ارتباط نوسانات در سه بازار عمده سهام: روش آربیتراژ مالی

This paper investigates the high frequency behavior of US, British and German stock market exuberance using an index provided by standard portfolio arbitrage relationships. Symmetric and asymmetric multivariate GARCH models are implemented to quantify international volatility linkages between January 1992 and April 2000. A shift in volatility transmission is detected from May 1997 onwards. Empirical analysis suggests that equity markets volatility modeling with exuberance indexes is more accurate than modeling with stock returns. Exuberance volatility comovements across countries are compared with the corresponding return comovements. An interpretation of their discrepancy is provided in terms of bond and stock returns international covariation.

The recent financial crises have brought about a renewed interest in theoretical and empirical investigations into international links between asset market volatilities. In most cases, however, the origins of turbulence are to be found in the emerging markets, involving financial assets often traded in a context of exchange rate and banking instability. These characteristics are incorporated in the burgeoning literature on asset market volatility “contagion” (see Masson, 1999 and Kodres and Pritsker, 2002 among others). The latter is ill-suited for investigation into the nature of the substantial stock return volatility shifts across large and sophisticated markets of industrialized countries such as the US, Britain and Germany presented in this paper. We introduce a simple model of financial arbitrage which quantifies an index of daily national stock market exuberance, and go on to investigate its behavior over time in an international context, thus encompassing two major aspects of stock market pricing analysis: international interlinkages and over-underreaction to news. Various interpretations of excess volatility have been given, rational bubbles initially seeming to provide an appropriate explanation. Indeed, a rational bubble is compatible with the forward solution of an expected stock return model whenever the transversality condition is violated (West, 1987, among many others). More recent developments favor an interpretation of excess stock volatility in terms of fads as theoretical and empirical results reduce the plausibility of rational bubble inception. Shiller (1984) and De Bondt and Thaler (1985) point out that economic agents follow irrational trading rules and overreact to news. De Bondt and Thaler show that US stock prices tend to overreact and that extreme movements are followed by subsequent shifts in the opposite direction. Their approach has recently been extended to a multi-market context by Richards (1997) and Schnusenberg and Madura (2000), who assess (national) portfolio volatility relative to a worldwide index. A major difficulty with over-underreaction analysis lies in the selection of a benchmark with appropriate theoretical and empirical characteristics. It can be provided either by the asset's own past history or by the (past) behavior of other assets, linked to the former by portfolio theory or arbitrage opportunities. The latter approach is followed here. The paper investigates the behavior of stock market exuberance, tentatively quantified as excess stock market return over expected long-term bond return.1 Any positive (negative) difference in returns can be interpreted as an over-underreaction of the stock market. Fads and bubbles do not usually affect bond markets, and bond prices are generally believed to reflect economic fundamentals as the use of daily data prevents us from introducing them directly into analysis.2 In the single country context stock, bonds and money markets are interlinked in the short run as economic agents readjust their portfolios and react to the spread of news. The relevance of the correlation between stock and bond returns is somewhat controversial. Shiller and Beltratti (1992), using the VAR methodology and the present value relationships of Campbell and Shiller (1988), find that the correlation between annual excess US (and British) stock and bond returns exceeds the theoretical warranted values, and identify a possible overreaction of the stock market to the long-term bond market. Zhou (1996) finds that the power of interest rates in explaining the variation of stock market returns rises with the maturity horizon of the assets involved. Campbell and Ammer (1993) find correlation between US monthly stock and bond returns fairly weak. Applying a VAR approach, they show that the variance of excess stock returns is explained by changes in expectations of future excess stock returns, whereas the variance of excess returns on long-term nominal bonds is accounted for primarily by news about future inflation rates (in turn related to the business cycle). More recently, Bodart and Reding (1999) arrive at analogous conclusions in an international context involving European stock and bond returns volatilities. These results seem to validate our choice of exuberance index (see Section 2). In this paper, the daily international comovement of conditional second moments of exuberance indexes from the US, British and German stock markets is investigated using multivariate GARCH parameterization, introduced in view of the volatility clustering evidenced in preliminary analysis of the data. With respect to standard VAR modeling, multivariate GARCH is more difficult to implement. It does, however, provide the required information on the evolution over time of the volatility of the exuberance indexes and its transmission across markets—information that would not be captured by the VAR estimation approach. Indeed, with analysis of the behavior over time of the conditional variances and covariances of the set of exuberance indexes, we are able to identify the timing of the shifts in volatility and of their international linkages which, in line with previous findings, tend to increase in periods of stress. This information is of paramount relevance in a time interval—from January 1992 to April 2000—affected by bouts of severe financial turbulence. Interestingly, equity market GARCH volatility modeling with exuberance indexes seems to be more accurate—according to standard econometric criteria—than modeling with stock return time series. This study innovates with respect to the existing literature in three ways: - it extends exuberance analysis to an international framework: studies on stock markets interlinkages use standard stock return indexes, and research on international stock market overreaction (exuberance) transmission is somewhat sparse, as pointed out by Schnusenberg and Madura (2000); - it compares exuberance volatility comovements across countries with the corresponding stock return comovements and provides an interpretation of their discrepancy in terms of bond and stock returns international covariation; - it investigates explicitly whether changes in volatility do in fact Granger cause changes in exuberance comovements across markets, a highly controversial issue in the recent literature of great relevance for portfolio balancing procedures. The paper is organized as follows. The second section introduces the theoretical model designed to extract the exuberance index and the multivariate GARCH methodology implemented to obtain estimates of conditional second moments and cross correlations between them. In the third section, the empirical findings are set out using two GARCH parameterizations of the conditional variation of the exuberance indexes over the full sample. In the fourth section, the relative accuracy of exuberance and stock return volatility estimates is assessed over two subperiods, characterized by a highly different degree of turbulence. The fifth section sets out the main conclusions.

Standard multivariate GARCH models are essentially descriptive, while economic and financial interpretations are usually superimposed a posteriori. In this paper, we introduce an ex ante structure—defining an arbitrage free stock return—and assess whether the ensuing restrictions are corroborated by the empirical evidence for three major equity markets. Multivariate symmetric and asymmetric GARCH models are estimated in order to investigate the daily volatility in the January 1992–April 2000 period. Second-moment linkages between the US, British and German stock markets are examined using an exuberance index derived from standard portfolio arbitrage relationships. We provide a definition of exuberance, although the mechanism that may trigger it is beyond the scope of our investigation. The main finding of the paper is that volatility transmission across countries is mostly accounted for by stock market exuberance, i.e., return covariances are de facto, exuberance covariances. Moreover, volatility modeling with exuberance indexes seems to be more accurate than modeling with stock returns. Two subperiods are identified due to a shift in the pattern of volatility transmission in May, 1997. The successive bouts of financial turbulence occurring since May, 1997 result in an increase in the conditional second moments of the exuberance indexes and a significant rise in their covariation across markets. Market interlinkages rise in periods of uncertainty as fads and herd behavior effects loom large even in sophisticated markets. Standard return volatility analysis seems to overestimate (underestimate) cross-market linkages in periods of low (high) volatility. However, investigation into the cross-country comovements of bonds and stocks yields ex ante information that may be of use, via analysis of exuberance indexes, in reducing portfolio risk. The introduction of exuberance indexes in dynamic portfolio hedging creates scope for further research. Acknowledgement The authors are grateful to Emilio Barone and especially to the anonymous referee for extremely useful and constructive suggestions. The authors remain solely responsible for any error contained herein.