CEEAplA WP No . 06 / 2010 PSI-20 Fluctuation : Correlation of the Portuguese Stock Market with Major Global Capital Markets

In this paper, we will analyze the increase of correlations in the market during periods of crisis, due to its paramount importance to the management and optimization of the portfolio, and especially for risk diversification in portfolio management. An evaluation of the level of correlation between the stock markets is important for several reasons. First, it enables to evaluate changes in the patterns of correlation, and thus to make the proper adjustments in portfolios’ investment. Second, policy makers are also interested in these correlations because of its implications for the stability of the financial system. The correlation coefficients are biased measures of dependence when markets become more volatile. This paper explores the correlation of the Portuguese capital markets with the Asian, American, European and Latin American Spanish stock markets. To this end, we used the PSI20 index, Nikkei 225, NASDAQ, S&P 500, Euronext 100 and Ibex-35. Our analysis results show that the correlation does exist as a phenomenon during financial crises (Bear Market), reducing the benefits of portfolio diversification when most needed. Moreover, we believe that correlations have increased between the markets in recent years.


Introduction
This study aims to analyze the correlation between the Portuguese Capital Markets and the Asian, American, European and Spanish stock markets, and for this propose we selected the main index for the evolution of the stock market in Portugal, the PSI-20, and compared the dynamics and major changes in the evolution of this index with some of the major stock indexes worldwide reference: Nikkei 225, S & P 500, Euro Stoxx 50, DJ Stoxx 600, Russell, Ibex-35.Using the correlation coefficients of Pearson we found that the correlation is higher with the Ibex 35, Eurostoxx 50 and DJ Stoxx 600; it is medium with S&P 500 and Russell; and low with the Nikkei 225, noting that in recent years it has increased significantly.The correlation is higher in the Bear Market than in the Bull Market.Despite the creation of the PSI-20 on December 31 st we will focus our analysis over the last 10 years, i.e., from January 1 st 1999 to December 31 st 2008.In this period of time it's intended to analyze some of the most significant moments in the capital markets, particularly, the end of the Asian crisis (1998), the technology bubble (2000( ), September 11 (2001)), the impact of Enron and telecommunications group Wordcom (2002) and, finally, the recent effect of Subprime (2008).For the sample period, we found that the correlation between returns in equity markets is strongly explained by market volatility.Furthermore, in terms of economic importance, note that large increases in volatility can change the correlations substantially.We found that the volatility of the Portuguese market is lower than the other indexes, and in the first years of our sample it's in counter cycle.The results show that the volatility in the markets is the main driver of correlation between the stock markets.The methodology for this work follows the work of Knif, Pynnonen and Kolari (2005); Flavin, Hurley and Rousseau (2001) and Serra (2007) and Short (2007).This paper is organized in six chapters.The first consists of this introduction.The second presents the literature review.The third chapter presents the methodology and development model.The fourth describes the data sample.The fifth presents the empirical study.Finally, the sixth presents the main conclusions.

Literature Review
To answer why so many markets experienced an adverse crash, King and Wadhwani (1990) developed the idea of spreading market in which heavy falls, such as the United States, overflow into other markets.
In their model, contagion occurs due to non-synchronous time in which market participants try to extrapolate the information from changes in market prices before the opening.This 'news' can be contaminated by the market, for specific information that should influence the market, being incorrectly incorporated into domestic prices.The contagion was found to increase the volatility of the markets.They also provide empirical evidence that stock prices of the London Stock Exchange tend to increase when the New York market opens, establishing a pattern of leader follower.King (1994) shows that little movement of cooperation in the stock market can be explained by observable economic factors, but this fact is mostly due to unobservable factors such as investor sentiment.Gillam, Ahmad, Casey, Cheng (2002) present a study in the FTSE where results show the strong correlation with the "good words" and "bad words" with the development of the index, showing that the correlation can be explained not only by volatility but also by market sentiment.Stulz and Karolyi (1996) analyzed the movements of stock market returns in Japan and United States, and cannot find a statistically significant relationship between asset returns and macroeconomic announcements, to the exchange rate shocks, the returns titles Treasure or the effects of the industry.Ammer and Mei (1996) consider that the risk premium of the shares, rather than fundamental variables account for most of the movements across national indices.Longin and Solnik (1995) find that correlations are unstable over time and covariance even more.In addition, they provide empirical evidence that conditional correlations can be influenced by income from dividends and interest rates of short-term.In a similar exercise, Ramchand and Susmel (1998) show that the correlations are time-dependent, since the correlation tends to increase when markets become more volatile.Bodart and Reding (1999) present the main empirical result to reduce the variability of the exchange rate that leads to an increase in international correlation of returns on securities and stock market.Groenen and Franses (2000) use a technique of graphical representation (graphs of heat) to investigate the correlations in the stock market and its evolution over time.They do not see a wallet on the world market, but three groups of markets that break along geographic lines, ie, Europe, Asia and the United States.These groups have become more pronounced over time.Heaney et al. (2000) report similar results.Among other studies that addressed the question of the relationship between markets with world crises, let's consider King and Wadhwani (1990) that investigated the impact of declining market in the United States in 1987 with the United Kingdom and Japan, and Kim and Lee (1993) having studied the same in 12 major stock markets.Calvo and Reinhart (1996) analyzed the impact of the Mexican peso crisis in 1994, about contagion in major financial markets.The general conclusion of these documents is that the correlation of the markets during the crisis increases significantly, indicating the existence of contagion effects in all markets.Hamao et al. (1990) and Edwards (1998) reach the same conclusion by looking at the impact of volatility.Furthermore, Longin andSolnik (1995), Solnik et al. (1996), Ramchand andSusmel (1998) andButler andJoaquin (2002) show that the correlation between markets increases during periods of high volatility in which the reduction of benefits to portfolio diversification is most evident at times when they are most needed, considering the increase of correlation of the asset's categories around the world.In an important study, Forbes and Rigobon (2002) investigate the question of equity markets being dependent of this contagion, defined as an increase in movement between the markets after a crash in one country and where the distance factor no longer remains.The study by Ang and Chen (2002) documented that the correlations are asymmetric for the rise and fall in markets, suggesting that volatility is not the factor driving up the market in times of crisis.In line with the analysis of correlations, both the upward and downward movements show that the correlations are, however, biased measures of dependence if taken in large general market movements (outliers).Consequently, since the real-world data cannot be characterized by homogeneity, the correlation coefficients are not necessarily so biased that require the adaptation of Forbes and Rigobon, suggesting that the infection can often be present as a true phenomenon during the great financial crises.This result has important implications for defining the allocation and management of risks, since Solnik et al. (1996), Ramchand andSusmel (1998) andButler andJoaquin (2002) show how the change in the market affects the performance of an internationally diversified portfolio, without dynamic rebalancing.Ramchand and Susmel (1998) also show that the correlations between the United States and other world markets are 2 to 3.5 times higher when the United States market is in a state of high volatility, than compared to a situation of low volatility.These results suggest that volatility is a major driver of the correlation.However, applying the analysis of extreme value, Longin and Solnik (2001) argue that the correlation is not related to the volatility of the market itself, but with this trend.In these studies, they show that in international markets, especially in the case of negative returns, the correlations tend to increase, i.e., the correlation tends to increase in the Bear Market, but not in the Bull Market.It is proposed that the correlation is mainly affected by market trends, rather than the volatility in periods of extreme returns.In this paper we present results showing that the correlations have increased between the markets from 1999 to 2008, which means that increasing the correlation found by Longin and Solnik (1995) for the period 1960 to 1990 has continued in recent years.
This trend is probably ascribed to the increasing integration of financial markets in national stock markets around the world.

Methodology
We began our investigation of the correlation of stock markets by adopting the correlation coefficient of Pearson or simply type "Pearson's r".The Pearson r is a concept well known to measure the linear relationship between two or more variables.It plays an important role in a number of conventional approaches in finance, such as the Capital Asset Pricing Model (CAPM) that have a correlation as a measure for the dependence of financial assets.The coefficient of correlation of Pearson is calculated using the following: In which The correlation is defined only if both standard deviations are finite and nonzero.For the corollary of the inequality of Cauchy-Schwarz, the correlation cannot exceed 1 in absolute value.When the value of r> 0 we use the term positive correlation, and in this case, as x increases y also increases, when the value of r<0 we use the term negative correlation, and in this case as x increases, y decreases.The higher the value of r (positive or negative), the stronger the association.The correlation takes an intermediate value in all other cases, indicating the level of linear dependence between the variables.If the variables are independent then r= 0, but the reverse is not possible because the correlation coefficient detects only linear dependencies between variables, as Cohen (1983).In the following table, Williams (1968), provide a guide on how to interpret a correlation in words, given the numerical value.The correlation between two markets becomes, therefore, important to calculate that an investor can diversify as much as possible and avoid the highly correlated.Overall this is the approach adopted to study the relationships between the various markets in the next chapters.

Data
This study aims to assess the correlation between the main index for the stock market in Portugal, the PSI-20 with some of the major stock indexes worldwide reference: Nikkei The PSI 20 (Portuguese Stock Index) is the benchmark stock market in Portugal, reflecting the evolution of prices of 20 stock issues with larger liquidity, selected in a universe of companies listed on Euronext Lisbon.The PSI 20 index was created on December 31, 1992.The market capitalization of emissions is set up by the Free Float (number of shares free), where each issue cannot be weighed more than 20% in the dates of regular review of the portfolio.This occurs every March (known in January) and the criteria to join the index are defined by the liquidity and market capitalization.The PSI-20 is an index of small caps, where only 5 companies have 61% of capitalization.The IBEX 35 (Iberia Index) is the benchmark stock market of the Madrid Stock Exchange, begun on 14 January 1992.It is an index weighted by market capitalization, according to the calculation of free float and is reviewed twice a year in which 51% of the weight of the index is in only 3 companies.
The data used in this study were daily taken from the rates above.The daily rate of return is defined as follows: A sample of the series begins on January 4 th 1999 and ends on December 31 st , 2008.The citation index is made with reference to the Portuguese market, i.e., for values not available in their indexes in PSI20 is assigned the index value of the previous trading days, resulting in N = total 2 528 daily observations.Data were obtained from Bloomberg Finance.
With the presented series we intend to go through some of the most significant moments in the capital markets, in particular, the Asian crisis of 1997 when the Thai currency was devalued, and afterwards fell Malaysia, Indonesia and the Philippines, which also affected Taiwan, Hong Kong and South Korea.The effect dragged the rest of the economy and this crisis that at first appeared to be regional, eventually became the first global crisis, partly influenced by the Ruble crisis in 1998, when the national banking system in Russia collapsed with the partial suspension of international payments, causing the devaluation of the Ruble and the freezing of foreign currency deposits.In 2008, as a result of the crisis caused by mortgage loans with high risk -Subprime, there was another collapse.The loans were granted at a variable rate to families so called "fragile", i.e., no income, no job and no assets.In fact, they were financing homes, often in conjunction with the issuance of credit to other family household; whom they knew didn't had sufficient income to assume those instalments.Then these banks created derivative products traded in financial markets on these mortgages, instruments to securitize, that is, turn them into freely tradable securities that were sold to other banks, financial institutions, insurance companies and pension funds around the world.Thus, creating the toxic assets.For a reason that is unknown, the global credit agencies gave AAA rating to these securities.
In 2005 the FED raised interest rates to try to reduce inflation, causing the fall in property prices, and making refinancing impossible for customers who had become non-compliant mass derived from these securities, becoming impossible to be traded at any price, which triggered a domino effect, swaying the international banking system, from August 2007 on.On September 15 th 2008, this crisis caused the collapse on a colossal area of banking investment -Lehman Brothers -and a few days after the bankruptcy of the largest insurer AIG, caused the most serious crisis since the thirties.The crisis created thunderous losses around the world in the most important financial institutions, Citigroup and Merrill Lynch, in the United States; Northerb Rock, in the UK, Swiss Re and UBS in Switzerland, Societe Generale, France; Sadia, Aracruz and Votorantim in Brazil.In Figure 1 we can see the periods of crisis represented by higher and longer falls.

Figure1. Daily change of indices
In the sample period it's characterized a null return of the daily average for all indices.The maximum variation occurs daily in all indexes on October 13 th 2008, the minimum variation also occurs in October but in different days, as we may see in the following Exchange causing declines in world stock markets.This phenomenon became known as the "Black Monday", is it typical of October?Or this is the "Black October"?

Empirical Study
Stock markets are typically volatile.However and contrary to the returns, volatility is not directly observable being necessary to proceed with the calculation by the annualized standard deviation of logarithmic returns.The volatility is presented, usually in an annualized way by multiplying the daily standard deviation by the square root of the number of observations considered normal frequency estimation: 280 for daily data.It is considered essential for determining the capital requirements of the various agents with known exposure to market risk.The presentation of volatility, together with the correlation is justified by the existence of relationship with the returns of the indices.On the analysis to the previous table we can see that on average, the indexes with more titles managed to get higher return indices with fewer titles.The most interesting is that this gain in terms of profitability was not achieved at the expense of an increase in overall risk.
As rI profitability index, xi the weight of asset i in the index and rI the return on asset i.On the other hand the variance of an index is represented by: If we assume that the variance of different assets that constitute the index equals ( Accurate estimates and correct predictions on the volatility of assets and the correlation is mandatory in most financial applications in order to provide a more comprehensive information to investors who are in face of uncertain markets.
Miscellaneous information about the correlation of the markets indicates that this is higher during the Bear Market, by way of example referring to an article published in February 2002 in the Financial Analysts Journal, Campbell, Koedijk and Kofman.In this chapter we find that for the Portuguese market this rule remains.-03-200023-10-200217-07-200731-12-2008GSPC 24-03-200009-10-200210-09-200731-12-2008STOXX50E 06-03-200012-03-200316-07-200731-12-2008RUT 09-03-200009-10-200213-07-200731-12-2008STOXX 06-03-200012-03-200301-06-200731-12-2008N225 14-04-200028-04-200309-07-200731-12-2008IBEX 06-03-200009-10-200208-11-200731-12-2008 We must first define the regimes where rates are falling or rising.Then assess whether the markets during these periods are more equal than the average of the sampling period.Periods of Bull and Bear Market are different, thus the table we present for the study of markets is different for the total sample, on the vertical is presented the correlation coefficients for the period Bull and Bear of that index.The first period of Bull Market is the result of recovery of the Asian crisis known as "the first great crisis of globalized markets" and the Russian financial crisis.The average correlation in this period is 0.414.The index that had a higher rise time was the N225.However, it is also the one that had less correlation with other indices.
There is a strong correlation between the indices STOXX50 and STOXX, the index PSI20 presents major correspondence on these.The first Bear Market referred in this study includes the DotCom crisis, the economic crisis in Argentina, September 11 th and the case of Eron and Wordcom.We found an exponential increase in the correlation of the GSPC and RUT indexes with the N225, although this remains rather weak.The correlation of PSI20 increased significantly, being the highest correlation now with the neighbouring market, IBEX35.
However, the biggest increase was the S & P 500, with 45%, due to the epicentre of this crisis being in the United States.The average correlation increased 14%, leaving in 0.474.The second period of Bull Market is the longest in this study.In the United States were implemented various measures to protect investors, such as low policy interest rates and the implementation of various financial innovations so complex that government financial authorities have become technically unable to assess the risks of these instruments.The correlation is moderate in this period, having increased by only 2%.We stress the very strong correlation, existing in the former Bear, among STOXX50 and STOXX indexes, and strong correlation with the IBEX STOXX.The PSI20 presents a breakdown of 17%, maintaining the highest correlation with the IBEX.In the latter period of Bear Market, our study focuses on Subprime crisis (the worst crisis since the crash of 1929) which is strongly related to measures designed to restore the crisis in 2000.In this period there is a clear increase in the average correlation across all indices, except in the RUT suffering a slight drop of -4%.The PSI20 has a strong correlation with the European indices, however, STOXX is the one with which it has a higher correlation.GSPC index is highly correlated with the RUT.The N225 is still the index that has less correlation, despite the increase of 14%.It was in this period that there was the greatest increase in average correlation of 14%.We can see how the PSI20 has a regional behaviour, i.e., a strong correlation with the close markets.
Thus, the effects of contagion occur among neighbouring markets, the same applies to foreign investment in the Japanese stock market, concentrated mainly in the large national companies, which have a greater international visibility.The entry in February 2002 of currency EURO also increases the correlation.This may be due to the high risk aversion rate, or even further evidence of asymmetric information, this time in relation to the expectations of the price of the currency.The overlap of working hours can also be instrumental in the correlation, especially in the N225, because the more common trading hours increased the degree of correlation of share price.For an advocate of the hypothesis of market efficiency, in which asset prices correctly anticipates the info from the movement in the market, this may indicate that the markets are reacting to the "simultaneously global news" and changes in prices lead to increased correlation.King and Wadhwani (1990) provide evidence of contagion between the markets of London and New York, where the results of synchronous trading does not occur due to an attempt by investors to infer information from price changes in another market.The common operating hours, can facilitate the dissemination of information among investors, reducing the asymmetries mentioned.
Opening times/overlap remains an important explanatory variable.This leads us to believe that differences in investor information, rather than to facilitate the negotiation can be noise for the same.We found that in the four presented periods the correlation increased, with greater focus on periods of Bear Market.The justification for this continuous increase in the correlation between the markets has been attributed to globalization and the integration of financial markets and therefore reverts to reduce the benefits of diversification.It is also thought that the correlation of extreme movements in asset prices, financial markets can significantly exceed the overall correlation between the returns of assets.The models for the selection of the investment portfolio and its success in real world applications, depend crucially on the correlation of the assets market.In terms of risk reduction, the correlation coefficient is the most important in any model of asset allocation.The study of the correlation is an important issue in financial econometrics, which has received great attention in the finance literature.Initially the correlation was regarded as one variable constant and unconditional, but several studies have provided empirical evidence that allowed the recognition of the connection as dynamic: for example, Von Füstenberg and Jeon, 1989.
We intend, therefore, with the analysis of the period 1999 to 2008 and the division of this period into Bull and Bear Market, to actually corroborate the idea that large movements in equity markets are more correlated during low periods and that there is some difference in behaviour between the Bull and Bear Markets.

Conclusions
One first remark is about the importance that the correlation factors have in fact, in the optimization of portfolios' investment.The second concerns the fact that the overlap of opening hours can capture many effects, namely the markets' reaction to the world news, through the contagion of market, the easiness on negotiations with other participants in other location.In particular, the major market indexes tend to be correlated, since they react more quickly and have a greater range of information.This result is consistent with empirical studies of Ang and Chen ( 2002 Considering the small size of the Portuguese stock market, this study provided an opportunity to investigate whether the correlations among the small markets behave differently from those that occur in major markets.The empirical analysis of the stock market returns is made with the daily data in the period 1999-2008.Samples confirmed that the correlation is stronger when the index of world market is trending downward.We found that large increases in volatility can substantially change the correlations. These results corroborate previous studies that found correlations with each other, as they considered many experts (Solnik, Boucrelle and Skin (1996), Ramchand andSusmel (1998), Dennis, Mayhew andStivers (2005), Baele (2005), and others).We also think that the correlations between the stock market returns have been increasing throughout the world during the Bear Market (Longin and Solnik (2001), Ang and Chen ( 2002), and others), but this relationship is presented in a smaller magnitude than volatility.Other results showed that most of the correlations between the indices have increased from 1999 to 2008.An example of this increase in correlation was Subprime crisis of 2008.Thus, the increase in market correlations reported by Longin and Solnik (1995) for the period 1960 to 1990 has continued in recent years.
This trend is probably due to the increase in global capital flows and financial market integration coincidental.Finally, it was found that the results of a simultaneous correlation, using daily returns for the European countries with trading hours/overlay to be more reliable than the ones of the world market, with trading hours that do not overlap.Using the Pearson coefficient we estimated correlations for each of the equity markets, as well as in Bear and Bull Markets.The results show that the correlation of markets has been increasing in recent years.However, this greater degree of correlation is not observed for the N225 here considered that in addition appears to be correlated with the markets of the Eurozone rather than with the United States.In times of financial crisis, we easily get the impression of contagion and its impact on all financial markets.This suggests that the returns of financial assets are more highly correlated for large negative returns.If this intuition is supported with repeatedly empirical evidence, we will have serious implications for the allocation of the portfolio based on the premise of diversification.
It appears that the benefits of diversification depend critically on assets that have low or negative correlation.These benefits would be severely affected by an increasing correlation.In fact, when these benefits of diversification are most need, quickly disappear.For investors worried about downside risk, this would imply a reformulation of the model of the average change in portfolio allocation.One of the advantages of diversification is that when one asset category is in decline the other is raising, that is, the theory is that diversification reduces risk and volatility of the portfolio.Harry Markowitz, Nobel Prize winner in 1990 and pioneer of the "Modern Portfolio Theory," devised a way to maximize return for a given level of risk: the basis is that diversification across many asset's categories should maximize the return for a given level of risk if the portfolio is invested according to the Markowitz Efficient Frontier.
But if all asset's categories move in unison, then this investment technique cannot provide protection against the risk heralded by the theory.The correlation seems to be increasing and investments may be linked more than ever, there are no mechanisms to protect their bets and thrive in highly correlated.With the increase of the correlations between the markets we cannot withdraw the benefit of diversification: Harry Markowitz showed that an investor can reduce risk in the portfolio simply if it has non-correlated assets, arguing that diversification leads to reducing the risk of a portfolio, but not necessarily reduce the profitability.
Recently, with markets increasingly moving in sync, it seems that the increase in correlation could disrupt this fundamental rule of portfolio theory.Based on the study of market behaviour over the past 10 years, and based on daily returns of major indices, we analyze how the correlations behave over time.There is an increased access of investors to asset categories, traditionally restricted to institutional investors and individuals of highly net valued.Investors must accept that the correlations do not establish immutable regularities.The development described here does not undermine the underlying principles of Markowitz with the modern theory of portfolio investment.Still, there is no reason to panic, because the benefit of diversification continues -although at a lower level.Indeed, there are opportunities even in times of turbulence.However, throughout the world the portfolio diversification remains essential.In order to continue to capitalize on the effect of reducing risk, investors should learn to adjust to market standards and make a proper analysis of the correlations in the construction of the portfolio.The contribution of the work proposed here is to analyze the correlation and we have found that it increases significantly during the crisis, indicating contagious effects in all markets.
of both variables, i.e.: The S & P (Standard & Poors) 500 is an index composed of 500 stock representing 70% of all companies traded on U.S. exchange.It is considered a thermometer for the U.S. economy.The criteria for incorporation are qualified because of their market size, liquidity and its representation in the sector group.This method of selection opposes to the stiffness of PSI 20, since the list of companies that constitute the index GSPC is prepared by the Committee for S & P indices, formed by several economists and analysts of reference.Standard & Poor's is a financial consulting company and published for the first time the GSPC in March 4 th 1957, with stock prices of large companies (Blue Chips) traded in the United States.The GSPC is the index followed by major U.S. companies.The Dow Jones EURO STOXX 50 is a leader in the euro area as a reference for the Blue Chips.The STOXX50 is a free-float market capitalization weighted index of 50 major companies from different sectors and countries of the Eurozone.It was developed on December 31 st 1991 to provide a representation of the leading companies in the Eurozone.The country with major representation in the index is France (with 32% weight and 15 companies in the index).Portugal is not represented in this index.The weight of each component is limited to 10% of the capitalization of the index by free float market total.The Russell 2000 index measures the performance of small cap segment of the universe of equity market in the United States.The RUT was developed on December 31 st 1986 and is a reference for second-line operations in the United States, in order to provide a comprehensive and unbiased barometer of the market for small caps.The Russell 2000 is the most widely cited of the overall performance of small caps, while the S & P 500 is mainly used for "blue chips".The Russell 2000 index is a subset of the Russell 3000 Index, representing approximately 8% of the total market capitalization of this index.The RUT includes the 2000 smallest companies in the Russell 3000 index, a broad-based index, which represents approximately 98% of the market value of investment capital in the United States, but leaves out the mini-micro and small units that make up the remaining 2%.The Dow Jones STOXX 600 is derived from the Dow Jones STOXX Total Market Index and a subset of the Dow Jones STOXX Global 1800.With a fixed number of 600 components, the STOXX includes large, medium and small size companies of 18 countries in Europe.Portugal has 10 companies in this index, with a total weight of 0.60%.The STOXX Index is a broad-based capitalization-weighted European market and designed to provide a broad representation of companies in the European continent.The index was developed on December 31 st 1991.The Nikkei-225 (Nikkei 225 Heikin Kabuki) is the main index of the Stock Exchange in Tokyo (TSE) which is the second largest stock exchange in the world and is only behind the New York Stock Exchange.It presents the top 225 blue chip Japanese high-capitalization companies listed in the First Section of Tokyo Stock Exchange.The N225 was first published on May 16 th 1949.Unlike other indices that have developed a system in real time, the Nikkei 225 is calculated by the traditional method and displayed daily by the business newspaper Nihon Keizai Shimbun.The N225 index is an index of weighted average price and its components are reviewed once a year.
In 2000 came the crisis of DotCom (tech bubble).The excesses of the new economy left a trail of bankruptcies, purchases and mergers in the Internet and telecommunications and a large hole in the accounts of risk capital.The attacks of September 11, 2001 against the Twin Towers in New York and the Pentagon in Washington caused the stock collapse, and consequently the closure of the New York Stock Exchange for a week, and in its reopening, the Dow Jones suffered the greatest loss of history.The forgery of the accounts of the American company Enron and the fraud of the telecommunications group Wordcom in 2002 destabilized the stock of the world, causing mistrust among investors in relation to reports made available by companies.
In order to compare the volatilities of the sample we calculated the annual volatility of the indices referenced in this study, represented in Figure2.We can see that in 2008 all the indices peaked and volatility more than doubled the 2007 figures, one factor in the entire sample in this study.2005 has the lowest volatility.

Figure 3 .
Figure 3. Correlation with other indices PSI20 ) indicating that the observed increase in dependency of the phenomenon during the Bear Market is not only resultant from a regime of greater volatility.Moreover, this study focused on the dependence of the correlation of the stock market returns in different countries and with volatility also quite different.Starting with the definition of correlation, our main contribution was to propose an analysis of the correlation PSI20 and 6 other indices for the period 1999 to 2008, and the division of Bear and Bull Market into these periods selected for the study.The basic idea was, therefore, select some indexes that we think have the greatest impact on the analysis of investments in capital markets.It was adopted an explicit model to investigate the contribution of the level of volatility and other variables concerning the mutual correlations between the returns of the stock market.The markets in our study were: North America (S & P500 [Blue Chips] and Russell 2000 [Small Caps]), Asia -Japan (Nikkei225) and Europe (DJ Stoxx 600), the Eurozone (Eurostoxx 50), Spain (IBEX 35).

Table 1 .
Interpretation of correlation coefficient of Pearson

Table 2 .
List of contents.

table :
Table3.Daily variations of the indices during the sampling period October can be explained due to so far unique factors in the world economy.The GDP of the eurozone fell by 1.5% in the fourth quarter of 2008 compared to the previous quarter, the biggest contraction in economic history of the area.The IMF on October 7 th presented losses from the subprime around 1.4 trillion dollars and total value of subprime loans still at risk amounted to 12.3 trillion, representing 89% of GDP.The fall of the fifth-largest investment bank Bear Stearns, despite the measures implemented by the Federal Reserve, was inevitable.On October 11 th the Secretary of the Treasury of the United States met with representatives of major banks in the United States in order to present the actions of that government to end the crisis in the financial system.The state injected 700 billion dollars in the bank to buy the toxic products and in return became a shareholder of the banks.On October 29 th 1929 took place the crash of the New York Stock Exchange and on October 19 th 1987 due to widespread mistrust of investors, there was a massive sale of shares in the New York Stock

Table 6
To go further into the nature of correlations, we divided the sample into periods of Bull and Bear Market in accordance with the slope of the trend index of the world market, and we verified that Bull and Bear Markets are consolidated when the index line overcomes the Moving Average of 150 days.

Table 7 .
Identification of periods Bull and Bear Market sample

Table 8 .
Correlations between the indices in the 1st period Market Bull

Table 9 .
Correlations between the indices in the 1st period Market Bear