اجرای مسائل پست مدل های سابق ارتباط بازار سهام جهانی

Analysis of ex post returns reveals the time series properties of correlations, but ex ante correlations are required for efficient diversification. We find that a time-varying parameter model offers the best fit to ex post global equity market correlations, suggesting changing mean correlations and changing rates of adjustment back to the means. Nevertheless, we do not find improved forecast performance from time-varying parameter models in holdout periods. The added complexity of time-varying models does not translate into lower forecast errors.

Empirical research on international diversification began in the early 1970s (e.g., Levy and Sarnat, 1970 and Solnik, 1974). Risk reduction from diversification across national markets should allow investors to reduce total portfolio risk without sacrificing return. The fundamental premise of international diversification is that phenomena unique to each country drive equity performance, resulting in low correlations between national market indices. Potential gains from international diversification rest on the correlation structure of return indexes for different global investment markets over a given planning period. These correlations are key inputs for construction of efficient portfolios and international diversification strategies. More recent research focuses on changes in correlations of international equity indexes and the consequences of such changes for diversification and hedging. The findings are controversial and new approaches are evolving to explore the time series movements of international equity correlations. Studies by Erb et al., 1994, Longin and Solnik, 1995 and Solnik, 1996 suggest that complex changes occur in correlations between national equity markets over time. Solnik, Boucrelle, and Le Fur (1996) (hereafter referred to as SBL) find a pattern where correlations between national market indices increase in periods of high overall market volatility. When long holding periods are analyzed, SBL find that long-run mean correlations have not changed, but deviations of correlations from the long-run mean are higher when major market shocks occur. Researchers commonly use the generalized autoregressive conditional heteroscedastic (GARCH) model or the multivariate version of GARCH (MGARCH) to control for changing volatility with either constant or varying correlations. For example, Karolyi (1995) used different versions of the MGARCH model to study the international transmission of stock returns and volatility. More recently, Longin and Solnik (2001) (hereafter L&S) use “extreme value theory” to show that relationships between international equity market correlations and volatilities found in prior studies are likely to be spurious. They find that correlations are related to market trends, not volatility. L&S do not identify the exact time-varying distribution of correlations, but they reject the use of multivariate GARCH (MGARCH) models with constant correlations. Ang and Bekaert (2002) extend the analysis of changing correlations and volatilities to portfolio construction by using a regime-shifting model. Their findings support L&S in two important ways. First, they find that bear market trends are not associated with high volatility, as suggested in prior research. Second, they also suggest that GARCH models are inconsistent with the asymmetric correlation pattern of international equity market returns. Tse and Tsui (2002) (hereafter T&T) provide a methodological breakthrough with their version of a MGARCH model with time-varying correlations. Preliminary results from small-sample Monte Carlo analysis of the maximum likelihood estimator in T&T's model are encouraging but more work needs to be done. The T&T paper assumes that the correlations follow an autoregressive moving average stochastic process. They also force the model to converge to this process by using imposed restrictions.1 We do not know how the model performs with other plausible stochastic processes and a forced convergence with a positive definite correlation matrix. In this paper we test for the time series process for international equity correlations directly as a first step in our analysis. Of all the various modeling approaches to international equity market correlations, L&S suggest that models allowing for changing correlations could be consistent with the observed international equity market correlation patterns. In this paper we first use a flexible time-varying parameter (hereafter noted as TVP) model to test for the stochastic process that best describes the ex post movements of international equity market correlations. Next, we examine the forecasting performance of alternative time series models of correlations to determine if statistically significant time series relationships have a material impact on forecasts of next period correlations. We do not find a material gain from more sophisticated forecast models when we use holdout data to measure the mean absolute error (MAE) and the Mean Square Error (MSE).

Studies of long-run correlations between global equity markets are common, but short-horizon correlations and their time series movements receive less attention in the literature. The issue is important since hedge ratios and portfolio diversification algorithms require ex ante correlations for shorter holding periods. The empirical question that we address is whether long-run mean correlations provide sufficient information for forecasts of the ex ante short-run correlation inputs for diversification models. Recent research suggests that more complex correlation relationships for global equity markets emerged in the post-1980s, suggesting a need for improved forecasting models of ex ante correlations. We first addressed the statistical significance of more complex forecasting models for global equity market correlations. We tested for the appropriate specification of time series models of global index correlations for ten different pair-wise correlation combinations over 128 periods. Results from these tests suggest that the time series of correlations between the global equity indices are not normally distributed. A model of time series variation estimated with the flexible TVP technique provided a better fit for all the correlation time series, judged by the Chi-square test. Specific findings from the TVP estimation for each pair-wise correlation are different depending on the indices chosen for measurement. In general, the TVP model offers a very good fit to the data for most of the correlations. Our findings are consistent with prior work suggesting statistical significance for tests of more complex relationships behind the movement of global equity market indexes. In the last phase of the analysis, we extended what we learned from ex post tests of market correlations to measure forecast performance of relevant models in a holdout period. Tests of forecasting accuracy suggest that the strong statistical fit of the TVP model to ex post data does not necessarily mean superior forecast performance in data going forward from the model's estimation period. We found little or no improvement in forecast accuracy from using the more flexible and sophisticated TVP model to predict the global equity index correlations. This outcome was robust across different pair-wise correlations and across alternative forecast models, to include a constant correlation estimate. From a forecasting perspective, there is no evidence that a more complex correlation series, suggested by studies of equity index fluctuations in other studies, offers practical improvement in forecasting accuracy of global equity index correlations. We believe several extensions of the work presented here are plausible and worthwhile. First, we believe there is potential for interesting results when the study is expanded to consider a range of measurement windows for correlations. Forecasting performance of alternative models may be sensitive to the length of the measurement window. Finally, our results complement the work of T&T in that we find empirical support for their assumption of an autoregressive moving average type of analog to the conditional-correlations. Application of the MGARCH model with time-varying correlations to forecasting correlations outside the measurement period would help establish the material benefits of the T&T specification.