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\title{An Empirical Validation of a Home Bias Model By Islem Boutabba}
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             \author[1]{Islem  Boutabba}

             \affil[1]{  IHEC Carthage}

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\date{\small \em Received: 4 February 2015 Accepted: 3 March 2015 Published: 15 March 2015}

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\begin{abstract}
        


To study world equity markets indices and their corresponding relationship with a portfolio consisting of U.S. MNCs, we conducted correlation, cointegration ad bivariate Granger causality tests.Using daily returns of the past five years, we have concluded that the inclusion of foreign equities increases returns of a diversified home portfolio. From the cointegration tests, we concluded that there is no long-term equilibrium relationship between the U.S. indices and the selected foreign indices. Finally, correlation tests led us to conclude that U.S. MNCs do not follow foreign indices in terms of returns.In summary, our empirical analysis suggests that U.S. investors should diversify their portfolios by including home equities traded abroad selected in developed and emerging markets. This result corroborates that of Salehizadeh (2003).Since U.S. MNCs could not substitute indices returns, home bias problem will continue to exist because, on the one hand, foreign investment has risks that are absent in home portfolios and on the other hand, U.S. institutional investors have an information advantage as well as higher international returns.

\end{abstract}


\keywords{portfolio consisting of U.S. MNCs, we conducted correlation, cointegration and bivariate Granger causality tests.}

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\let\tabcellsep& 	 	 		 
\section[{I. Introduction}]{I. Introduction}\par
uring the past two decades, investment in international portfolios has become widespread among American investors. Economic reforms and liberalization of markets including those related to the United States have developed more attractive international markets. This change has prompted individual and institutional investors based in the United States to place a greater share of their respective portfolios in overseas markets. Such investments have been approved by theoretical foundations and empirical evidence in the literature that supports international diversification.\par
At the same time, although previous studies \hyperref[b0]{(Ahearne, Griever and Warnock (2001)}, \hyperref[b6]{Rowland (1999)} and Suh  {\ref (2000)}) showed that the continued existence of a number of factors, including some risks (e.g political and exchange rate factors), differences in transaction costs (which are significantly higher in the European Union and many other countries other than the United States), restrictions on foreign ownership and information asymmetries arising from poor quality and low credibility of financial information in several countries, may cause a home bias for U.S. investors while investing their equities.\par
Under ideal conditions, the international model of asset pricing predicts that individuals hold equities in proportion of the global market capitalization of each Author: IHEC Carthage. e-mail: islemboutabba@hotmail.com stock. However, estimates have revealed that holdings of U.S. investors in foreign stocks constitute almost 12\% of their total holdings. This puzzle can be expected to influence the method selected by investors to maximise the benefits of international diversification.\par
Investors who have direct access to foreign markets can purchase overseas equities or equivalent American Depository Receipts (ADRs) if they are available. For others, investment in diversified international mutual funds (including country funds) offers a semi-direct alternative.\par
However, these two methods (especially investments that target the equities of companies based in emerging economies) suffered significant reversals of capital flows following a series of economic and financial crises (currency) that took place in the second half of 1990s.\par
Therefore, for most investors based in the United States who continue to exhibit a home bias, it appears that there is a safer way to achieve the benefits of international diversification through investments in multinational corporations (MNC) based on U.S. territory.\par
However, empirical research has generated mixed results for the previous hypothesis. Some studies argue that U.S. MNC behave more like home firms with their respective share prices that vary in tandem with U.S. indices instead of international indices. U.S. investors who hold equities in home and multinational companies are cited as the main force that leads to such behavior in share price.\par
These results combined with additional evidence indicating low correlation between home and foreign indices lead us to include international share in a well diversified U.S. portfolio. On the other hand, some researchers have drawn conclusions in favour of diversified portfolios in home equities (composite MNC equities and other exchanged U.S. assets) that mimic the gains from investments in foreign equities.\par
Moreover, some previous empirical studies that put focus on the increasing levels of financial and economic interdependence in the world have shown that several sectors have gradually become global leaders through synchronized movements of equities and prices and have found increasing correlation between U.S. indices and foreign indices.\par
In this section, we will try to test the relationship between U.S. indices and other international indices, which will measure the benefits of international Year 2015 ( H ) diversification, and then, we will explain home bias among U.S. investors. 
\section[{II. Methodology and Hypotheses}]{II. Methodology and Hypotheses}\par
We will follow the methodology adopted by Salehizadeh  {\ref (2003)}. The author used techniques based on cointegration (like in Dickey, Jansen and Thornton (1991) and \hyperref[b3]{Hamilton (1994)}) to examine degree of integration between U.S. and foreign markets indices.\par
Methods of cointegration have been used by Ely and Salehizadeh (2001) and Jiang (1998) to test the presence of a long-term equilibrium relationship between indices. More specifically, a time series vector of order (?? × 1) is called cointegrated if each of its elements is individually integrated of order 1 (denoted ??(1)).It is then non-stationary with a unit root and there is a nonzero vector ? of order (?? × 1) such that ???? 1 is stationary. In this case, ?is called a cointegrating vector.\par
Cointegration means that one (or more) linear combinations of variables is stationary even if these variables are not individually stationary. Since stock prices and indices are considered non-stationary variables that are frequently a ??(1) process, the cointegration test is specified to determine any longterm relationship between such variables.\par
The empirical approach consists in the following steps. First, it should be ensured that the variables are non-stationary and have the same order of integration. The unit root tests (using ADF 1   1 Augmented Dickey-Fuller ) are conducted on the ?? ?? 1 series (degrees) and ?? ?? 1 series (at first difference). Then, if we accept the hypothesis of integration of order 1 for each variable, then cointegration of ?? ?? can be tested using Johansen's likelihood ratio test. The procedure is based on the estimation of the following regression equation (in vector form):??? ?? = ?? + ?? 1 ??? ???1 + ? + ?? ???1 ??? ???(???1) + ???? ????? + ?? ??\textbf{(1)}?? ?? = ?? + ? ?? ?? ?? ????? + ?? ?? =1 ? ?? ?? ?? ????? + ?? ?? , ?? ?? =1\par
(2)?? ?? = ?? + ? ?? ?? ?? ????? + ?? ?? =1 ? ?? ?? ?? ????? + ?? ?? , ?? ?? =1\textbf{(3)}\par
Where ?? ?????? ?? are two different market indices observed at time t, where p denotes lag length and ?? ?????? ?? are assumed to be uncorrelated in series with a zero mean and a finite covariance matrix.\par
For the ?? index to be Granger causally linked to ??, the ? coefficient should be different from zero in equation (  {\ref 2}) and the ? coefficient should be zero in equation \hyperref[b2]{(3)}. The opposite is checked in order for ?? to be Granger causally related to ??. 
\section[{a) The Hypotheses}]{a) The Hypotheses}\par
Our empirical study aims at testing the validity of one of these two hypotheses:\par
? Hypothesis 1: Investment should be made in foreign markets in order to diversify well portfolios and consequently reduce risk and increase home portfolio efficiency.\par
? Hypothesis 2: Investment in foreign markets does not increase home portfolio returns. 
\section[{b) Presentation of data}]{b) Presentation of data}\par
Volume XV Issue IV Version I Where k is the number of shifts for the assumed VAR process, ? is a vector of constant terms ?? ?? and ?? represent (n × n) matrices of OLS coefficients and ?? ?? denotes the (n × 1) vector of OLS residuals. The likelihood ratio test is used to test the null hypothesis which states that there are no co-integrating relationships against the alternative hypothesis of ?? cointegrating relationships (where n is the number of elements of ?? ?? ).\par
For series found not cointegrated, we use several other tests based using the bivariate causality model proposed by  {\ref Granger (1969)} and Sims (1972): Data are daily frequency. We will select ten indices namely: Euro (developed European countries index) EAFE Index (twenty-one developed countries) 2 , WOR (index of all developed markets in the world: twenty three countries), WORE (the world without Europe Index) WORU (the world without the United States of America index), NA (North American countries index: the United States of America and Canada), LA (index of Latin American countries), EM (Emerging Markets Index: twenty six countries) EMEURO (European Emerging Markets Index) and Amasya (Asian emerging markets index). Then, we will consider four U.S. indices: the Dow Jones Industrial Average, NYSE, NASDAQ and SP 500. Daily closing values are taken from YAHOO-Finance.\par
International equity markets indices are in USD. They are taken from Morgan Stanley Capital International (MSCI). These indices consist of weighted data largely representative of equities of different countries. They are weighted with respect to equities with larger capitalization.\par
From these rates, which are end of period values , we will calculate returns. The study period stretches from 5 July 2006 until 04 July 2011. 
\section[{III. Empirical Results and Interpretations a) Descriptive statistics of time series}]{III. Empirical Results and Interpretations a) Descriptive statistics of time series}\par
Table \hyperref[b0]{(1)} gives us the descriptive statistics of the examined fourteen markets indices:  Observed trends of the descriptive statistics show that the U.S. markets have higher and mixed values than those of developed markets but lower than those emerging markets. This conclusion contrasts that of  {\ref Salehizade (2003)} where the study period spans from January 1995 to May 2001. Consequently, we can locate a significant reversal in world markets which can induce changes in investor behavior.\par
However, standard deviations exhibit high volatility in all markets and especially the European markets (developed and emerging). This volatility is mainly due to financial crises. 
\section[{b) The results and interpretations i. Correlation of returns}]{b) The results and interpretations i. Correlation of returns}\par
Correlations of returns are given in table \hyperref[b1]{(2)}. The correlation of returns between the U.S. market index and another world index MSCI tells us about the extent of the benefits of international diversification. The lower the correlation, the greater the potential gains of a U.S. investor. Therefore, the inclusion of foreign equity in a diversified U.S. portfolio is highly recommended. This result is consistent with those of Kanas (1998), \hyperref[b5]{Longin and Solnik (1995)} and Solnik  {\ref (1996)}.\par
As expected, the largest correlations (possible winning month) are between the U.S. indices. However, although some markets include U.S. firms (NA and WOR), correlations with U.S. markets are very low. This can be explained by the decreasing capitalization of U.S. firms relative to foreign firms in the world index and the weak correlation between prices of the same U.S. firms in different markets.\par
Examining the DJIA index, which is small in terms of number of firms, but large in terms of capitalization, we find a very low correlation (-0.0004) with the WORE index (implying the greatest potential gain for U.S. investors). Then, we see that correlations for the LA, WOR, EURO and NA indices are -0.0008, -0.0033, -0.0050 and 0.0172 respectively with the DJIA.\par
In summary, investment in any foreign index will induce significant gains, especially the five indices that are less correlated with DJIA: WORE, LA, WOR, EURO and NA. This is in contrast to research that states that a high correlation is needed to obtain potential gains: Ammer and Mei (1996), Brooks and Catão (2000), Cheng (1998) and  {\ref Kaplanis (1988)}. Table \hyperref[b1]{(2)} shows the correlations between the different studied indices:  
\section[{ii. Cointegration and causality test}]{ii. Cointegration and causality test}\par
To examine the long-term relationships between the remaining indices, we will perform cointegration tests. First, each time series of a variable will be checked by the unit root test. Table  {\ref (}3) reports the ADF test results of the remaining indices: The ADF statistics show that all series are nonstationary and integrated at first order, implying that the returns are stationary. Then, we will apply the Johansen trace test for cointegration on the y\textunderscore t vector of equation \hyperref[b0]{(1)}. This test will be applied to each pair of indices. Table \hyperref[b3]{(4)} reports the different statistics: We used two lag intervals in the VAR and cointegration equations. The critical value at the 5\% level starts at 15.41\%. The values of the Trace statistics show that the hypothesis of non-existence of cointegration cannot be rejected for all pairs of indices and at all significance levels. Then we will conduct Granger causality Wald tests for each pair of indices. Lag length is 1. The following table shows the different relationships between pairs and decisions on hypotheses: The failure to show the presence of a long-run equilibrium relationship between the four U.S. indices and the other indices support correlation and hence the potential gains from international diversification. To better understand the relationship between the non cointegrated pairs, we applied the Granger causality test as indicated by equations (  {\ref 2}) and (3). Like Salehizadeh (2003), we will use the SP500 index as a home benchmark. It consists of five hundred selected stocks based on the criteria of size, liquidity and industry. It is an index weighted by market value (share price multiplied by outstanding equities). Each weighting of a stock in the index is proportionate to its market value.\par
Then, we will build a diversified home portfolio that includes 46 MNCs to test the possible substitution of foreign equities by U.S. MNCs. We will calculate portfolio correlation with world indices and the correlation of the combination of SP500 and the portfolio with these indices (equal weights combination).\par
Table \hyperref[b5]{(6)} reports the correlation of daily returns between the home portfolio (SP500), MNCs portfolio and the combined portfolio on the one hand, and the market indices previously used (WORE, LA, WOR, EURO and NA) on the other hand: Correlations reported in this table leads to conflicting conclusions. If we reason in absolute value, we note that the MNC portfolio is more correlated with the world indices of WORE, EURO and NA. This can be explained by the presence of these MNCs in these indices. However, the SP500 portfolio is better correlated with WOR and LA. More precisely, we know that WORE is the world index without Europe, LA is the Latin American markets index and NA is the North American markets index. Then, the incorporation of MNCs increased portfolio correlation with the selected five markets. However, this correlation remains low and hence we can conclude that it is necessary to diversify home portfolio by purchasing foreign equities.\par
For the WOR and EURO indices, the incorporation of MNCs in the home portfolio had a negative effect on the correlation with world markets. U.S. multinational corporations have failed to follow the potential equity additional returns. Therefore, there is a need to invest in foreign markets in order to diversify well the portfolio and consequently reduce the risk and increase the home portfolio efficiency. Accordingly, and as proposed by \hyperref[b2]{Errunza et al. (1999)} and Salehizadeh (2003), we confirm the first hypothesis.\par
In summary, U.S. investors have missed opportunities to maximize returns on their portfolios and minimize home-bias risk. This bias is caused mainly, first, by information asymmetry, second, by hunting down returns phenomenon and thirdly, by investors' preference for geographic proximity.\par
Since 1980, economic reforms and liberalization of world markets have attracted U.S. investors. Therefore, researchers assumed that international diversification is beneficial. However, the continued existence of risks and international barriers produced home bias in these investors who trusted more U.S. MNCs to acquire more gains from international diversification.\begin{figure}[htbp]
\noindent\textbf{}\includegraphics[]{image-2.png}
\caption{\label{fig_0}}\end{figure}
 \begin{figure}[htbp]
\noindent\textbf{}\includegraphics[]{image-3.png}
\caption{\label{fig_1}}\end{figure}
 \begin{figure}[htbp]
\noindent\textbf{2}\includegraphics[]{image-4.png}
\caption{\label{fig_2}Table 2 :}\end{figure}
 \begin{figure}[htbp]
\noindent\textbf{1} \par 
\begin{longtable}{}
\end{longtable} \par
 
\caption{\label{tab_0}Table 1 :}\end{figure}
 \begin{figure}[htbp]
\noindent\textbf{3} \par 
\begin{longtable}{P{0.2009090909090909\textwidth}P{0.3786363636363636\textwidth}P{0.27045454545454545\textwidth}}
\tabcellsep SP500\tabcellsep -35,351\\
\tabcellsep \multicolumn{2}{l}{WORE -36,673}\\
\tabcellsep LA\tabcellsep -36,591\\
\tabcellsep WOR\tabcellsep -36,882\\
\tabcellsep EURO\tabcellsep -36,224\\
\tabcellsep NA\tabcellsep -36,935\\
\multicolumn{2}{l}{Index Statistic}\\
DJIA\tabcellsep -35,361\\
NDX\tabcellsep -35,094\\
NYSE\tabcellsep -35,415\end{longtable} \par
 
\caption{\label{tab_1}Table 3 :}\end{figure}
 \begin{figure}[htbp]
\noindent\textbf{4} \par 
\begin{longtable}{P{0.18004926108374383\textwidth}P{0.33916256157635466\textwidth}P{0.008374384236453201\textwidth}P{0.012561576354679803\textwidth}P{0.30147783251231525\textwidth}P{0.008374384236453201\textwidth}}
\tabcellsep WORE\tabcellsep LA\tabcellsep WOR\tabcellsep EURO\tabcellsep NA\\
DJIA\tabcellsep \multicolumn{3}{l}{512,391 511,8536 522,6881}\tabcellsep \multicolumn{2}{l}{531,0546 508,7223}\\
NDX\tabcellsep \multicolumn{3}{l}{504,7409 509,4754 512,1067}\tabcellsep \multicolumn{2}{l}{525,9046 505,3028}\\
NYSE\tabcellsep \multicolumn{3}{l}{512,6021 512,3334 522,7783}\tabcellsep \multicolumn{2}{l}{529,0053 508,8457}\\
\multicolumn{4}{l}{SP500 512,5072 512,7601 520,6628}\tabcellsep \multicolumn{2}{l}{528,7656 509,7517}\end{longtable} \par
 
\caption{\label{tab_2}Table 4 :}\end{figure}
 \begin{figure}[htbp]
\noindent\textbf{5} \par 
\begin{longtable}{P{0.6029265873015873\textwidth}P{0.10540674603174603\textwidth}P{0.14166666666666666\textwidth}}
Null Hypothesis\tabcellsep Chi2\tabcellsep Decision\\
DJIA is not causally related to WORE\tabcellsep 7,2688\tabcellsep Accepted\\
DJIA is not causally related to LA\tabcellsep 2,6368\tabcellsep Rejected\\
DJIA is not causally related to WOR\tabcellsep 4,4929\tabcellsep Accepted\\
DJIA is not causally related to EURO\tabcellsep 0,50922\tabcellsep Rejected\\
DJIA is not causally related to NA\tabcellsep 7,2724\tabcellsep Accepted\\
NDX is not causally related to WORE\tabcellsep 5,4069\tabcellsep Accepted\\
NDX is not causally related to LA\tabcellsep 2,4532\tabcellsep Rejected\\
NDX is not causally related to WOR\tabcellsep 3,4822\tabcellsep Rejected\\
NDX is not causally related to EURO\tabcellsep 0,53134\tabcellsep Rejected\\
NDX is not causally related to NA\tabcellsep 5,9313\tabcellsep Accepted\\
NYSE is not causally related to WORE\tabcellsep 8,0091\tabcellsep Accepted\\
NYSE is not causally related to LA\tabcellsep 2,8495\tabcellsep Rejected\\
NYSE is not causally related to WOR\tabcellsep 5,0159\tabcellsep Accepted\\
NYSE is not causally related to EURO\tabcellsep 0,66927\tabcellsep Rejected\\
NYSE is not causally related to NA\tabcellsep 8,1122\tabcellsep Accepted\\
SP500 is not causally related to WORE\tabcellsep 7,6743\tabcellsep Accepted\\
SP500 is not causally related to LA\tabcellsep 3,058\tabcellsep Rejected\\
SP500 is not causally related to WOR\tabcellsep 4,7494\tabcellsep Accepted\\
SP500 is not causally related to EURO\tabcellsep 0,59431\tabcellsep Rejected\\
SP500 is not causally related to NA\tabcellsep 7,73\tabcellsep Accepted\end{longtable} \par
 
\caption{\label{tab_3}Table 5 :}\end{figure}
 \begin{figure}[htbp]
\noindent\textbf{5} \par 
\begin{longtable}{}
\end{longtable} \par
 
\caption{\label{tab_4}Table 5}\end{figure}
 \begin{figure}[htbp]
\noindent\textbf{6} \par 
\begin{longtable}{P{0.1364963503649635\textwidth}P{0.1551094890510949\textwidth}P{0.14270072992700727\textwidth}P{0.14890510948905109\textwidth}P{0.1302919708029197\textwidth}P{0.1364963503649635\textwidth}}
Portfolio\tabcellsep WORE\tabcellsep EURO\tabcellsep WOR\tabcellsep LA\tabcellsep NA\\
SP500\tabcellsep -0,0096\tabcellsep -0,0024\tabcellsep -0,0084\tabcellsep -0,0040\tabcellsep 0,0079\\
MNC\tabcellsep -0,0176\tabcellsep 0,0192\tabcellsep -0,0031\tabcellsep 0,0009\tabcellsep -0,0212\\
Mixed\tabcellsep -0,0170\tabcellsep 0,0197\tabcellsep -0,0026\tabcellsep 0,0026\tabcellsep -0,0209\end{longtable} \par
 
\caption{\label{tab_5}Table 6 :}\end{figure}
 			\footnote{© 2015 Global Journals Inc. (US) -} 			\footnote{Europe, Australia and far East countries.} 		 		\backmatter  			  				\begin{bibitemlist}{1}
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\end{document}
