Global diversification: developed and emerging economies.

Bhatnagar, Chandra Shekhar ; Ghosh, Dipasri

ABSTRACT

Within the strait jacket of diversification a la Markowitz and Roy efficient portfolio structures are first enunciated, and then within that generic structure of analytical framework benefits of diversification are studied for developed and emerging economies. The study attempts to examine the level of market segmentation/integration in the emerging markets of South-East Asia. It is found that opportunities for profit making exist for investors by appropriate diversification because the markets are largely segmented in the region. The returns are positively correlated with risk, but not significantly so. Non-market related factors appear more important in deciding the returns, thereby hinting at either a lack of beta's predictive capacity in a global context or operating inefficiencies in the business/economic mechanisms.

JEL: G11, G15

Keywords: Equity diversification; Market segmentation/integration; Developed and emerging markets

I. INTRODUCTION

Diversification is the driver of portfolio selection, revision, and rebalancing of asset holdings. Since the classic works of Markowitz (1952), and Roy (1952), portfolio theory has become a fascinating area for examination, further insights and empirical studies for both academics and practitioners in view of risk, uncertainty and expectation. The research alluded to have the theoretical arguments for risk minimization at the core of the analytical examination or at the trade-off between return and risk of any portfolio. Markowitz mean-variance frontier brings out that trade-off structure. In yet another classic piece, Tobin (1958) derives the mean-variance locus with the additional insight on the choice of a risk-loving or risk-averting investor. The analysis of diversification highlighting the principle of safety first has initially been applied to domestic assets alone until Grubel (1968), Levy and Sarnat (1970, 1979), Solnik (1974), Losq (1979), Vaubel (1979), Friend and Losq (1979), among others, have brought diversification applied in the setting of international markets. Asset holdings in international capital markets certainly extend the efficiency envelope to the further benefits of investors. In all of the cited works and beyond, it is empirically established that international diversification reduces the risk.

Essentially extending the methodology of Evans and Archer (1968), Solnik (1974) presents the following exhibits (Figure 1: a, b) and illustrates the relationship between risk for diversified U.S. stock portfolios vis-a-vis internationally-diversified stock portfolios of different sizes.

[FIGURE 1 OMITTED]

Table 1 shows that the proportion of the average common stock's total variance for each developed country selected which was un-diversifiable ranges from 19 percent in Belgium to 43.8 percent in West Germany. In other words, the average portfolio of domestic stocks achieved with only random diversification in Belgium has 19.0 percent as much risk as the typical individual stock traded in Belgium. Internationally diversified portfolio of randomly selected stock has only 11.7 percent as much variance as the typical individual stock. Here we see the effect of diversification as risk reducer, but the risk reduction is much higher in diversification across nations. In the work of Blume and Friend (1978) we observe that 66 percent of investors in NYSE with holding of one stock suffered loss compared to only 31 percent of the investors holding more than 20 securities. Lessard (1976) measures the following ratio of unsystematic risk to total risk (in percentage terms) in these domestic market portfolios after complete domestic diversification (Table 2):

It is now evident that investors in United Kingdom can reduce 83 percent of risk by diversifying international, and Italy can eliminate 94 percent of its risk by the same method. Going further, Lessard further presents the betas of different domestic portfolios with world market, and then, on the basis of the security market line, calculates the difference in expected returns per annum between each national market portfolio and the portfolio of the same dispersion but with full international diversification. The difference in expected return yields a recognizable measure of the losses due to incomplete diversification, and Table 3 provides the picture as follows:

Notice that diversification has measurable benefits in terms of risk reduction and return increase, and international diversification has the magnification effect. However, we must note now that all the discussions thus far are in the context of the computations in the developed economies. In this study we go beyond the developed economies and make the issue of global diversification by looking at some emerging economies and examine the potential gains and losses at length. Before we go into this examination, we must examine the theoretical underpinning on diversification. Section II is devoted to the analytical exposition of diversification. Section III brings out the empirical results on emerging and some developed economies, and Section IV concludes with some observations.

II. THEORETICAL STRUCTURE OF DIVERSIFICATION

Consider a rational investor who has $M and he decides to invest on n assets with the expected returns on these assets being [r.sub.1], [r.sub.2], [r.sub.3], ........, [r.sub.n], and variance of returns on these assets are [[sigma].sup.2.sub.1], [[sigma].sup.2.sub.2], [[sigma].sup.2.sub.3], ........., [[sigma].sup.2.sub.n], respectively. The investor's expected portfolio return ([R.sub.P]) is then as follows:

[R.sub.P] = [n.summation over (i=1)][w.sub.i][r.sub.i] (1)

where [w.sub.i] is the proportion of investible funds put in asset i (alternatively called, weight for i = 1, 2, 3,...., n), and

[n.summation over (i=1)][w.sub.i] = 1. (2)

His portfolio risk, measured by variance ([[sigma].sup.2]p) is:

[[sigma].sup.2.sub.P] [n.summation over (i=1)][n.summation over (j=1)][w.sub.i][w.sub.j][[sigma].sub.i][[sigma.sub.j][[rho].sub.ij] (3)

Here [[rho].sub.ij] is the correlation coefficient and [[sigma].sub.ij] is the covariance between the returns of i-th asset and j-th asset. In this n-asset portfolio there are n terms involving variances of n assets, each multiplied by the squared value its weight plus nC2 (= n(n-1)/2) terms involving covariance terms (or correlation coefficient terms). In other words, expression (3) is as follows:

[[sigma].sup.2.sub.P] = [n.summation over (i=1)][w.sub.i.sup.2][[sigma].sup.2.sub.i] + [n.summation over (i=1)][n.summation over (i[not equal to]j])[w.sub.i][w.sub.j][[sigma].sub.i][[sigma].sub.j][[rho].sub.ij] = [n.summation over (i=1)] [w.sub.i.sup.2][[sigma].sup.2.sub.i] + [n.summation over (i=1)][n.summation over (i[not equal to]j] [w.sub.i][w.sub.i][[sigma].sub.ij] (3A)

or

[[sigma].sup.2.sub.P] = [[w.sup.2.sub.1] [[sigma].sup.2.sub.1] + [w.sup.2.sub.2][[sigma].sup.2.sub.2] + [W.sup.2.sub.3][[sigma].supb.2.sub.3] + ..... + [w.sup.2.sub.n][[sigma].sup.2.sub.n]] + {2[w.sub.1][w.sub.2][[sigma].sub.1][[sigma].sub.2][[rho].sub.12] + 2[w.sub.1][w.sub.3][[sigma].sub.1][[sigma].sub.3][[rho].sub.13] + 2[w.sub.1][W.sub.4][[sigma].sub.1][[sigma].sub.4][[rho].sub.14] + ..... + 2[w.sub.m][w.sub.n][[sigma].sub.m][[sigma].sub.n][[rho].sub.mn]} (3B)

Note that the terms within the square bracket ([]) in the first part on the right-hand side of the (3B) is the non-removable component of the portfolio risk. But if many of the [[rho].sub.ij]'s in the second part of (3B) in the second bracket ({}) are negative, negative terms are added to the first component of portfolio risk, total portfolio risk gets smaller in value. This is what diversification is and why it is meaningful. In a special case of two-asset portfolio total portfolio risk is:

[[sigma].sup.2.sub.P] = [w.sup.2.sub.1][[sigma].sup.2.sub.1] + [w.sup.2.sub.2][[sigma].sup.2.sub.2] + 2[w.sub.1][w.sub.2][[sigma].sub.1][[sigma].sub.2][[rho].sub.12] (4)

[w.sub.1] + [w.sub.2] = 1 (5)

Combining (5) and (4), one gets:

[[sigma].sup.2.sub.P] = [w.sup.2.sub.1][[sigma].sup.2.sub.1] + [(1-[w.sub.1]).sup.2] [[sigma].sup.2.sub.2] + 2[w.sub.1](1-[w.sub.1])[[sigma].sub.1][[sigma].sub.2][[rho].sub.12] (6)

Differentiating [[sigma].sup.2.sub.P] with respect to [w.sub.1] and setting that to zero, - that is, by:

d[[sigma].sup.2.sub.P] / [dw.sub.1] = 0,

one can obtain the following risk-minimizing proportions of funds that should be invested in asset 1 and asset 2:

[[??].sub.1] = [[sigma].sup.2.sub.2] - [[sigma].sub.1][[sigma].sub.2][[rho].sub.12] / [[sigma].sup.2.sub.1] + [[sigma].sup.2.sub.2] - 2[[sigma].sub.1][[sigma].sub.2][[rho].sub.12] = [[sigma].sup.2.sub.2] - [[sigma].sub.12] / [[sigma].sup.2.sub.1] + [[sigma].sup.2.sub.2] - 2[[sigma].sub.12] (7)

and [[??].sub.2] = 1 - [[??].sub.1] (g)

Now, taking note of the expected portfolio return:

[R.sub.P] = [w.sub.1][r.sub.1] + [w.sub.2][r.sub.2] = [w.sub.1][r.sub.1] + (1 - [w.sub.1])[r.sub.2] (9)

the investor's utility maximization is as follows:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (10)

where 1/2 A [equivalent to] - [partial derivative]U/[partial derivative][[sigma].sup.2.sub.P] / [partial derivative]U/[partial derivative][R.sub.P] = [dR.sub.P]/d[[sigma].sup.2.sub.P].

Here A determines the additional expected return the investor requires to be willing to take for additional amount of portfolio risk. This maximization yields the following optimal proportions:

[[??].sub.1] = [[[sigma].sup.2.sub.2] - [[sigma].sub.1][[sigma].sub.2] [[rho].sub.12] / [[sigma].sup.2.sub.1] + [[sigma].sup.2.sub.2] - 2 [[sigma].sub.1][[sigma].sub.2][[rho].sub.12]] + [[r.sub.1] + [r.sub.2] / A([[sigma].sup.2.sub.1] + [[sigma].sup.2.sub.2] - 2[[sigma].sub.1] [[sigma].sub.2][[rho].sub.12])] (11)

In the n-asset portfolio case, the maximization problem is as follows:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (12)

where w and r are n-tuple column vectors of weights (proportions) and asset returns, and [OMEGA] is an n x n variance-covariance matrix. That is,

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII], and

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

and the optimal weight structure is given by:

[??] = [(e'[[OMEGA].sup.-1]e).sup.-1][[OMEGA].sup.-1]e + 1/A[[[OMEGA].sup.-1]r-[(e'[[OMEGA].sup.-1]e).sup.-1] e'[[OMEGA].sup.-1]r[[OMEGA].sup.-1]e] (13)

where e is an n-element column vector. The first part in (13), as in (11), shows the weights on minimum-variance portfolio, which can be construed as the hedging demand for the set of risky assets since it is independent of A which measures the degree of risk aversion. The second component, which involves A, is the investor's speculative demand for risky assets as A measures the investor's trade off between expected return and risk.

An alternative way to look at the problem of allocation of the investor's investible funds in terms of different assets is as follows: assume that at the initial point the investor finds the normalized prices of all assets as 1, and he expects the prices to be [p.sub.1], [p.sub.2], [p.sub.3], ......., [p.sub.n] with the standard deviations of [[sigma].sub.1], [[sigma].sub.2], [[sigma].sub.3], ............, [[sigma].sub.n]. If [s.sub.1], [s.sub.2], [s.sub.3], .............., [s.sub.n] are the units of assets 1, 2, 3, .., n, then:

[n.summation over (i=1)][p.sub.i][s.sub.i] = M (14)

[n.summation over (i=1)][n.summation over (j=1)][s.sub.i][s.sub.j] [[sigma].sub.i][[sigma].sub.j][[rho].sub.ij] = [[sigma].sup.2.sub.p] and (15)

[n.summation over (i=1)][s.sub.i] = Z (16)

With an appeal to Wong-Viner theorem [see Silberberg (1999)] one can easily derive Markowitz-Roy envelope of efficient frontier when the following holds:

[(M - Z [theta]'[[GAMMA].sup.-1][zeta] / [zeta]'[[GAMMA].sup.-1] [zeta]).sup.2] = [[sigma].sup.2.sub.P] - [Z.sup.2] / [zeta]'[[GAMMA].sup.-1] [zeta]){([theta]'[[GAMMA].sup.-1][theta])([zeta]'[[GAMMA].sup.-1][zeta]) - [([theta]'[[GAMMA].sup.-1][zeta]).sup.2] / [zeta]'[[GAMMA].sup.-1][zeta]} (17)

Here [GAMMA] [equivalent to] [([[rho].sub.ij]).sub.n x n] is the correlation matrix, [theta] [equivalent to] ([p.sub.i] / [[sigma].sub.i], 1 [less than or equal to] i [less than or equal to] n), and [zeta] [equivalent to] (1 / [[sigma].sub.i], 1 [less than or equal to] i [less than or equal to] n) are n-element column vectors. Upon routine exercise we can find the optimal allocation of investible funds is given by the following:

[[??].sub.i] = [eta]/[[sigma].sub.i] [n.summation over (j=1)] ([p.sub.j] - [chi]/Z) / [[sigma].sub.j] [[GAMMA].sub.ij] / [absolute value of [GAMMA]], 1 [less than or equal to] i [less than or equal to] n (18)

where [eta] is chosen so that [n.summation over (i=1)][s.sub.i] = Z is satisfied. [chi] is the floor of the probable value of the return, and [[GAMMA].sub.ij is the cofactor of [[rho].sub.ij] in the matrix [GAMMA].

Now, it is time to indicate that optimal weights or asset holdings in the risk-return framework in these theoretical paradigms hold for any domestic economy since everything is expressed in the single currency terms. When the holdings are in different country assets, foreign exchange rates come into picture, and additional risks surface in the calculation of risk and returns. In our discussion thus far,

[r.sub.i] = ([p.sub.t] - [p.sub.0]/[p.sub.0]) and [w.sub.1] = ([e.sub.i][M.sub.i]/M), i = 1. 2, 3, ..., n (19)

where [M.sub.i] ([equivalent to] [p.sub.i][s.sub.i]) is the total investment in the i-th country asset denominated in the i-th currency, and [e.sub.i] is the exchange rate of the i-th currency in terms of the domestic currency (say, U.S. dollar), and [e.sub.i] = 1 obviously for U.S. dollar. Note that for an infinitesimally small change, expressions in (19) can be written as follows:

[r.sub.i] = [dp.sub.i]/[p.sub.i] [equivalent to] [p.sup.*.sub.i] (20A)

[w.sup.*.sub.i] = [e.sup.*.sub.i] + [M.sup.*.sub.i] - [M.sup.*] [equivalent to] [e.sup.*.sub.i] + [p.sup.*.sub.i] + [s.sup.*.sub.i] - [M.sup.*] (20B)

For an investment in the domestic economy, rate of return on i-th asset is measured by (20A), but for investment abroad, rate of return must equal to [e.sup.*.sub.i] + [p.sup.*.sub.i] (assuming that the American investor holds [s.sub.i] and M constant). On a more discrete situation of change, the rate on return on foreign investment ([r.sup.f.sub.i]) is given by the following Fisher relation:

1 + [r.sup.f.sub.i] = [(1 + [r.sup.d.sub.i])(l + [e.sub.t] - [e.sub.t-1]/[e.sub.t-1]) (21)

whence:

[r.sup.f.sub.i] = [r.sup.d.sub.i] + [e.sub.t] - [e.sub.t-1] / [e.sub.t-1] + [r.sup.d.sub.i]([e.sub.t] - [e.sub.t-1]/[e.sub.t-1]) (22)

and

Variance([r.sup.f.sub.i]) = Variance([r.sup.d.sub.i]) + Variance([e.sub.t] - [e.sub.t-1]/[e.sub.t-1]) + 2Co variance([r.sup.d.sub.i], [e.sub.t] - [e.sub.t-1]/[e.sub.t-1]) (23)

From (23) it is evident now that if the variance of exchange rate movement is very low (close to zero), and covariance between the domestic rate of returns and exchange rate changes are negative, investment in foreign investment is Markowitz-efficient risk-reducer. If the emerging markets are not integrated with the developed markets, or, in other words, emerging and developed economies are segmented, covariance terms become zero, and in case, those markets are negatively correlated, variances of foreign returns become smaller than the variance of domestic return. Solnik (1974), and Levy and Sarnat (1970) corroborate this reality. Let us look at the return side in terms of percentage change now. From equation (1), we derive:

[R.sup.*.sub.P] = [[lambda].sub.1]{([w.sub.1] + [r.sup.*.sub.1])} + [[lambda].sub.2] {([w.sub.2] + [r.sup.*.sub.2])} + [[lambda].sub.3] {([w.sub.3] + [r.sup.*.sub.3])} + ... + [[lambda].sub.n] {([w.sub.n] + [r.sup.*.sub.n])} (24)

or alternatively,

[R.sup.*.sub.P] = [[lambda].sub.1]{([e.sup.*.sub.1] + [p.sup.*.sub.1] + [r.sup.*.sub.1])} + [[lambda].sub.2]{([e.sup.*.sub.2] + [p.sup.*.sub.2] + [r.sup.*.sub.2])} + [[lambda].sub.3]{([e.sup.*.sub.3] + [p.sup.*.sub.3] + [r.sup.*.sub.3])} + ... + [[lambda].sub.n]{([e.sup.*.sub.n] + [p.su.*.sub.n] + [r.sup.*.sub.n])} (25)

Here [[lambda].sub.i] [equivalent to] [w.sub.i][r.sub.i]/[R.sub.p], i = 1, 2, 3, ..., n is the i-th country's share of return in the total portfolio return in percentage measure. In most of 1980 through 1995, Asian emerging asset markets have exhibited very high asset appreciations compared to the returns in the developed countries, and exchange rates of the Asian currencies remained either pegged or stable, and some cases have shown appreciations in terms of U.S dollars. The picture, however, has changed in 1997--the first 6-month period of the Asian crisis--as the following tables (Tables 4 and 5) indicate:

III. EMPIRICAL EVIDENCE

It is now time to examine the data from Morgan Stanley Capital Index (MSCI) and ascertain effects of global diversification. Since [[sigma].sub.ij] = [[sigma].sub.i][[sigma].sub.j][[rho].sub.ij] (that is, covariance between i-th asset returns and j-th asset returns is equal to the product of standard deviation of i-th returns, standard deviation of j-th returns, and the correlation coefficient of i-th asset returns and j-th asset returns), we may take a close look at the correlation matrix (Tables 6) below.

Table 6 exhibits the annual correlation coefficients. Take a close look, and note that in 1997- 1999 the correlation coefficients between Malaysia and U.S, and Malaysia and Germany has been -1 and between Malaysia and Great Britain is -0.7. Similar correlation coefficients exist between Indonesia and the other three developed countries. On monthly basis, similar patterns emerge, as is evident from Table 6B.

Let us now look at the asset returns (again computed from MSCI), and Table 7 exhibits the results:

Note the asset returns in the developed economies: US (0.12, 0.27), GB (0, 0.2), DE (0.2, 0.4), FR (0.36, 0.34), and then note IDF (2.28, 0.77), KR (0.94, 0.004), MYF (0.24, 0.33), PHF (0.4, 0.63), TW (1.2, 0.8), and THF (0.42, 1.06) in year 1988 and year 1989, respectively. Take the last two years (2002 and 2003), and note the returns: US (-0.24, 0.27), GB (-0,2, 0.3), DE (-0.3, 0.6), FR (-0.22, 0.38), and then note IDF (0.38, 0.7), KR (0.074, 0.326), MW (-0, 0.23), PHF (-0.3, 0.39), TW (-0.3, 0.4), and THF (0.24, 1.35). The Asian crisis was beginning in the middle of 1997, and in that year returns were all negative in the emerging economies. Though the crisis plagued those countries till the end of 1998, return turned positive for Korea and Philippines, but Malaysia, Taiwan and Indonesia stayed in the negative territory. The developed economies had positive return in both 1997 and 1998.

It should be noted that these returns are in US dollars terms,--that is, we have here the returns equal to ([e.sup.*.sub.i] + [r.sup.*.sub.i]), as noted in equation (24) and equation (25). We use the following Morgan Stanley Formula as follows:

A. Standard Index Calculation Formula by MSCI

The MSCI Indices are calculated using the Laspeyres' concept of a weighted average, together with concept of chain linking. The general expression of the index is set forth below. Index in US Dollar at time 't' is equal to:

[Index Level.sub.t-1] + [[n.summation over (i=1)][Price (i).sub.t] No. of shares [(i).sub.t] x [ADJ(i).sub.t] x 1/Exchnage rate (t)] / [[n.summation over (i=1)][Price(i).sub.t-1] x No. of shares [(i).sub.t-1] 1/Exchnage rate (t-1)]

where,

t = Time of calculation

n = Number of securities in the index at time T

[ADJ.sub.t] = (Security Price before ex-date of corporate action/Theoretical Price after ex-date of corporate action)

Exchange rate used is time-variant

Let us now bring out the standard treatments on the issue of diversification once again, and in that context CAPM framework has been quite extensively brought out. Roll and Ross (1994) note that CAPM may not correctly show the relationship between risk and return, and yet a vast crop of research exists [Stulz 1981a,b), Solnik (1983), Campbell and Hamao (1992), Chan, Karlyi and Stulz (1992), Heston,Rouwenhorst and Wessels (1995), Beakart (1995), Harvey (1991,1995) and Beakert and Harvey (1996), Beakert, Erb, Harvey and Viskanta(1997)]. They examine the asset pricing theory based on two attributes: the beta of all countries index and conditional volatility. They fmd that in completely segmented markets, volatility is the correct version of risk because higher expected returns are associated with higher volatility and vice versa.

In this study, we have drawn a sample of ten emerging markets from the countries that constitute the Emerging Markets Free index (EMF) of the Morgan Stanley Capital International (MSCI) (1). All the markets chosen for the study are from the Southeast Asian region in order to keep the focus on a defined geographical territory for isolating region specific characteristics. Further motivation for such a sample selection has come from the work of Obaidullah (1994) who has made the case that in the internationalization of equity portfolios from the point of view of global investors some of the South Asian countries have made a strong case for inclusion in an international portfolio. Specifically, the results of his research pointed that the benefits of including countries like India followed by Thai and the Taiwanese markets were "too immense and clear cut to be ignored".

In order to have an insight into any potential diversification benefits amongst the sample countries, correlation coefficients have been computed between the monthly returns. The significance of the correlation coefficients is tested at 5% and 10% levels of significance.

As noted earlier, low and insignificant correlation coefficients would make a case for diversification between countries. The risk-return characteristics of the sample countries have been studied by their descriptive statistics: mean returns and variance of returns (total risk).

The variance has been decomposed into systematic and unsystematic components as follows:

Systematic Risk = [R.sup.2] x [[sigma].sup.2.sub.i] (26)

where [R.sup.2] = coefficient of determination between the country's mean return and the return on the market index (EMF) x [[sigma].sub.i.sup.2] = variance of country's return (total risk), and Unsystematic Risk ([[sigma].sup.2.sub.ei]) = [[sigma].sub.i.sup.2]--Systematic Risk

The mean return is correlated with the measures of total risk, systematic risk and unsystematic risk to find out whether and in what manner the risk and return series are related to each other.

In order to determine any diversification benefits, the Single Index Portfolio Optimization Model a la Elton and Gruber (1994) has been used to rank the countries according to their 'excess return to Beta" ratio [For further clarification, see Sharpe (1964)]. This is done as follows:

Excess return to beta ratio = [[bar.R].sub.i] - [R.sub.f]/[[beta].sub.i] (27)

where [[bar.R].sub.i] = the expected return of the country i, [R.sub.f] = the return on a risk less asset, and [[beta].sub.i] = the expected change in the rate of return on country i associated with a 1% change in the market return.

This ranking is done to represent the desirability of any country's inclusion in the portfolio. For deciding the number of countries that will formulate the portfolio, a unique cut-off rate ([C.sup.*]) has been computed, where, all countries having [[bar.R].sub.i] - [R.sub.f]/[[beta].sub.i] higher than [C.sup.*] would be included and vice-versa. The cut-off rate is calculated as follows:

[C.sup.*] = [[sigma].sup.2.sub.m] [i.summation over (j=1)]([[bar.R].sub.j] - [R.sub.f])[[beta].sub.j]/[[sigma].sup.2.sub.ej] / 1 + [[sigma].sup.2.sub.m] [i.summation over (j=1)] [[beta].sup.2.sub.j]/[[sigma].sup.2.sub.ej] (28)

Once the countries to be included in the portfolio are finalized, the proportion of investment in each country is found out by computing the value of [[omega].sub.i] as follows:

[[omega].sub.i] = [[psi].sub.i]/[N.summation over (j=1)][[psi].sub.j] (29)

where,

[[psi].sub.i] = [[beta].sub.i] ([[bar.R].sub.i] - [R.sub.f]/ [[beta].sub.i] - [C.sup.*]) (30)

A Simple Linear Regression is fitted between the country returns and the returns on the EMF index to find out the extent to which the market determines the returns of the countries. It has been followed up by a stepwise regression between the returns of the sample countries and the returns on the EMF index to reveal the sensitivity of countries' return amongst themselves and with the market. This has been done to determine whether the markets in the study region are segmented or otherwise and to detect any regional affinities amongst the sample countries. Low and/or insignificant (as indicated by the t-statistic) betas will indicate market segmentation, which can be used gainfully by an investor and vice-versa. The data are checked for any serial correlation and multicollinearity by using the Durbin--Watson statistic and the Variance Inflation Factors, respectively.

Table 8A presents the correlation matrix between the returns of emerging economies in the Southeast Asian region. Three more countries; India (IN), Pakistan (PK) and Sri Lanka (SL) have been added to the analysis at this stage to give more coverage to the region. For the purpose of consistency, all returns are in the U.S. currency. It can be observed that 38 out of a total of 55 coefficients are below 0.5 (69.09% cases). Also, the mean correlation is 0.056. Although the coefficients are statistically significant in about 32 cases (58%), only 7 of them (11%) are significant at 5% level of significance. This seems to point towards a more than average degree of segmentation in the markets, which can be used as a profit-making opportunity if investors can find a way to circumvent the segmentation.

Each sample country shows a significant correlation with the MSCI's EMF index, indicating that there is a relationship between the returns of the sample countries and the emerging markets across the globe, which is significant at 10% level of significance. However, except Korea, Taiwan and Thailand, none of the other countries exhibit any marked correlation above 0.5. A closer look at the correlations amongst individual sample countries reveals signs of some geographical affinity in their returns. The returns of countries from far-east show a relatively higher degree of correlation between themselves as compared to their correlation with countries form South West Asia. Similarly, returns of the countries from South Asia exhibit a better relationship amongst each other with the exceptions of Sri Lanka, whose returns are not significantly correlated with any of the sample countries, and India, whose returns show a significant correlation with Korea and Taiwan.

The initial analysis indicates that there may be a benefit in constructing a diversified portfolio containing the sample countries. The Single Index Portfolio Optimization Model has been applied to confirm this finding. The results of portfolio optimization are presented in Tables 8B through 8D

The countries are ranked as per their 'Excess Return to Beta' ratio and [C.sub.i] for each country is found. The results are presented in Table 8B.

The 'Excess Return to Beta' ratio [R.sub.i] - [R.sub.f]/[[beta].sub.i] exceeds the cut off rate [C.sub.i] for all countries form Korea through China, including Pakistan, Thailand, Malaysia, Taiwan and Indonesia as well. As such, the optimal portfolio must comprise of these countries. For India, Philippines and Sri Lanka [R.sub.i] - [R.sub.f]/[[beta].sub.i] < [C.sub.i], and therefore these countries do not form a part of the portfolio and the unique cut-off rate [C.sup.*] = - 4.811, which is the [C.sub.i] for China.

Table 8C shows the proportion of money ([[omega].sub.i]) that must be invested in each country for effective diversification results.

Maximum percentage (86%) of investment goes to Pakistan followed by Korea (31 %) and Malaysia (17%). For China and Indonesia, the stocks must be sold short to the extent of 18 percent and 46 percent, respectively.

The resultant portfolio return and risk are computed and compared with those if a plain portfolio comprising of all countries was held during the time frame of the study. The results show that after optimizing the portfolio, the return has increased from 0.42 percent to 2.84 percent--an increase of 2.42 percent. Also the risk measures show a substantial reduction with 116.77 as portfolio variance as compared to the plain variance of 132.52. The preliminary observation had revealed that there might be diversification benefits from the sample countries due to small correlations amongst them (Table 8). At the end of the optimization exercise, the prior fording gains strength.

For having further insight into the nature of return and risk among the sample countries, mean expected returns (2) and variances of returns are computed for each country during the period of this work. Risk is further decomposed into systematic and unsystematic component to ford out as to which part of the risk is related to return more. In other words, the attempt is to know whether the return is related to a source of risk that is market-related or otherwise.

Pakistan, Malaysia and Korea with a mean return of 2.10 percent, 1.51 percent, and 1.38 percent return, respectively, emerge on the top, and Philippines comes out as the least-return country during the study period with a mean return of -1.7269 percent. The return on the market has been 0.37314 percent, which is just above the average of all countries' return of 0.4233 percent. Indonesia, Thailand and Pakistan appear as the countries with maximum variances in their returns, whereas the returns of Malaysia, India and Philippines are relatively most stable.

The foregoing results seem to be somewhat in coherence with the recent general economic indicators of developing Asian nations.

Table 8D shows the decomposition of variance into its two sources, systematic and unsystematic.

An examination of the table reveals that Korea, Thailand and Taiwan are the top three economies where the risk is related mostly to market forces as is evident from the values of their systematic risk components of 103.78, 73.41 and 64.43, respectively. On the other hand, market has played a limited role in the risk for countries like Malaysia, Pakistan and Sri Lanka where the risk has been mostly due to non-market related forces, which may be related to operating inefficiencies in their business or the way they financed their businesses or simply because the beta computed by taking all emerging countries around the world as the definition of the market has not played a major role in deciding the equity returns of the countries.

On comparison of the risk components with corresponding mean returns, it appears as if either the market has not been very efficient in rewarding the systematic component of the risk or it values something more than just the beta measure. This appears consistent with what Douglas (1969) has found about the predictive power of beta. He indicates that unsystematic risk did seem to explain average returns, which is contrary to the predictions of the Capital Market theory. The Asian Development Outlook Update 2002 also emphasizes the country specific factors as far as the performance in equity markets is concerned.

Similar results are obtained when the mean returns and risk (and its components) are put to a bi-variate correlation test3 to find out the direction and significance of relationship, if any. The results indicate that though the correlation coefficients are not very significant but the relationship between return and risk is positive. Also, the relationship between return and unsystematic risk is more pronounced as compared to the relation between return and systematic risk. It is worth noting that not only the correlation between return and systematic risk is very meager, it also assumes significance at about 42 percent level of significance. It appears as if the market-related forces have little role in explaining the country returns and they are more segmented than integrated during the time frame of the study.

Driessen and Laeven (2002) have found that, ".... there are substantial regional and global diversification benefits for domestic investors in both developed and developing countries, provided that these investors can short sell local and foreign stock indices. Consistent with conventional wisdom, the benefits of international portfolio diversification are larger for developing countries relative to developed countries. This is consistent with the fording that developing countries on average are much less integrated in world financial markets".

The analysis of the Tables 9 and Table 9A just about confirms most of the above findings. Table 9 presents the results of the simple linear regression between the country returns and the returns on the index.

The regression results reveal that most of the beta values are highly significant at 5% level of significance with the exception of Sri Lanka, whose beta value assumes significance at 33% level of significance. Same is the case with the F-values, which are significant for all countries except Sri Lanka. The values of the Durbin-Watson statistic hover on and around 2 and 2.5 in all cases except Taiwan, where it nearly has reached 3. This is indicative of a slightly negative correlation between the residuals but it is not pronounced enough to contaminate the inferences drawn from the least squares. As such, it appears that the EMF index should be useful in explaining the country returns. However, the relatively low value of coefficient of determination [R.sup.2] does not take the case for market integration very far and hints at the presence of more localized and country specific factors than the market which may be responsible for returns [Also see, Jurion and Schwartz (1986) and Ghosh and Khaksari (1993)]. These can range from exchange rate risk, legal barriers or high taxation rates to simply an inadequate transmission and/or interpretation of information.

Stepwise regression has been employed to find out the sensitivity of the country returns to the returns of their neighboring countries in the sample as well as to the market index returns. The stepwise criteria for a variable to enter the model are the probability of F [less than or equal to] 0.050 and for the removal of variable, the probability of F [greater than or equal to] 0.100 is considered. The results are furnished below in Table 9A

The most eye-catching observation from the table is the geographical affinity amongst the countries in the region. Countries from Far East show a marked tendency to explain each other returns, whereas the South Asian nations seem to be more responsible returns amongst themselves. This tendency looks more pronounced in the far-eastern countries where the [R.sup.2] ranges from 41% to 74% than in the South Asian nations where it is very small (7% to 34%). Sri Lanka and Pakistan look particularly aloof in this matter with a [R.sup.2] of 7% and 15% respectively. However, the [R.sup.2] values are not high in any of the cases except where the EMF, China and Thailand account for 74% variation in the Korean market and in the case of Thai market whose return is taken care of by Philippines, Korea and Malaysia to the extent of 69%. It appears that the regional markets respond a bit to the immediate neighborhood but when an integrated view is taken, it is observed that except India and Korea, the EMF does not play any role in return determination. The values of Variance inflation factors (below 10) and the Durbin Watson test (around 2) do not reveal any serious problems of multi-collinearity and residual correlation in the data set and as such the observations from the data seem credible which reconfirm the finding of Table 9 of primarily segmented markets with a definite potential diversification benefits (Table 8D).

VI. CONCLUDING OBSERVATIONS

The study has been undertaken with twin objectives of ascertaining the benefits of international diversification amongst the developed and the emerging countries of South-East Asia and to determine the degree of market integration (or otherwise) amongst these countries. The principal findings of the study are: first, the stock markets of the sample countries exhibit more segmentation than integration during the period of study; second, there exist sub-regional affinities amongst the markets. In spite of a lesser degree of integration, the returns of the far eastern stock markets respond to each other. Similarly, the South Asian nations behave as "good neighbours" amongst themselves; third, the investors seem to be at a less than optimum situation in terms of return-risk trade-off. The opportunities for risk reduction and return magnification exist by way of diversifying beyond local markets; fourth, non-market-related factors account for most of the returns amongst the sample countries. However, it should be noted that during the currency crisis period the benefits have been mostly negative partly because of currency depreciation beyond expectation and that itself pushing the asset returns to negative territory. With hardly any readily available currency hedging in the emerging economies [See Eun and Bruce (1988)], the financial distress has escalated beyond tolerable level.

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ENDNOTES

(1.) The MSCI EMF (Emerging Markets Free) Index[SM] is a free float-adjusted market capitalization index that is designed to measure equity market performance in the global emerging markets. As of April 2002 the MSCI EMF Index consisted of the following 26 emerging market country indices: Argentina, Brazil, Chile, China, Colombia, Czech Republic, Egypt, Hungary, India, Indonesia, Israel, Jordan, Korea, Malaysia, Mexico, Morocco, Pakistan, Peru, Philippines, Poland, Russia, South Africa, Taiwan, Thailand, Turkey and Venezuela.

(2.) Results not reported here are due to the paucity of space. However, the unreported computations are available from the authors upon request.

(3.) Results not reported here are due to the paucity of space. However, the unreported computations are available from the authors upon request.

Chandra Shekhar Bhatnagar (a) and Dipasri Ghosh (b)

(a) Department of Management Studies, The University of the West Indies St. Augustine Trinidad cbhatnagar@fss.uwi.tt, csbhatnagar@rediffinaiLcom

(b) Department of Finance, Florida International University Miami, Florida 33199 dghos001@fiu.edu, dipasri@alumni.caltech.edu

Table 1
Randomly diversified portfolio's variance measured as a percentage of
the variance of the average individual stocks with in a country

Belgium 19.0%
France 32.7
West Germany 43.8
Italy 38.0
Netherlands 24.1
Switzerland 44.0
United Kingdom 34.5
United States 27.0
International 11.7

Table 2

 Proportion of unsystematic risk

Belgium 74%
France 90
West Germany 78
Italy 94
Norway 54
United Kingdom 83
United State 12

Table 3

 Beat of domestic Loss in expected return
 portfolio

Belgium 0.55 2.1
France 0.5 4.5
West Germany 0.86 3.9
Italy 0.5 6.1
Norway 0.94 1.8
United Kingdom 0.61 3.3
United States 1.1 0.31

Table 4
Changes in exchange rates and stock prices: 1997

 Exchange rate
 Asian currency per U.S. dollar

 End of June December 1 Change (%)

Singapore 1.4305 15965 -10.40
Hong Kong 7.7470 7.7380 0.21
Taiwan ROC 24.812 32..2200 -13.39
South Korea 888.0000 1185.0000 -25.06
Thailand 24.7000 40.8500 -39.53
Philippines 263760 35.0000 -24.64
Malaysia 25245 35360 -28.61

 Stock price index

 End of June December 1 Change (%)

Singapore 198795 1665.47 -16.22
Hong Kong 15196.79 10750.88 -29.26
Taiwan ROC 9030.28 7400.64 -18.05
South Korea 745.50 393.16 -47.26
Thailand 527.28 389.33 -26.16
Philippines 2809.21 1777.04 -36.74
Malaysia 107730 531.46 -50.67

Source: The Central Book of China. 1997

Table 5
Changes in exchange rates

 July 1997 December, 15, 1997 Change(%)

South Korea 880 1564 -43.7
Thailand 22.88 47.95 -46.0
Philippines 26.38 38.85 -32.1
Malaysia 2.504 392 36.3
Indonesia 2650 5750 -53.9

Source: Bank of Thailand, 1997

Table 6A
Time block 1 (1988-1996) correlation among annual index returns

 FR DE GB US

FR 1
DE 0.8 1
GB 0.49 0.7 1
US 0.62 0.5 0.6 1
IDF 0.68 0.5 0.1 -0.02
KR 0.44 0.3 -0.3 -0.18
MYF 0.57 0.7 0.5 0.12
PHF 0.62 0.6 0.3 0.26
TW 0.83 0.8 0.3 0.16
THF 0.61 0.7 0.2 0.15
EMF 0.69 0.7 0.4 0.3

 IDF KR MYF PHF

FR
DE
GB
US
IDF 1
KR 0.8 1
MYF 0.51 0.242 1
PHF 0.3 0.281 0.79 1
TW 0.78 0.669 0.62 0.63
THF 0.5 0.445 0.79 0.78
EMF 0.4 0.309 0.76 0.94

 TW THF EMF

FR
DE
GB
US
IDF
KR
MYF
PHF
TW 1
THF 0.6 1
EMF 0.7 0.85 1

Time block 2 (1997-1999) correlation among annual index returns

 FR DE GB US

FR 1
DE 0.42 1
GB -0.55 0.5 1
US -0.36 0.7 1 1
IDF 0.34 -0.7 -1 -1
KR 0.98 0.2 -0.7 -0.54
MYF 0.29 -0.7 -1 -1
PHF 0.96 0.1 -0.8 -0.62
TW -0.08 -0.9 -0.8 -0.9
THF 0.76 -0.3 -1 -0.88
EMF -0.04 -0.9 -0.8 -0.92

 IDF KR MYF PHF

FR
DE
GB
US
IDF 1
KR 0.52 1
MYF 1 0.473 1
PHF 0.6 0.995 0.56 1
TW 0.91 0.111 0.93 0.21
THF 0.87 0.872 0.84 0.92
EMF 0.92 0.156 0.94 0.25

 TW THF EMF

FR
DE
GB
US
IDF
KR
MYF
PHF
TW 1
THF 0.6 1
EMF 1 0.62 1

Table 6B
Correlation among monthly index returns: 1988-2003

 FR DE GB US IDF

FR 1
DE 0.82 1
GB 0.67 0.64 1
US 0.6 0.58 0.6 1
IDF 0.19 0.18 0.1 0.2 1
KR 0.21 0.2 0.3 0.3 0.3
MYF 0.28 0.32 0.3 0.3 0.4
PHF 0.26 0.27 0.3 0.4 0.5
TW 0.24 0.27 0.1 0.3 0.1
THF 0.26 0.31 0.3 0.4 0.4
EMF 0.45 0.46 0.4 0.6 0.4

 KR MYF PHF TW THF EMF

FR
DE
GB
US
IDF
KR 1
MYF 0.28 1
PHF 0.26 0.54 1
TW 0.27 0.39 0.41 1
THF 0.49 0.54 0.64 0.4 1
EMF 0.4 0.58 0.56 0.47 0.6 1

Correlation among monthly index returns: 1997- 1999

 FR DE GB US IDF

FR 1.00
DE 0.84 1.00
GB 0.67 0.64 1.00
US 0.60 0.65 0.64 1.00
IDF 0.46 0.34 0.37 0.47 1.00
KR 0.23 0.15 0.29 0.28 0.37
MYF 0.43 0.37 0.46 0.45 0.65
PHF 0.52 0.43 0.45 0.58 0.66
TW 0.34 0.38 0.37 0.55 0.45
THF 0.39 0.43 0.50 0.56 0.55
EMF 0.57 0.56 0.59 0.73 0.63

 KR MYF PHF TW THF EMF

FR
DE
GB
US
IDF
KR 1.00
MYF 0.32 1.00
PHF 0.35 0.71 1.00
TW 0.25 0.60 0.58 1.00
THF 0.64 0.60 0.72 0.58 1.00
EMF 0.37 0.67 0.70 0.76 0.67 1.00

Correlation among monthly index returns: 2000- 2003

 FR DE GB US IDF

FR 1
DE 0.93 1
GB 0.85 0.81 1
US 0.77 0.77 0.8 1
IDF 0.14 0.2 0.3 0.2 1
KR 0.5 0.54 0.5 0.7 0.3
MYF 0.23 0.36 0.1 0.2 0.3
PHF 0.1 0.19 0.2 0.3 0.5
TW 0.37 0.45 0.3 0.4 0.1
THF 0.25 0.29 0.4 0.5 0.5
EMF 0.72 0.77 0.7 0.8 0.4

 KR MYF PHF TW THF EMF

FR
DE
GB
US
IDF
KR 1
MYF 0.27 1
PHF 0.49 0.14 1
TW 0.66 0.62 0.35 1
THF 0.62 0.28 0.67 0.51 1
EMF 0.84 0.44 0.47 0.75 0.6 1

Table 7
Annual index returns (1988-2003)

 FR DE GB US

Dec 30, 1988 0.36 0.2 0 0.12
Dec 29, 1989 0.34 0.4 0.2 0.27
Dec 31, 1990 -0.15 -0.1 0.1 -0.06
Dec 31, 1991 0.16 0.1 0.1 0.27
Dec 31, 1992 0.01 -0.1 -0.1 0.04
Dec 31, 1993 0.19 0.3 0.2 0.07
Dec 30, 1994 -0.07 0 0 -0.01
Dec 29, 1995 0.12 0.1 0.2 0.35
Dec 31, 1996 0.19 0.1 0.2 0.21
Dec 31, 1997 0.11 0.2 0.2 0.32
Dec 31, 1998 0.4 0.3 0.1 0.29
Dec 31, 1999 0.28 0.2 0.1 0.21
Dec 29, 2000 -0.05 -0.2 -0.1 -0.14
Dec 31, 2001 -0.23 -0.2 -0.2 -0.13
Dec 31, 2002 -0.22 -0.3 -0.2 -0.24
Dec 31, 2003 0.38 0.6 0.3 0.27

 IDF KR MYF PHF

Dec 30, 1988 2.28 0.94 0.24 0.4
Dec 29, 1989 0.77 0.004 0.53 0.63
Dec 31, 1990 0.05 -0.285 -0.1 -0.5
Dec 31, 1991 -0.5 -0.17 0.03 0.83
Dec 31, 1992 -0 5E-05 0.16 0.37
Dec 31, 1993 1.02 0.291 1.07 1.21
Dec 30, 1994 -0.3 0.221 -0.2 -0.1
Dec 29, 1995 0.07 -0.046 0.04 -0.1
Dec 31, 1996 0.25 -0.384 0.25 0.17
Dec 31, 1997 -0.7 -0.672 -0.7 -0.6
Dec 31, 1998 -0.3 1.375 -0.3 0.13
Dec 31, 1999 0.92 0.902 1.12 0.02
Dec 29, 2000 -0.6 -0.503 -0.2 -0.5
Dec 31, 2001 -0.1 0.46 0.02 -0.2
Dec 31, 2002 0.38 0.074 -0 -0.3
Dec 31, 2003 0.7 0.326 0.23 0.39

 TW THF EMF

Dec 30, 1988 1.2 0.42 0.3
Dec 29, 1989 0.8 1.06 0.6
Dec 31, 1990 -0.6 -0.3 -0.1
Dec 31, 1991 0.1 0.18 0.6
Dec 31, 1992 -0.2 0.3 0.1
Dec 31, 1993 0.8 0.98 0.7
Dec 30, 1994 0.2 -0.1 -0.1
Dec 29, 1995 -0.3 -0.1 -0.1
Dec 31, 1996 0.4 -0.4 0
Dec 31, 1997 -0.1 -0.7 -0.1
Dec 31, 1998 -0.2 0.11 -0.3
Dec 31, 1999 0.5 0.47 0.6
Dec 29, 2000 -0.5 -0.6 -0.3
Dec 31, 2001 0.1 0.03 -0
Dec 31, 2002 -0.3 0.24 -0.1
Dec 31, 2003 0.4 1.34 0.5

Table 8A
Correlation among returns of emerging markets

 CNF IN IDF KR

 CNF 1
 IN 0.06 1
 IDF 0.34 * 0.18 1
 KR 0.65 ** 0.36 ** 0.41 ** 1
 MYF 0.23 0.13 0.50 ** 0.31 *
 PK -0.125 0.41 ** -0.01 0.12
 PHF 0.36 ** 0.13 0.56 ** 0.51 **
 SL 0 0.12 -0.02 0.13
 TW 0.47 * 0.31 * 0.26 0.62 **
 THF 0.48 ** 0.17 0.61 ** 0.68 **
 EMF 0.56 ** 0.51 ** 0.46 ** 0.82 **

 MYF PK PHF SL

 CNF
 IN
 IDF
 KR
 MYF 1
 PK 0.02 1
 PHF 0.31 * 0 1
 SL -0.11 0.29 * -0.15 1
 TW 0.55 ** 0.10 0.38 ** -0.02
 THF 0.50 ** 0.08 0.73 ** -0.13
 EMF 0.43 ** 0.27 * 0.52 ** 0.12

 TW THF
 EMF

 CNF
 IN
 IDF
 KR
 MYF
 PK
 PHF
 SL
 TW 1
 THF 0.54 ** 1
 EMF 0.75 ** 0.64 ** 1

* Correlation is significant at .05 level of significance

** Correlation is significant at .10 level of significance

Table 8B
Ranking of excess return to beta and [C.sub.i]

COUNTRY [R.sub.i]-[R.sub.f]/ ([R.sub.i]-[R.sub.f])
 [[beta].sub.i] [[beta].sub.i]/
 [[sigma].sub.
 ei.sup.2]

SL -11.12 -0.003
PHF -7.13 -0.05
IN -4.00 -0.03
CNF -3.83 -0.03
IDF -3.35 -0.018
TW -2.67 -0.073
MYF -2.59 -0.01
THF -1.82 -0.027
PK -1.75 -0.003
KR -1.10 -0.04

 [i.summation
 over (j=1)]
 ([R.sub.i]-[R.sub.f])
COUNTRY [[beta].sup.2]/ [[beta].sub.i]/
 [[sigma].sup. [[sigma].sub.
 2.sub.ei] ei.sup.2]

SL 0.0003 -0.003
PHF 0.007 -0.06
IN 0.007 -0.08
CNF 0.009 -0.12
IDF 0.005 -0.14
TW 0.027 -0.21
MYF 0.004 -0.23
THF 0.014 -0.25
PK 0.001 -0.26
KR 0.04 -0.30

 [i.summation
COUNTRY over (j=1)]
 [[beta].sup.2]/
 [[sigma].sub.
 ei.sup.2] [C.sub.i]

SL 0.0003 -0.169
PHF 0.008 -2.467
IN 0.01 -3.536
CNF 0.024 -4.811
IDF 0.030 -5.441
TW 0.057 -7.657
MYF 0.062 -8.022
THF 0.077 -8.613
PK 0.078 -8.677
KR 0.121 -8.881

Table 8C
Proportion of investment per country

COUNTRY [[psi].sub.i] [[omega].sub.i]

CNF -0.01 -0.18
IDF -0.02 -0.46
TW 0.009 0.15
MYF 0.01 -0.17
THF 0.007 0.14
PK 0.05 -0.86
KR 0.01 -0.31

Table 8D
Country wise risk decomposition

 [[sigma].sup.
COUNTRY [R.sup.2] 2.sub.i] [[beta].sup.2]

CNF 0.31 120.76 0.77
IN 0.26 79.97 0.43
IDF 0.21 231.6 1.01
KR 0.67 154.89 2.15
MYF 0.19 85.74 0.32
PK 0.08 162.97 0.26
PHF 0.27 77.68 0.44
SL 0.02 123.81 0.04
TW 0.57 113.03 1.33
THF 0.42 174.78 1.5
EMF . . .

 Systematic Risk Unsystematic Risk

 [r.sup.2]x[[sigma]
 .sup.2.sub.i] or,
 [[sigma].sup. [[beta].sup.2]x [[sigma].sup.
COUNTRY 2.sub.m] [[sigma].sup.2.sub.m] 2.sub.ei]

CNF . 37.44 83.32
IN . 20.79 59.18
IDF . 48.64 182.96
KR . 103.78 51.11
MYF . 16.29 69.45
PK . 13.04 149.93
PHF . 20.97 56.71
SL . 2.48 121.33
TW . 64.43 48.6
THF . 73.41 101.37
EMF 48.37 . .

Table 9
Simple linear regression: countries and index

COUNTRY [[beta].sub.i] T- STAT (SIG.) F VALUE (SIG.)

CNF 0.88 4.74 (0.00) 22.54 (0.00)
IN 0.66 4.23 (0.00) 17.86 (0.00)
IDF 1.005 3.65 (0.001) 13.35 (0.001)
KR 1.467 10.11 (0.00) 102.31 (0.00)
MYF 0.57 3.38 (0.001) 11.42 (0.001)
PK 0.511 2.05 (0.45) 4.2 (0.45)
PHF 0.663 4.34 (0.00) 18.86 (0.00)
SL 0.205 0.913 (0.336) 0.833 (0.366)
TW 1.15 8.14 (0.00) 66.18 (0.00)
THF 1.22 5.95 (0.00) 35.46 (0.00)

 ADJUSTED
COUNTRY [R.sup.2] DW

CNF 0.297 1.91
IN 0.263 2.45
IDF 0.19 1.99
KR 0.665 2.04
MYF 0.17 2.27
PK 0.06 2.5
PHF 0.26 2.1
SL -0.003 2.3
TW 0.561 2.7
THF 0.403 2.5

Table 9A
Stepwise regression: countries and index returns

Country Predictors ModeL[R.sup.2] Betas

CNF KR,PK 0.45 0.60, -0.18
IN EMF,PK 0.34 0.55, 0.20
IDF PHF,MYF 0.41 0.77, 0.59
KR EMF,CNF,THF 0.74 0.96,0.28, 0.20
MYF TW,IDF 0.42 0.39, 0.23
PK IN 0.15 0.59
PHF THF 0.52 0.48
SL PK 0.07 0.26
TW KR,MYF 0.51 0.43, 0.45
THF PHF,KR,MYF 0.69 0.69, 0.39,0.34

Country T-STAT F-Value VIF

CNF 6.56, -2.03 22.26 1.017
IN 3.57, 2.43 12.75 1.084
IDF 3.93, 3.19 18.76 1.11
KR 5.35,2.90,2.31 49.8 1.98,1.5,1.77
MYF 4.08, 3.5 19.58 1.074
PK 3.2 10.3 1
PHF 7.52 56.57 1
SL 2.19 4.77 1
TW 4.88, 3.85 27.94 1.108
THF 4.96,4.04,2.87 39.29 1.42,1.41,1.15

Country DW

CNF 2.07
IN 2.53
IDF 1.9
KR 2.17
MYF 2.28
PK 2.56
PHF 1.93
SL 2.16
TW 2.27
THF 2.32