macroeconomic variables and stock market returns - Editorial Express

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variables. Roll and Ross (1980) tested the APT, as a better alternative to the CAPM, using data .... according to statistics provided by Arouri and Jawadi (2009). As the two authors ... Their recent development (economical, political, financial and.


ALEXANDRA HOROBET* Faculty of International Business and Economics, University of Economics 6, Piata Romana, Bucharest -1, Romania Phone: +40-213191900; Fax: +40-213191999; E-mail: [email protected] ROXANA OLARU Faculty of International Business and Economics, University of Economics 6, Piata Romana, Bucharest -1, Romania Phone: +40-213191900; Fax: +40-213191999; E-mail:[email protected]

The purpose of this paper is to analyze and empirically test the validity of a linear multifactor asset pricing model, inspired by the Arbitrage Pricing Theory (Ross, 1976), which could explain the influence of macroeconomic factors on the expected returns of investors in capital markets. Our approach was to test the model from an international perspective and to conduct a comparative analysis between two sets of markets, developed and emerging, most of them from the European Union. We find that the APT model is not valid in an international framework and the only two variables with a significant influence on returns are the global market return and the exchange rate changes, as they represent links among multiple markets. Our results are similar for developed and emerging markets therefore we may state that the influence of macroeconomic variables on returns does not depend on the type of the economy.

Keywords: multifactor models, stock market returns, developed countries, emerging countries JEL codes: G12, G15


Corresponding Author


1. Introduction1 The risk-return relationship has been intensely studied in the past course of history, as people can never make any decisions in completely risk-free conditions. This is also the case in finance, where investors deal with economic uncertainty in their everyday activities on capital markets, where they take on risks in order to access future gains that can only be approximated through economic and econometric models. Asset prices react to changes in the market, caused by specific or systematic variables. As portfolio diversification eliminates almost fully specific risks, modern financial theories focused on the systematic, pervasive forces as the main source of investment risk – those forces that influence to some extent the majority of assets on a market, depending on its economic or political situation and on the degree of regional integration or segmentation. Our paper presents the results of a test based on an asset pricing multifactor linear model, resembling the Arbitrage Pricing Theory (Ross, 1976) at an international level. In order to investigate how the performance of macroeconomic variables on asset pricing is influenced by regional integration we conducted a comparative analysis between eight developed and eight emerging markets, most of them from the European Union. The basis for our analysis is the framework of explanatory variables proposed by Chen et al. (1986) accompanied by the assumption of a certain degree of market integration among countries. We added to our analysis a factor that approximates the influence of global evolutions, as returns should be determined by national and international forces in a framework of at least partial integration of international financial markets. The paper is structured as follows: Section 2 briefly explores the differences between the two famous asset pricing models: CAPM and APT and reviews the existing literature on this topic


Acknowledgment: This paper presents results achieved within the research project “Modeling the interaction between the capital market and the foreign exchange market. Implications for financial stability in emerging markets”, Project code IDEI_1782, Project’s financer: CNCSIS, PNII/IDEI.


so far. Section 3 explains the data and methodology; also, it describes the explanatory factors, the ways they were computed and the reasons they were included in the model. Section 4 reports, analyzes and interprets the empirically obtained results. Section 5 summarizes the main results, states the conclusions of the paper and makes further research suggestions. Additional materials are presented in Annexes.

2. Literature Review In international finance, the risk-return relationship is a highly discussed and analyzed subject, since asset prices are sensitive to economic news and various unexpected events. The general goal of investors - achieving high returns assuming the lowest possible risk - was subject to many theories that evaluated several risk factors. The most used asset pricing models are the Capital Asset Pricing Model (CAPM) and the Arbitrage Pricing Model (APT). Sharpe (1964), Lintner (1965) and Mossin (1966) developed in the mid ‘60s the CAPM, a model based on risk diversification and modern portfolio theory. They determined the rate of return of an asset added to an already well diversified and efficient portfolio, through a linear process:    =  +     −  ,


where E(Ri) is the expected return of asset i, Rf is the risk-free return, E(Rm) is the market return. βi measures the sensitivity of the expected return to the return on the market portfolio. It is a measure of systematic risk on the market and it can be computed using the formula:  =   ,  /  


where cov(Ri,Rm) is the covariance between the asset’s return and the market return, while var(Rm) denotes the variance of market return. Although theoretically sound, the CAPM performed poorly in empirical tests, because of its unrealistic assumptions: all investors are rational, risk-averse and focused on economic utility


maximization, not being able to influence prices (price takers); they invest in diversified industries and can borrow unlimited amounts of money at the risk-free rate; there are no trading fees and all the needed data is available in the market, which is perfectly competitive. Because of these limitations, Ross (1976) discarded the model and developed the Arbitrage Pricing Theory, an econometric multifactor linear model further extended by Huberman (1982) and Connor and Korajczyk (1986). Ross’s theory has many advantages and performs better than the CAPM in empirical tests as the analyzed portfolios do not necessarily need to be efficient, there are multiple explanatory variables and there are no arbitrage possibilities disturbing the market equilibrium. According to the APT, investors expect returns to be generated through a k-factor model:  =   +   + ⋯ +   + 


with i=1,2,…,n;   is the ith asset's expected return in equilibrium conditions;  is the sensitivity of the ith asset to factor k (factor loading);  , the systematic factor, with mean 0;  is the asset's idiosyncratic random shock, with mean 0. All random errors are assumed to be uncorrelated across assets and uncorrelated with the factors. Factors are uncorrelated with each other and their number must be significantly smaller than the number of analyzed assets. In equilibrium conditions, portfolios that do not require additional capital investments2 and bear no risks bring no returns. After a series of transformations, the APT equation can be rewritten, in vector form, so that any vector X, which is orthogonal to the constant vector and with each coefficients vector ( ), must be orthogonal to the expected returns vector as well. The later one can be considered a linear combination between the constant vector and  vectors, existing k+1 values λ0, λ1, …, λk so that:   =  +   + … +   for each i.



Any new portfolio differs from old ones through changes in the weights of assets, so the purchase of new assets is strictly dependent on the selling of existing ones – Roll and Ross (1980) 4

If there exists a risk-free rate, its return would be E0 = λ0. The other values λ1, …, λk can be considered risk premiums corresponding to factors f1, …, fk. Therefore, the expected return has two components: the risk-free return and a global risk premium as the sum of all the risk premiums for each influence factor. We also know that there exist two risk sources: macroeconomic uncorrelated variables with a systematic influence on all the assets on a market, that cannot be diversified; and specific, unique risk sources that can be removed in a well diversified portfolio. The arbitrage theory allows us to divide the risk in components and to individually analyze them. The CAPM may be regarded as a special case of APT, with only one risk source – the market. The APT takes into account the market (through the use of a market index), but uses other explanatory factors as well, being able to offer investors better and more realistic prediction possibilities. Dhankar and Singh (2005) studied the Indian market and concluded that the APT performs better than the CAPM in approximating the expected returns. The model was tested, until now, on many other markets as well: New York Stock Exchange (Chen, 1986), the Japanese Stock Exchange (Hamao, 1988), London Stock Exchange (Antoniu, 1998) and so on. Even so, some authors consider the model too general, as it offers little inside on the best way to select the influencing factors: factor analysis, principal components analysis, a-priori selection, etc. In empirical tests, the APT does not identify the precise influencing factors, as their nature varies in time. The approach only offers the existence of a linear model with k factors that affect all the assets on a market. None of these factors can be diversified in a portfolio and there is no “theoretical guide” to help in their selection. This is why the k factors in the model often vary according to the sample under analysis, their only requested characteristics being: values different than 0; complete unpredictability of their evolution at the beginning of each period; universal effect on asset returns, as stated by Berry et al. (1988).


One way of testing the APT is using factor analysis, a two steps procedure that uses time series of asset prices in order to estimate a set of influencing forces for each individual asset and then uses the mean of these sensitivity estimates to run cross-sectional regressions. This method, as well as the principal components analysis, compares the economic observations to means of unobservable variables, called factors or principal components. This way, one can identify and statistically characterize an appropriate number of influencing factors and the sensitivities of asset prices to their variations. The downside of using factor analysis is that it cannot offer an accurate economic meaning to the identified factors and that their number increases alongside with the sample size3. Factor analysis was first used by Gehr (1978), for the US market, and then was improved by Roll and Ross (1980), Chen (1983) or Cho (1986). Principal components analysis was also used by many authors, including Diacogiannis and Diamandis (1997) who developed three multifactor risk-return models in order to explain asset returns through a set of macroeconomic variables. Roll and Ross (1980) tested the APT, as a better alternative to the CAPM, using data from the American stock market during 1962-1972. They searched for a linear explanatory process (suggested by both models) and found, through factor analysis, three factors that consistently affected the expected returns for securities traded at NYSE and American Exchange and other two factors with important influence only after cross-section analysis. This multifactor model was then compared with two testing alternatives: the “specific” alternative, where the own variance is the most important explanatory factor of future returns, as it is highly correlated to average returns of analyzed samples – empirical results do not support this alternative; and the “non-specific” alternative, where APT was tested on several groups of securities and it performed well as an asset pricing model since empirical results did not reveal any significant differences among groups.


Empirical tests have identified so far between zero and ten possible significant factors in explaining asset returns in various markets. 6

Afterwards, other researchers tested the APT on various markets. Chen (1983) tried to explain the variations in S&P 500 index returns through APT as a better model than CAPM, using daily data from 1963 to 1978. Estimating the parameters through factor analysis, he tried to reject the APT including in the analysis two other variables strongly correlated to portfolio returns: portfolio’s own variance and firm size, while using a linear programming technique that minimizes possible errors. Still, his results could not reject the validity of APT. Firm size effects were analyzed separately by Chan et al. (1985) who observed that the risk-adjusted difference in returns between the largest (top 5%) and the smallest (last 5%) companies listed at NYSE is only about 1-2 pp, while the initial difference was about 12 pp. The authors chose a five-factor model, including the level of real economic activity, inflation, interest rates, changes in the term structure of interest rates and changes in risk premium. Grouping the US companies into groups by size and taking into account the economic cycles, they tested the model and found that smaller companies are more influenced by economic conditions and therefore riskier, providing higher returns. The authors specified the influencing factors apriori, using the Fama and MacBeth (1973) methodology– time-series regressions to estimate beta coefficients and then cross-sectional regressions to estimate risk premiums for each explanatory variable. This way, they were able to attribute economic meaning to the model factors, as innovations in macroeconomic variables influencing the stock market returns. Chen et al. (1986) applied the Fama and MacBeth (1973) methodology for the US financial market. They identified the following macroeconomic explanatory factors: industrial production growth rate, inflation variations (expected and unexpected), unexpected variations in the risk premium (using excess junk bond portfolios returns over long-term government bond portfolios returns) and changes in the term structure. Other macroeconomic factors taken into account were insignificant in asset pricing, proving that the model performed well with only five factors. This work represents the basis of future APT empirical tests. Hamao (1988) tested a similar asset pricing model over a ten-year period on the Japanese market, adapting it 7

to the local specificities and completing it with a fifth factor (which proved insignificant): the exchange risk or the oil price, as the Japanese economy is highly dependent of foreign trade. His findings were similar to those of Chen et al. (1986). As the globalization process accelerated and investors started expanding internationally, news and innovations on the international markets, as well as markets’ interactions begun to affect expected and actual stock market returns. Influenced by the degree of integration or segmentation among markets, some international factors like changes in the exchange rates or oil prices may represent a basis for investors’ earnings in an international framework. This is why asset pricing models are nowadays being rethought, in order to include at least one international component. Because it is not enough to test a domestic pattern on several markets, authors expanded the APT and tried to find a set of global common risk factors, a difficult task to accomplish since their importance varies on each different national market and the available data is scarce (for example, Hamao (1988) used the Gensaki rate instead of the inexistent Tbills rate in order to approximate the short term risk-free rate for the Japanese market). Solnik (1977, 1983) analyzed different asset pricing models in an international perspective. He first tested, through the CAPM model, the hypothesis that efficient portfolios differed among investors on different markets, due to currency risk, which he defined as inexistent, generated from the monetary inflation or caused by investors’ heterogeneous tastes. He concluded that currency risk has a low impact on expected returns, as compared to market risk. More recent papers contradict his findings, assigning a premium to currency risk. The second paper expanded the APT at an international level, with regard to investors’ different tastes. The author stated that if a factorial model is valid for a certain currency, the same structure should be invariable for all currencies, but this International APT (IAPT) model proved to be valid only for integrated markets and a very small number of explanatory factors. Cho et al. (1986) rejected the validity of the APT in an international framework, but also the idea that capital markets were integrated, using inner-battery factor analysis to find around 8

three or four global influencing factors and five common factors for all the eleven countries analyzed in pairs. Bodurtha et al. (1989) searched for the “universal” factors that determine the covariance of asset returns, through inner-battery factor analysis or a-priori specification of macroeconomic influencing factors, for seven countries: United States, Japan, United Kingdom, Germany, France and Canada. After performing several tests, they chose the following factors to include in model specifications: the national stock market index, the industrial production index for the rest of the world, the stock and bond returns indexes for the rest of the world and the oil price. They found there may be identified a set of global factors that determine asset returns through a linear model and that the markets under scrutiny are strongly integrated. There are many macroeconomic variables influencing returns on stock markets, but the currency risk and the degree of segmentation seem to be extremely important, as the exchange rates’ volatilities can considerably reduce the benefits of international diversification. The influence of the exchange rate depends on the development of the economy: developed, highly integrated and correlated markets reduce the risk premiums required for currency risk, as proven by Hamao (1988) and Jorion (1991). More recent tests (Vassalou, 2000) find that currency risk is an influencing factor for stock market returns. Emerging markets offer different conditions to foreign investors: high potential for diversification, but also high uncertainty. Carrieri and Majerbi (2005) study these circumstances on three layers: aggregate level, portfolio level and individual level. Even if the theoretical relationship between exchange rates and asset prices had been identified earlier in the models of Shapiro (1974), Dumas (1978) and Choi (1986), empirical tests had never been done before. The results show that currency risk (measured as deviations in the purchasing power parity) is an important factor in asset pricing and is rewarded with a risk premium expected by investors. In all these papers, the influencing factors were chosen with regard to the objectives taken into account and to the unique characteristics of the analyzed markets. For emerging markets, 9

Bilson et al. (2000) offer a detailed description of ways to choose the appropriate macroeconomic explanatory variables and theoretical justifications of how these variables influence stock market returns.

3. Data and methodology From the 1980s, and mainly after the collapse of communist regimes in Central and Eastern Europe, emerging markets started their way to privatization and capitalism, applying a series of structural programs that led to low inflation levels and budgetary deficits and also an increase in their market capitalization from 4% in 1987 to almost 20% of the global market in 2000, according to statistics provided by Arouri and Jawadi (2009). As the two authors state, the attractiveness of emerging markets mainly comes from various diversification opportunities and higher returns on securities. Their recent development (economical, political, financial and social) accelerated the integration and globalization processes, all national economies being now influenced by some global factors. Despite these considerations, emerging markets are far from homogeneity and the dynamics of their financial integration depends on various national and international factors. Researchers now try to answer an important question: do investors in emerging markets react to economic news and sudden changes like those in developed markets, or differently? In order to answer this question, one can apply different models that include national or international macroeconomic forces and try to explain asset prices and expected returns on emerging markets and contrast them against findings on developed markets. In order to highlight the resemblances and differences between the two categories of markets, we chose to test the econometric multifactor model on sixteen markets, eight of them developed (Belgium, Norway, France, Germany, Austria, Spain, United Kingdom and United States) and eight emerging (Czech Republic, Hungary, Poland, Russia, Slovenia, Slovakia,


South Korea and Mexico) – following the Morgan Stanley Capital International (MSCI) classification. Data was gathered from various sources. Time series for the industrial production index, interest rates, consumer price index and trade balances were collected from the OECD Database. For Slovenia, we used the industrial production index provided by the Eurostat Database. The real effective exchange rates were collected from the official site of the European Commission and global market indexes were collected from MSCI – All Country World Index and Emerging Markets Index. National indexes from MSCI were highly correlated with global indexes, so we used national indexes computed by OECD (share price indexes that measure changes in market capitalizations of the composing assets)4. Two different time periods were chosen for the markets under scrutiny: January 1995 – December 2009 for developed markets and January 2001 – December 2009 for emerging markets, but as we included more than three explanatory factors in the model, we decided to work with a common period for all markets: January 2001 – December 20095. In our empirical analysis we tested a multifactor linear asset pricing model with a-priori selected factors. Starting from the model proposed by Chen et al. (1986), we developed it in the following directions: (1) we added a global factor, building on the hypothesis of partial capital market integration; (2) we considered changes in inflation using only the CPI; (3) we replaced the factor called “risk premium” with a measure of currency risk, due to lack of available data; (4) we added the changes in trade balances as an influencing factor, since international trade relations have significantly intensified in the past decades. As Annex 1 shows most of the developed markets recorded a decrease in the market capitalization in the second half or 2002 and first half of 2003, which was inexistent or very small for emerging markets. This might be a sign of partial segmentation between the two 4

Graphic representations for the market indexes are presented in Annex 1. The nine-year period is rather short, due to the lack of available data about the markets, this being a serious limitation in our research. 5


types of economies. Further on, after a general period of economic boom, the financial crisis of 2008-2009 visibly affected all the markets, on a global scale, the graphs showing dramatic decreases in their market capitalizations. The collapse of capital markets debuted in the US and extended internationally, causing share prices to fall by more than 50%, and sometimes even 70%. First post-crisis recoveries were recorded in the second half of 2009. The only country in our sample with a different evolution was Slovakia – it recorded a slower downfall that continued in 2010. The risk factors in the model were the same for all the countries, in order to see the differences among them. We included the following macroeconomic variables: changes in unexpected inflation, sudden exchange rate changes, unexpected changes in real economic activity, the term structure of interest rates, changes in trade balance and the global market return. Changes in the real economic activity - industrial production On the long run, capital markets are dependent on real economic activity as asset prices are influenced by future cash flows estimations. Although monthly asset returns might not be highly correlated with monthly changes in the contemporaneous industrial production, but with unanticipated changes over several months, there can still be found a link between the first two. The data about the industrial production indexes for the 16 countries were collected in the u.m. 2005=100 from OECD and Eurostat and are seasonally adjusted (using X12-ARIMA or TRAMO-SEATS). The compositions of the indexes make them comparable around the 16 countries and include the following activity sectors according to NACE Revision 2: mining and quarrying, manufacturing, electricity and gas, water supply and constructions. The unexpected changes in the industrial production, called innovations (MP), were obtained as monthly percentage changes, using the formula: !" = #!" − #!"$ /#!"$ where IP(t) is the month t industrial production, and MP(t) is the monthly percentage change.



Unexpected Inflation The unexpected inflation is obtained from the CPI, as logarithmic monthly changes: #%&'" = log +!#" − log +!#"$ 


where CPI(t) is month t CPI and measures the average changes in prices of goods and services purchased by households, offering insight about the movements of inflation or about seasonal variations (which are insignificant, therefore the indexes are not seasonally adjusted). The data on CPI was collected from OECD Database, in m.u. 2005=100. The CPI uses prices of specific goods baskets, different for each country, that reflect national consumption habits. Inflation affects discount rates and future cash flows, influencing the entire economic activity of a country and the returns on the composing firms. Term structure of interest rates To approximate the importance of yields term structure we used ten-year maturity long term government bonds rates and short term bonds rates: either 3-months maturity interbank rate or 3-months maturity T-bills rate. Annual data was collected from OECD and Eurostat Databases and adjusted for monthly maturity. The difference between these two rates influences asset prices because it affects long term future payments as compared to short term ones. This way, one can predict future evolutions of long term bond returns, which often are included in the capital structures of many companies. We used the following formula to compute term structures: ,-" = ',." − -,."$


where LTB(t) is the monthly interest rate on long term bonds, STB(t) is monthly short term interest rate, both in month t, and TS(t) is the term structure in month t, which effectively measures unexpected changes in long term bond returns. Exchange rates


Changes in the exchange rates, depending on trade flows elasticity, may cause resource reallocations among industries, affecting asset returns. Also, considerable exchange rates fluctuations impact companies’ cash flows from foreign affiliates. On the demand perspective, if the national currency depreciates, as compared to the currency of an important commercial partner, import prices go up, causing rises in inflation and deviations from the purchasing power parity will influence asset returns on the long run. O the supply perspective, national currency depreciation favors domestic producers and exports. For this explanatory factor we used a real effective exchange rate (a weighted currency index, adjusted with the CPI, GDP and export prices deflators), computed by the European Commission for a 41-countries basket, worldwide, in m.u. 1999=100. In order to extract only unexpected changes in exchange rates, we worked with monthly percentage changes. Net trade In order to capture the international competitiveness of countries, we included the net trade in the model. Changes in competitiveness in the traded goods sector must be balanced by changes in capital flows or reserves. Growing commercial deficits become increasingly worrisome to financial markets and changes in net trade may signal cash flows changes and financial uncertainty, influencing securities prices. Data about net trade (difference between exports and imports) were collected from OECD Database, in billions of $US. To highlight unexpected changes in net trades, we worked with monthly first differences (that also eliminate the trend in net trade). Global market return The increasing globalization process of the last 20 years created strong interdependences among national markets, so any international asset pricing model should take into account the global market factors. We included in our model two international gross indexes (that included retained earnings), computed by MSCI in $US, from which we extracted global market returns: MSCI All Country World Index (weighted index of market capitalizations for 45 countries – 24 14

developed and 21 emerging) and MSCI Emerging Markets Index (weighted index of market capitalizations for 21 emerging economies). We computed the returns as monthly percentage changes of these indexes. The model and research methodology We transformed the data as described above in order to illustrate “change rates” in the chosen factors and to obtain a stable multifactor regression model. Thus, we made all the data timeseries stationary, eliminated trend components and worked only with innovations and unexpected changes in the macroeconomic variables as the model’s explanatory variables, following Cheng (1996). Like any valid linear regression model, ours was based on some specific assumptions regarding idiosyncratic errors, which were necessary in order to ensure that the estimates of the coefficients α and β are linear, stationary and efficient: the residuals have a zero-mean, are homoscedastic, independent of one another and normally distributed (with zero-mean and σ2 variance); there is no correlation between the errors and the corresponding explanatory factors. To make sure that the random errors are homoscedastic, we ran ordinary least squares regressions (OLS), including the Newey-West estimator in the analysis. To test for degree one auto-correlation of residuals, we computed the Durbin-Watson statistic test: 3

/0 = ∑2" − 2"$  / ∑ 2"3


The values of this coefficient were analyzed from the resulting tables after running the multiple factors regressions. In order to test whether the random errors are normally distributed, we ran the normality Jarque-Bera test. Besides these assumptions regarding residuals, the explanatory variables must meet certain characteristics: they must be stationary and independents of one another. To test for stationarity, we used the Augmented Dickey-Fuller and Phillips-Perron tests (when the ADF was not precise enough) and found that all the input variables were stationary. We also


analyzed the autocorrelation of time-series, using correlograms6. As macroeconomic variables are usually highly correlated, we tested to see if the explanatory variables are independent of one another using multicollinearity tests. We also tested for correlation among national capital market returns (as an indicator of similar evolution of the markets) using the correlation matrix and we observed that developed stock markets have a highly similar evolution in time. In our paper, we used a three-step methodology, as follows: the first step consisted in selecting the working sample, data collecting and processing, so as to best illustrate the factors to be included in the model. In the second step, we estimated the exact returns’ exposure on each national market to the chosen macroeconomic variables; we accomplished this by running time-series regressions on each national market, for specific periods. We first used 48-months periods and then 60-months periods, which were rolled until the end of 2008, with a one-month step. The third step consisted of running cross-sectional regressions. The explanatory variables were the β coefficients previously determined for each country and the explained variables were the next 12 months national returns – let us assume for step 2 we used the first 48 months to determine the β coefficients for each of the 16 countries; then we used these betas to explain the returns of months 49, 50, … and 60 through cross-sectional regressions. Therefore, we used time-series coefficients of a single period to run 12 cross-section regressions, obtaining, for each factor, 12 new coefficients ( from equation 10). Their mean represents, at the level of all the 16 countries, a good estimation of the risk premium (if existing) associated to each macroeconomic variable included in the model. Steps two and three were repeated until the 48 or 60 months periods and were translated through the whole nine years period (the periods constantly varied by one month: removing the first one and adding a new month each time, until December 2008; cross-section regressions were run for the next 12 months returns). This way, we created time-series of risk premia associated with each macroeconomic variable. In order to make the analysis more insightful, 6

All data, computations and results are available at the authors, upon request 16

we repeated steps two and three for the whole period as well (96 months for time series regression and the last 12 months for cross-section). In the end, the most important three periods we worked with were: the first and the last 48 months periods (with no overlaps) and the whole 96 months period. For all our empirical tests, we supposed that the returns of the 16 national countries were generated through a multifactor model like the one bellow: " = 4 +  ∗ &6" + 3 ∗ #%&'" + 7 ∗

!" + 8 ∗ %," + 9 ∗ ,-" + : ∗ 0 ;#" + 


where Rit is the market i return on month t, α1 is the constant term, MPt, INFLt, TSt, FXt, NTt and WMkIt are the explanatory variables described above and εi is the random error. Each β coefficient represents the sensitivity of the market return on the influencing factor. After approximating the coefficients β1i, β2i, β3i, β4i, β5i and β6i for each of the 16 countries, we ran cross-section regression as follows: 

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