Multiple asymmetries in index stock returns from boom/bust and stable/volatile markets states- an empirical study of US and UK stock markets

Abstract

This article tries to answer the question: is the response of current returns to past returns asymmetric when the returns follow an autoregressive, spillover GARCH model? Our empirical findings are consistent with the following notions. First, both US and UK markets appear to overreact to the drastic events in the 1990s. Second, the impacts of the 1-week-ahead foreign market returns were marked during the 1980s, especially when the home market returns were both volatile and negative. In contrast, the impacts were insignificant during the 1990s. Third, in the 1990s, the UK (US) investors' behaviour during the bust appears to be consistent (inconsistent) with the leverage effects.

Notes

¹ In finance literature, autocorrelations observed in the security return time series are regarded as ‘market inefficiency’ in the sense that security returns do not react to market news events efficiently. Specifically, if the stock prices do not adjust to new information instantaneously, the market is viewed to be subject to autocorrelation anomalies. Positive autocorrelation suggests underreactions while negative autocorrelations suggest overreactions. Alternatively, if there were no autocorrelations in the stock markets, we may conclude that prices immediately reflect all new information and thus markets are efficient.

² The ideafeature of the leverage effect by Black (1976) is that the negative past returns (higher leverage) sequence would be associated with an increase in will lead to higher future return volatilities, and positive returns (lower leverage) will lead to lower future return volatilities.

³ The Engle's (1982) ARCH or the Bollerslev's (1986) GARCH are the most commonly used methods to characterize the stock return volatilities.

⁴ Moreover, for all competing models, we use OPTIMUM, a package program from GAUSS, and the built-in BFGS algebra to get the estimators that maximize the value of log-likelihood function. For the convergence problems, we randomly generate 50 sets of initial values. We then derive the ML function value for each of the 50 sets of the initial value, respectively. The mapped converging measure of the greatest ML function value then serves to estimate the parameters.

⁵ Except the UK market, in the first sub-period, the first-order ARCH parameter, λ was insignificant.

⁶ In the first sub-period, the US market's b ⁺⁺ parameter estimate was significantly positive in 5% level.

⁷ Please refer to Li and Lin (2004) and Li (2007) for the related discussions.