmetric volatility. More importantly however, the conditional mean is also an asymmetric function of past innovations, in most cases. Interestingly, the asymmetry in the conditional mean case is the reverse of that observed in the conditional variance, that is, positive innovations have a greater impact than negative innovations of an equal sign. Equivalently, positive innovations (up markets) are more persistent than negative innovations (down markets). Overall, the evidence suggests that taking into account both size as well as the sign of past innovations can improve forecasts of the conditional first and second moments of stock returns.

Some exotic options under symmetric and asymmetric conditional volatility of returns

For a plain vanilla call and three of the more popular exotic (path-dependent) types of options, this study examines the impact of symmetric and asymmetric GARCH processes in returns. The price, delta and gamma of European call options, Black–Scholes implied volatilities and convergence of these factors are all studied, through a simulation of price paths. For comparison, we ensure that the unconditional volatility of each process is identical. The impact of a standard symmetric GARCH volatility structure on the option parameters is usually to bias price and delta downwards, but to bias gamma upwards, sometimes quite considerably. Asymmetric GARCH effects exacerbate this effect, and it varies across the different options. GARCH effects appear not to induce a smile. Finally, as time to maturity shortens, at-the-money call prices and deltas converge slowly but gammas can change wildly when GARCH effects are added.

TIME VARIATIONS IN RISK PREMIA, VOLATILITY, AND REWARD‐TO‐VOLATILITY

AbstractIn this paper I relate the risk premia in the stock and bond markets to the conditional volatility of returns and time‐varying reward‐to‐volatility variables. I find that the relation between the expected returns on the stocks and bonds and the volatility of returns is time varying. I provide an approach for evaluating the relative importance of the time‐varying volatility of returns and reward‐to‐volatility variables to explain the predictability of risk premia for stock and bond returns. I show that changing reward‐to‐volatility variables explain more predictable variation in the risk premia for stocks and bonds than changing volatility of returns.

Indicatori tecnici e volatilità di serie storiche finanziarie

The econometric analysis of financial markets has recently focussed on the effects of possible non-linearities in the returns time series for the market efficiency hypothesis. In fact, one of the empirical regularities next to the lack of autocorrelation in the returns is the time dependence in positive-valued non-linear functions of the returns themselves. The lack of independence in the returns signals that there exists a structure which calls for deeper economic interpretation and statistical analysis. In this paper we focus on the link between the tools used by technical analysts and widely popular among traders to isolate the most suitable moments to purchase or sell securities, and the econometric/statistical methodology used to study conditional volatility of returns. In particular we want to analyze whether the presence of a consensus on the short-run trend of prices translates into an impact on volatility introducing asymmetric effects whether the technical signals relate to sales or purchases. The applications are performed on daily data from the New York Stock Exchange.

Testing for seasonal patterns in conditional return volatility: evidence from Asia-Pacific markets

Several previous studies have focused upon seasonal patterns in the unconditional volatility of intraday and daily returns data. But these investigations could be misleading without considering a fuller structural model of the time series properties of return volatility. The seasonal pattern in the volatility of five Asia-Pacific stock markets is investigated using the unconditional modified Levene statistic (Ho, Y. K. and Cheung, Y. L., 1994, Seasonal pattern in volatility in Asian stock markets, Applied Financial Economics, 4, 61-67) and by estimating the conditional variance of each market using an ARCH procedure.

Some tests of market microstructure hypotheses in the foreign exchange market

In this paper we examine a number of hypotheses stemming from the market microstructure literature. In particular, we use a disaggregate survey data base, consisting of the foreign exchange expectations of over 150 forecasters, to construct both aggregate and disaggregate measures of dispersion. These measures are then used to examine the relationship between volatility, volume and heterogeneity. GARCH modelling techniques are also employed to test a set of hypotheses relating to the conditional volatility of exchange rate returns. The tenor of the results contained in this paper may be interpreted as supportive of the usefulness of market microstructure concepts in analysing foreign exchange markets.