The Choice of Target’s Advisor in Mergers and Acquisitions: the Role of Banking Relationship

This paper investigates the forecasting performance of three popular variants of asymmetric GARCH models, namely VS-GARCH, GJR-GARCH and Q-GARCH, with the symmetric GARCH(1,1) model as the benchmark. The application involves three Asian and ten European stock price indexes. Forecasts produced by each asymmetric GARCH model and each index are evaluated using a common set of classical criteria, as well as forecast combination techniques with constant and non-constant weights. With respect to the standard GARCH specification, the asymmetric models generally lead to better forecasts in terms of both smaller forecast errors and lower biases. In-sample forecast combination regressions are better than those from single Mincer-Zarnowitz regressions. The out-of-sample performance of combining forecasts is less satisfactory, irrespective of the type of weights adopted. Asymmetric GARCH models (see Hentschel, 1995, for a survey) extend the seminal contributions by Engle (1982) and Bollerslev (1986) to incorporate the asymmetric impacts of shocks or news of equal magnitude but opposite sign on the conditional variance of asset returns. In this paper we investigate the forecasting performances of three popular variants of asymmetric GARCH specifications, namely Volatility Switching (VS-GARCH), GJR-GARCH and Quadratic (Q-GARCH), using the symmetric GARCH(1,1) as the benchmark. The application involves three Asian and ten European stock market indexes. Following Poon and Granger (2003), it is possible to divide the current literature on forecasting volatility in financial markets in two main veins. The first one refers to models based on historical prices (time series approach), whereas the second comprises those techniques aimed at forecasting volatility from actual option prices via the link with the Black-Sholes’s model (option implied standard deviation approach). This paper belongs to the time series approach, which starts with the work by Taylor (1987) on forecasting the future volatility of the DM/$ exchange rate series. Dimson and Marsh (1990) investigate the forecasting performance of some simple models applied to the U.K. stock market, such as Random Walk (RW), Historical Average, Moving Average, Exponential Smoothing and linear regressions. Akgiray (1989) is the first who uses the GARCH model to forecast volatility, showing that the GARCH(1,1) outperforms some of the techniques discussed in Taylor (1987). On the contrary, Cao and Tsay (1992) point out that the Threshold Autoregressive model produces better forecasts than GARCH, Exponential GARCH e ARMA models on the U.S.A. stock market. The forecasting behaviour of the Stochastic Volatility (SV) model is even more controversial. On the one hand, Heynen (1995) and Yu (2002) confirm the validity of the SV model when applied to stock market indexes, on the other hand Dunis, Laws and Chauvin (2001) document some difficulties for this model to forecast exchange rate volatility. Tse and Tung (1992) strongly prefer the Exponentially Weighted Moving Average model to the GARCH(1,1) for the Singapore stock market. This is mainly attributable to the non-stationary variances of Singapore stock market indexes, while the standard GARCH model imposes stationarity. Brailsford and Faff (1996) select the GJR-GARCH(1,1) as the best model for the Australian stock index, although they point out that the final choice is not independent of the adopted evaluation criteria. On the same Australian stock index, Walsh and Tsou (1998) reject the GARCH model, whereas Brooks (1998) is not able to select the most appropriate model for the Dow Jones composite. Finally, Franses and van Dijk (1996) compare RW, GARCH, Q-GARCH and GJR-GARCH specifications and show that Q-GARCH is the most successful in forecasting the volatility of stock price indexes for Italy, Spain, Germany and Sweden. Such different and often contrasting results are mainly due to the lack of any common procedure to produce and evaluate competing sets of forecasts, especially in terms of number of time series subject to scrutiny, frequency of the data, forecasting horizons and loss functions. With respect to the existing literature, this paper contains several distinguishing elements. First, a number of relevant Asian and European stock markets is analyzed. Second, samples and data frequencies are kept homogeneous throughout the empirical investigation. Third, forecasts produced by different models are compared using a common set of classical criteria and more recent forecast combination techniques with constant and non-constant weights. The structure of the paper is as follows. Section 2 presents the main characteristics of the asymmetric GARCH models used in the empirical analysis. Section 3 is dedicated to a discussion of the criteria adopted to compare different sets of forecasts. In Section 4 the data set is briefly described, and the forecasting performance of each asymmetric GARCH model for each stock market index is analyzed. Section 5 contains some concluding comments