نکته ای درباره هم انباشتگی شاخص های بازار سهام بین المللی
|کد مقاله||سال انتشار||مقاله انگلیسی||ترجمه فارسی||تعداد کلمات|
|16365||2013||7 صفحه PDF||سفارش دهید||7220 کلمه|
Publisher : Elsevier - Science Direct (الزویر - ساینس دایرکت)
Journal : International Review of Financial Analysis, Available online 10 July 2013
Cointegration is frequently used to assess the degree of interdependence of financial markets. We show that if a stock's price follows a stock specific random walk, market indices cannot be cointegrated. Indices are a mere combination of n different random walks which itself is non-stationary by construction. We substantiate the theoretical propositions using a sample of 28 stock indices as well as a simulation study. In the latter we simulate stock prices, construct indices and test whether these indices are cointegrated. We show that while heteroscedasticity misleads cointegration tests, it is not sufficient to explain the high correlation between stock market index returns. A common random walk component and correlated price innovations are necessary to reproduce this feature.
Building on the time series properties of stock market index data, a vast literature has emerged which studies the dependence and the degree of integration of international financial markets by means of cointegration analysis. Due to the relatively strong comovement of financial markets, the assumption of a shared common trend seems plausible at first sight. This is the reason why cointegration analysis has been a major tool in the study of interrelations between financial markets. However, there are two major issues that have to be taken into account. First, the cointegration relationship seems to be a very fragile one. Different studies using the same indices do not necessarily find an identical number of cointegrating vectors. Most of the studies are conducted in the spirit of Kasa (1992) who can identify one common stochastic trend for the stock markets of the USA, Japan, United Kingdom, Germany, and Canada. He uses monthly and quarterly data over a period of almost 16 years which suits the notion that cointegration is a long term concept while short run deviations from the common trend are possible. As opposed to these findings, Pascual (2003) finds no cointegration relationship between the French, German, and UK stock market using quarterly data for an even longer sample from 1960 to 1999. Statistically, if the time series are not found to be cointegrated in the larger sample, they should not be found to be cointegrated on any subsample like the one employed by Kasa (1992). There are numerous further examples in the literature where a slight alteration of the approach leads to different results. For example, Aggarwal and Kyaw (2005) and Phengpis and Swanson (2006) both investigate the NAFTA countries. While Aggarwal and Kyaw (2005) find evidence for cointegration in the post-NAFTA era, Phengpis and Swanson (2006) do not. Detecting cointegration, thus, seems to critically depend upon the time span under consideration and the precise specification of the statistical model. The second issue is that Johansen's (1988) test for cointegration—the major tool in empirical work—is prone to misjudgement. Financial data are marked by heteroscedasticity which is known to bias the test (cp. Lee & Tse, 1996). Also, in particular in early studies like Kasa (1992), a small sample size has been a major issue. Even though accounting for heteroscedasticity (e.g. Cavaliere, Rahbek, & Taylor, 2010) and small sample size is possible (cp. Barkoulas and Baum, 1997 and Johansen, 2002), it is hardly ever done. Recent studies, however, use in general daily data so that at least the latter issue can be regarded as overcome. The fact that cointegration among stock market indices is a delicate issue has first been addressed by Richards (1995). He relies on the Capital Asset Pricing Model (CAPM) for stock prices and shows that indices, constructed as weighted averages of stock prices in a country, cannot be cointegrated. We contribute to the literature by translating his argument to international stock markets. In addition, we abandon the CAPM assumption in favour of the more flexible random walk model for stock prices, pursuing a twofold aim: Building on theoretical and statistical arguments, we demonstrate that stock market indices cannot be cointegrated. Furthermore, we foster an intuition for the heterogeneous results found in the literature. The argumentation is based on three pillars. First, we use the random walk model for stock prices to derive that statistically cointegration between two markets is impossible. In our setting, stock market indices are a weighted average of random walk asset prices. These individual stochastic trends never cancel out in a cointegration regression and consequently prevent the indices from being cointegrated. Second, we perform an empirical exercise to show that using standard methodology cointegration is very unstable and that the results are at odds with the notion of long term comovement. In particular, we employ subsamples and show that detection of cointegration among pairs of stock market indices is basically random. And third, we simulate the theoretical model to gain an idea of the components of stock market indices. The aim of the simulation study is to reproduce data series which exhibit similar properties as the observed stock market indices in a cointegration framework. We document that in a cointegration analysis of international stock market indices, every desired outcome can be produced by suitably restricting the sample period and adjusting the model. Standard cointegration tests will reject the null hypothesis of no cointegration far too often if the properties of the data (in particular heteroscedasticity) are disrespected. Our simulation study suggests that most likely stock market indices share an additional common stochastic trend and that returns are correlated. However, cointegration analysis is not a suitable methodology to investigate the comovement of stock markets if individual stocks are random walks themselves. The paper proceeds as follows. Section 2 reviews the related literature and points out the critical issues raised in the Introduction. Section 3 outlines the random walk model of stock prices and highlights the implications for stock indices and cointegration. Section 4 presents the results of a cointegration analysis of 28 stock market indices in order to highlight inconsistencies when applying the cointegration methodology to empirical data. Section 5 holds a simulation study of the theoretical model and Section 6 concludes.
نتیجه گیری انگلیسی
The paper shows that under the assumption that stock prices follow the common random walk model, stock market indices of international financial markets cannot be cointegrated in the sense of Engle and Granger (1987). Cointegration is eventually inhibited by company specific innovations which are permanently absorbed into stock prices. These individual random walk components do not cancel out in a cointegration regression. Therefore, the resulting regression residuals are always non-stationary. The price model most likely includes a common global or local trend (as is usually the case in factor models) as well as correlated price innovations which is suitable to explain the observed high correlation between market indices, but not sufficient for cointegration. If the stock market indices were indeed cointegrated, only this one (!) global factor would be responsible for the price movement of all stocks worldwide which is rather unlikely. In an empirical analysis using 28 stock market indices, we document that the detection of cointegration is rather coincidental. This is particularly highlighted by the fact that the time period which is analysed has a huge impact on the outcome of cointegration tests. Even though structural breaks might be an issue for the whole sample (from 2001 to 2009), conducting the analysis on subperiods of four years should not alter the results as dramatically as was found in our analysis. A further feature which is known to influence cointegration tests (but largely ignored in studies dedicated to the analysis of international financial markets) is heteroscedasticity. It leads to an over-rejection of the null hypothesis of no cointegration and, thus, to faulty detection of cointegration between financial markets. Based on the theoretical considerations in Section 3 and the empirical evidence in Section 4, we conclude that cointegration is not a suitable framework to analyse the interdependence or the integration of international financial markets. Even though a common stochastic trend may exist, it cannot be identified by means of cointegration analysis. Studying the interrelatedness or the degree of integration of financial markets via cointegration properties of stock market indices is therefore not fruitful and even inappropriate.