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Factors affecting returns across stock markets
FACTORS AFFECTING RETURNS ACROSS STOCK MARKETS Jeff Madura Alan L. Tucker Marilyn Wiley
ABSTRACT Complementing recent research on the factors explaining differences in mean returns across stocks within the U.S. (Fama & French, 1992) and Japanese (Chan, Hamio, & Lakonishok, 1991) markets, this article reports the results of an investigation of factors hypothesized to explain differences in mean returns across entire national stock markets. Unlike most studies focused solely on U.S. stocks, this study does not find a beta or size effect in the assessment of national stock market movements. The most relevant factor for explaining disparate returns across markets is country risk.
Under perfect market conditions, the risk and return characteristics of national stock markets would not depend on features unique to each country. Although the risk levels of firms could differ according to firm-specific characteristics, country characteristics that inhibit cross-border investing would be non-existent. Country markets would be integrated, essentially allowing for a single unified stock market. That is, stock markets would only be distinguished by location and not by unique restrictions. In reality, stock markets are somewhat segmented because of various imperfections, with each market exhibiting unique characteristics that distinguish it from other markets. The disparity in characteristics may explain differences in returns across markets. The objective of this paper is to determine whether market-specific characteristics affect the returns of stock markets. Results of this analysis imply whether differences in stock returns of firms around the world
Jeff Madura, Florida Atlantic University, Florida Atlantic University. Global Finance Journal, S(1): l-14 ISSN: 1044-0283
Alan L. Tucker,
Pace University,
and Marilyn
Wiley,
Copyright 0 1997 by JAI Press Inc. All rights of reproduction in any form reserved.
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8(l), 1997
are attributed to market-specific risk characteristics as well as firm-specific risk characteristics. Such findings would suggest that the firm’s required rate of return is dependent on a market-specific risk characteristic beyond its control and may explain why some firms in high-risk markets list their stocks on other national exchanges. First, literature directly related to this objective is reviewed. Then hypotheses on factors that affect returns across markets are formulated. Next, a methodology is developed to test whether market returns are cross-sectionally related to these factors. Finally, results of the analysis are disclosed, along with implications.
I.
RELATED
RESEARCH
According to Sharpe (1964) and Lintner (1965), the expected returns on securities are a positive and linear function of their betas. Black, Jensen, and Scholes (1972) and Fama and MacBeth (1973) empirically confirmed a positive relationship between mean return and beta across firms. However, Reinganum (1981) found that the cross-sectional relationship between mean returns and betas of firms was not significant over the 1964-1979 period. Lakonishok and Shapiro (1986) report similar results. Recent research by Fama and French (1992) determined that the relationship between mean returns and betas of firms over the fifty-year period from 1941 to 1990 is weak. There is some evidence that factors other than beta may be related to mean returns across firms. Banz (1981) found that the size of the firm (as measured by market value of the firm’s equity) was inversely related to mean returns across firms over the 1936-1977 period, after controlling for beta. Thus, low capitalization stocks experienced excess risk-adjusted returns over this period. The size effect appeared to be about as strong as the beta effect. Rosenberg, Reid, and Lanstein (1985) found a positive and significant relationship between the book value of equity in proportion to the market value of equity and mean returns across firms. Recent research by Fama and French documents this relationship over the 1963-1990 period. Basu (1983) found that earnings-price ratios contribute to explaining cross-sectional variation in mean returns after controlling for the beta and size of each firm. In addition, the earnings-price ratios are positively related to mean returns across firms. Fama and French (1992) state that these additional variables scale stock prices and offer information about risk and expected returns. One dimension of risk is measured by the size of the firm, while another dimension is measured by book value/market value and earnings/price ratios (also see Chan & Chen, 1991). Aggarwal, Rao, and Hiraki (1990) assessed whether there were E/P and size effects on securities listed on the Tokyo Stock Exchange (TSE). They confirmed the existence of E/P and size effects for TSE-listed securities that were similar to the effects documented for firms listed on U.S. exchanges. Furthermore, they found that the E/P effect interacted with the size effect, as it was more pro-
3
Factors Affecting Returns
nounced for smaller firms. Related research by Chan, Hamao, and Lakonishok (1991) also found evidence of a size effect for stocks listed on the TSE.
II.
HYPOTHESES
FOR MARKETS
The size effect found for individual firms may be partially explained by transaction costs. Small firm stocks are generally not as liquid, which could result in higher bid-ask spreads. Thus, the excess returns for low capitalization stocks are necessary when considering the relatively large transaction costs associated with trading such stocks. An alternative explanation is that low capitalization stocks are monitored less by investment analysts. Consequently, there may be more uncertainty about these stocks, and the uncertainty may not be completely captured by the firm’s beta. (See Thornton, 1988 for a modified CAPM which incorporates prior uncertainty about the distribution of returns into the traditional CAPM framework.) Similar arguments could be used to suggest that mean returns across markets in a given period may be partially attributed to capitalization. Markets with a low capitalization may be less liquid and therefore require higher transaction costs. In addition, these markets are probably monitored less than the more established and larger markets. To the extent that less monitoring creates more uncertainty, one would expect the markets with lower capitalization to exhibit relatively high returns. The earnings/price ratio and capitalization levels of firms are somewhat related. In fact, Basu (1983) and Reinganum (1981) view these two variables as imperfect substitutes for each other. Market capitalization may serve as an adequate proxy for the size of a stock market, and therefore can be employed to test for a size effect. However, if the returns of markets vary because of differences in market liquidity, they will not necessarily be related to the market capitalization measure. Thus, the relationship between the value of shares traded per period and the mean returns across markets is also tested as value traded measures the volume of trading within each market. The value of shares traded in proportion to the number of listed companies is assessed since some markets may be viewed as active when viewed on a per firm basis even if the volume of trading is small. A final variable to be considered is country risk. This variable reflects an additional risk dimension that is not necessarily captured by the other factors described above. Country risk may be priced in a return generating process if investors require higher returns to compensate for a higher level of country risk. Given that U.S. investors have a choice of markets to invest in, the country risk proxy should be positively related to mean returns across markets. An exception would be markets that are dominated by local investors who have restricted investment opportunities; country risk may not necessarily be influential in this case, because all possible investments available to those investors may exhibit country risk. To the extent that outside investors affect stock prices, the country risk should be significantly related to returns across countries. Country risk is not completely measured by the market’s beta, because it reflects a degree of under-
GLOBAL FINANCE JOURNAL
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Table 1 Descriptive Statistics
Marmots
Period
pr Year
Year
Australia
0.0770
S4W42.2
$37.2010
29~7-~~~92 -_-_II-1,241.4
Belgium
0.0470
0.826
62,332.2
7,244.0
39.3370
184.0
Canada
-0.0313
0.772
252‘163.8
76,2%0.2
67.3362
1,133.6
France
0.1112
0.818
299,502.O
-0.2028
0.693
3320,594.2
Germany
101,621.4
137.241%
735.2
634,908.8
1,017.2788
612.0 291.8
1.093
82,268.g
36,648.4
125.6776
Italy
-0.0357
0.688
145,459.2
37,779.%
161.2734
240.0
Japan
0.1810
0.569
3‘430,154.O
2,008,776.6
1,004,9819
2,015.2
0.809
135~085.8
Hong Kong
0.0651
Netherlands
0.028%
South Africa
-0.1477
-0.016
64,263.4
235.1400
267.4
129,467.4
7,563.g
9.9095
761.6 140.4
0.0461
1.173
31,970.o
12,6%0.4
87.8112
-0.0190
0.807
157,088.6
68,836.O
378.2198
U.K.
0.1808
0.976
%29,X61.6
377,557.%
185.879%
2,025.o
U.S.
0.4020
11.000
300.8148
6,7%5.8
Singapore Switzerland
Emergiq M~rk~fs
_..“““..” .-
?,231,650.0
-l.-.l.“-..~
-..~..--._.--
.~._
~_..__._
0.7525%
0.574
Brazil
0.2567
0.530
30,506.O
Chile
0.3167
0.629
12681.2
Colombia
0.3117
0.230
1,797.6
98.2
1.1603
85.4
Greece
0.3175
0.572
X,694.2
1,534.0
11.4993
125.0 6,059.g
Argenti na
-
$5‘909.2
2,045,760.0
173.6
$1,6%7.2
$9.5309
1%4.6
12,664.O
21.6440
584.4
932.4
4.3374
212.6
India
0.0125
-0.047
30,858.h
16511.8
2.672%
Jordan
0.0050
0.156
2,310.2
449.6
4.3284
103.8
Korea
0.1225
0.434
94,%49.2
77,355.2
130.7220
574.4
Malaysia
0.1250
1.039
37,785.8
6973.6
25.3433
264.8
Mexico
0.4250
1.562
35,121.6
14,20.6
70.7901
200.8
Nigeria
0.1517
0.0605
0.2092
1,238.6 33,410.6
7.2
Pakistan
0.146 0.077
281.6
0.5937
117.2 450.4
Philippines
0.1875
0.907
7,063.4
1,506.2
10.2574
147.4
Portugal
0.230%
0.767
9,092.2
10.5480
171.4
Taiwan
0.345%
0.591
126,247.4
481,162.6
2,573.%480
181.0
Thailand
0.2642
0.973
19,931.0
15333.2
73.926%
186.2 78.8
1,%14.2
Turkey
(I.7542
-0.113
9,181.4
3,0%5.2
27.4685
Venezue la
0.365%
-0.179
5028.2
l,lSh.%
17.8976
72.4
Zimbabwe
0.1842
-0.159
1,269.6
45.2
0.8029
555.4
Factors Affecting Returns
5
lying uncertainty about economic and political conditions within the market’s stock movements.
III.
DESCRIPTIVE
STATISTICS
that is not captured
ON MARKETS
Monthly price data on stock indexes of all countries whose data were consistently available were compiled over the 1987-1991 period from The Wall Street Journal. Stock price information on emerging stock markets was drawn from the Emerging Stock Markets Factbook: 1992. In aggregate, the data base includes 33 countries. Summary statistics of the mean returns and betas for each country are disclosed in Table 1. The model developed by Fama and French used the U.S. market as a basis for empirical tests, so that betas derived in that study were measured from a U.S. investor perspective. Since the foreign country markets are assessed from the perspective of the U.S. investor the U.S. market is also used as the independent variable to derive the betas of the national markets. To the extent that U.S. investors use the U.S. market when deriving betas for individual U.S. securities or portfolios of U.S. securities, they are likely to use a similar approach when deriving the betas from a portfolio of foreign securities. The mean monthly return accounts for exchange rate movements relative to the U.S. dollar since all markets are viewed from a U.S. perspective. The exchange rate data were also drawn from The Wall Street Journal and the Emergitig Stock Markets Factbook: 1992. Each market is treated as a portfolio of securities. Twenty-nine of the 33 betas were significantly different from zero at the .05 level, implying a significant relationship between the foreign market and U.S. market returns. The betas of the South Africa, India, Jordan, and Pakistan markets were not significant. Since the beta of a foreign market reflects the sensitivity of a large portfolio of stocks to the U.S. market it is not necessarily representative of every individual stock in that market. The focus of this research is on a return-risk relationship across markets rather than on the selection of individual foreign stocks. The implications from this cross-market analysis provide important insights into optimal asset allocation decisions for U.S. based investors, and focus on whether the return from foreign market investing is conditioned on systematic risk from the U.S. perspective. The information on market capitalization, number of shares traded, and the proportion of shares traded to the number of firms was drawn from the Emerging Stock Markets F&book: 1992 for all countries.
IV.
METHODOLOGY
For the five-year period extending from 1987 through 1991, the cross-sectional relationship between the market characteristics just described and returns of the foreign market is assessed, using the following model:
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rj = ~0 + ~1 BETAj + ~$n(MCAI’)j + vsln(VALUE)j WsEMERGj + cj
8(l), 1997
+ v,Jn(VALFIRM)j
+ (1)
where:
9 BETAj MCAI’j VALUEi VALFIRMj
EMERGj
ej wo, -.w5
= mean monthly return of the jth market over the 1987-1991 period less exchange rate gains or losses = beta, or systematic risk of the jth market over the 1987-1991 period = mean market capitalization of the jth market over the 1987-1991 period = mean value of shares traded per year in the jth market over the five-year period = mean value of shares traded per year in proportion to the number of firms listed per year for the jth market over the five-year period = 1.0 for markets considered to be emerging, zero otherwise (since emerging markets tend to have a higher level of country risk than other markets, the EMERG variable serves as a proxy for country risk) = error term = parameters.
Ordinary least squares regression analysis is employed to test the model described above. This model is analogous to the cross-sectional model used by Fama and French in that it captures risk and size proxies. However, since the objective of this study is to explain the cross-sectional variation in market returns rather than firm returns, a country risk proxy is also incorporated. The independent variables were averaged over a five-year period that begins one year before the five-year period used to measure returns. This procedure captures the lagged relationship between the variables and returns. Fama and French also use data for variables in the year before the returns they model. In addition to a five-year analysis, the relationship between market-specific variables and mean returns is assessed on an annual basis. Each year from 1987 through 1991, the cross-sectional relationship between the variables described earlier and returns of the market is assessed by applying least squares regression analysis to the following model: rjt = h + hlln(MCAP)j,,_l
+ hzln(VALUE)j,,_l 3LhEMERGj + Uj,t
+ h31n(VALFIRM)i,t_1 + (2)
where: rjJ
MCAPj,,_l VALUEj,,l
= mean monthly return of the jth market in year t = market capitalization of the jth market in the previous year = value of the shares traded for the jth market in the previous year
Factors Ajfecting Returns
VALFIRMj,,_l EMERGj,t
7
= value of the shares traded in proportion to the number listed firms for the jth firm in the previous year = 1.0 for emerging markets, zero otherwise = error term = parameters.
Each country’s systematic risk was not included short time horizon per observation.
V.
of
in this model because of the
RESULTS
Correlation coefficients between the variables used in the two models are displayed in Table 2. The correlation coefficients in the top matrix of Table 2 are based on the five-year model, while the coefficients in the lower matrix are based on the annual model. The VALUE and VALFIRh4 variables are highly correlated, which suggests that markets with a relatively large value of outstanding shares traded per year also have a relatively large value of shares traded per year when adjusted for the number of firms. Both variables are highly correlated with market capitalization, which suggests that the larger markets (in terms of capitalization) experience the most trading. All three variables exhibit a negative correlation with mean returns across markets. The correlation coefficients between variables are somewhat similar for the five-year and one-year time horizons. Given the high correlations among independent variables, multicollinearity may present a serious bias in the tests of statistical significance on regression coefficients. For this reason, the model was revised by systematically removing one of the correlated independent variables. Models excluding combinations of correlated variables were also applied; these results are not shown, as the significance status of each variable remaining in the model was unaffected.
Correlation
Table 2 Coefficients for Variables in Model Five-Year Period
r Y
Beta ln(MCAP) ln(VALUE) ln(VALFIR M)
BETA
/n(MCAPj
h(VALUE)
ln(VALFIR M)
1.00 .95 .82
1.00 .92
1.00
1.00
-.09
1.00
-.28
.48
-.15 -.19
.55 .50
One-Year Period Y
In(M;AI’) ln(VALUE) ln(VALFIRM)
-.55 1.00 -.52 -.49
ln(MCAP)
ln(VALUE)
ln(VALFIRM)
1.00 .90 .79
1.00 .92
1.00
Notes:
‘S@ificant 2Significant
.33000
-.32437 .02130 .04650 -.02381 -.02791
at the 45 level. at the .lO level.
Number of cases
EMERG R2 Adj. R2 F-Value
BETA ln(MCAP) ln(VALSHARE) ln(VALNUM)
Constant
Coefficient
33
.3250 .2000 2.60
Model 1
2.73l
-.71 .23 .58 .52 -.41
t-value -
.27978
-.08920 .02681 .00893 .00815
Coefficient
33
.3164 .2188 3.242
3.34l
.24 .27
-.42 .30
t-value
.30815
p.26609 .03462 .02346 .00148
Coefficient
33
.3182 ,220s 3.272
2.76l
-.61 .40 .36 .04
t-value
Period
Model 3
Table 3 Analysis Over the 1987-1991
Model 2
Results of Cross-Sectional
.30515
p.21305 .02570 .01767 .00862 -
Coefficient
33
.3209 .2238 3.312
Model 4
3.02l
-.59 .28 .51 .33 -
t-value
Note:
The Goldfeld-Quandt confidence level.
Number of cases
F-Value
ln(MCAP) ln(VALSHARE) ln(VALNUM) EMERG R2 Adj. R2
Constant
161
test and White’s test for heteroskedasticity
were applied
to the data series/ Neither
-.41 .09 -1.22 .0094 -.0096 .50
-.04032 .01046 -.35196
-.47 -.Ol 0.00 -1.30 .0108
-.05679 -.00107 .00041 -.40483
161
1.21144 -.05743 -.00036 -.40472
1.32
.91267
1.29
1.21199
-.0146 .43
Coefficient
t-value
Coefficient
t-value
CoefjCicierzt
Model 2
test showed
161
,010s -.OOSl .57
evidence
1.30 -.63 -0.00 -1.31
t-value
Period
Model 3
Analysis Over the 1987-1991
Model 2
Results of Cross-Sectional
Table 4
of heteroskedasticity
161 even at the 10%
-1.31 .OlOS -.OOSl .57 -.40481
t-value 1.37 -.48 -.Ol
Model 4 1.21097 -.05686 .0007
Coefficient
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GLOBAL FINANCE JOURNAL
8(l), 1997
Results of the cross-sectional analysis over the 1987-1991 period are disclosed in Table 3. The results are shown for four different models. The first model includes all independent variables, while each of the remaining models excludes one of the correlated independent variables. The general results for each variable are somewhat similar, regardless of the model used. The betas and mean returns across markets are positively related, as hypothesized. However, the relationship is not statistically significant. The next three independent variables reflect a “size effect,” since mean returns may be larger for markets that are not as capitalized or are characterized as having thin trading. These variables are not significant in any model, which suggests no evidence of a “size effect” across global stock markets. The EMERG variable distinguishes between markets that are emerging (set equal to one) versus those that are well developed (set equal to zero). This variable was positive and highly significant in all models, implying that the mean return for emerging markets is significantly above that of the well developed markets after controlling for other market-specific characteristics. The higher returns for emerging markets do not appear to be due to differences in beta, market capitalization, or trading volume since these variables were not found to be significant. Results of the cross-sectional analysis using annual observations are disclosed in Table 4. The mean monthly returns per year per country are regressed against the annual values of the independent variables. Given 33 countries and five years per country, there are 165 observations. Since there are missing data on 4 observations, 161 observations are used. Table 4 reports results for four models, each of which excludes one of the independent variables. None of these models are significant in explaining cross-sectional variation in the returns across countries. It appears from these results that either the cross-sectional variation in market returns cannot be explained or that an annual period is insufficient to capture any relationships. The results suggest no significant relationship between the market capitalization or market trading volume variables and mean returns across markets. Furthermore, the EMERG variable is not significant in this model. Thus, the disparate annual returns across markets is not attributed to some markets’ being more developed than others. While the EMERG dummy variable distinguishes between the emerging and well developed markets, it does not distinguish among emerging markets or among well developed markets. An alternative measurement of each country’s status is its perceived degree of country risk by country risk analysts. Therefore, the EMERG variable is replaced with RISK, which represents the country risk rating in each year for each country (as quoted in Instittltional Investor) based on a survey of country risk analysts. Results from applying this revised model are disclosed in Table 5. When applied to the five-year period, the country risk rating was negative and significant, implying that mean returns are higher for countries with a lower country risk rating (i.e., a higher level of country risk.) Thus, it appears that country risk can be a relevant factor in the global market return generating process.
11
Factors Ajjfecting Returns
Table 5 Results of Cross-Sectional Analysis Incorporating the Country Risk Rating Variable Five-Year Period Coeficient
Constant BETA ln(MCAP) ln(VALSHARE) ln(VALNUM) RISK
.52146
1.90
-.04758 .01036 .04747 -.00551
-.73 .22 .45 -2.08’
X2
26
Adj. X2 F-Value
.12
Number of cases N&s:
VI.
Annual Observations
t-value
Coefficient 44603
t-value
.02606 -.02604 -.01891
.27 -.23 -.14 -.lO .92
.67
-.01221
.00730 ,013 -.02
1.87
.22
33
161
The Goldfeld-Quandt test and White’s test for heteroskedasticity were applied to the data series. Neither test showed evidence of heteroskedasticity even at the 10% confidence level. ‘Significant at the .05 level.
COMPLEMENTARY
ANALYSIS
OVER A LONGER TIME PERIOD
Since the results previously obtained may be time dependent the tests are repeated using weekly market indexes for 11 countries over the 1976-1989 time period. Data were collected from the Federal Reserve’s Macro Data Tape to compare the effects observed in the more recent time period to the longer time horizon of returns. Data for smaller markets were not available for these earlier periods, since many of the emerging markets had no active participation in the early part of the period. For the 1976-1989 period, 9 of 11 stock markets had betas which were significantly different from zero. The Canadian and German markets exhibited insignificant betas over this period. When replicating the cross-sectional model derived from Fama and French (1992), beta is again shown not to be a significant determinant of returns, but country risk rating is. To isolate the possible impact of the 1987 stock market crash the tests are repeated adding a dummy variable with a value of 1 in 1987 and zero in other years. The coefficient on this variable is insignificant, indicating there was no impact from the U.S. market crash. Given the longer time period used for these complementary tests, it is possible that the regression coefficients are intertemporally unstable, and may be conditioned on time. Therefore the data were tested to determine whether aggregation across time periods was obscuring the effects of the relationships among variables. A random effects model was used incorporating BETA and RISK as the independent variables to allow for the tendency of the error term to be higher for some countries than others and higher for some time periods than others. This model requires a two-stage process. In the first step OLS is used to estimate
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GLOBAL FINANCE JOURNAL
rjt = ~0 + WlBETAj, + v~RISK~, + ejt
8(l), 1997
(3)
where: = annual return of the jth market over the tth period less exchange rate gains or losses BETAj, = beta, or systematic risk of the jth market over the tth year RISKj, = the risk rating for country j in year t = error term ejt wo, ...w2 = parameters. rjt
The residuals from this regression are saved and decomposed into a time effect, an individual (country) effect, and a random effect. The decomposition is
where:
5
I4 rljt
=individual (country) effect, = time effect =purely random effect
The model is reestimated using generalized least squares using the structure imposed by the error decomposition. Table 6 shows the result of this test. As before beta does not contribute to market returns, but country risk is a significant explanatory variable. Since this model allows for error variance to change over time, the general results remain even after accounting for the existence of heteroscedasticity. VII.
SUMMARY
This analysis addresses whether the returns (from a U.S. perspective) across stock markets are related to the market’s beta (sensitivity of returns to U.S. market returns), the market’s capitalization, the annual value of shares traded in that market, the mean value of shares traded per firm, and the market’s country risk. The results suggest that over the five-year period, the most relevant variable for explaining disparate returns across markets is country risk. The risk-return relationship specified for individual stocks by the capital asset pricing model does not seem to apply to entire markets. That is, the higher returns of some markets are not significantly related to the systematic risk of these markets. The riskreturn relationship may depend on the definition of risk; for this analysis the sensitivity of foreign market returns to the home investor’s market was used. It should also be mentioned that these empirical results are ex post, while the riskreturn relationship specified by the CAPM is ex ante. The three variables that serve as proxies for the market’s size effect were not significantly related to mean returns across markets. Thus even though other
13
Factors Aflecfing Returns
Table 6 Long-Term Analysis Thirteen-Year
Constant Beta
Coefiicienf 0.01109 -0.00034 -0.00010
t-value
2.56951’ XI.26984 -1.98798l .06 .04 2.21
R2 Rating Adj. R2 F-value Number of Cases Note:
Period
143
‘Significant at the .05 level
studies have documented a significant inverse relation between size and returns within a market, there does not appear to be any empirical support for a size effect in explaining disparate mean returns across markets. The methodology used for this analysis could be applied to assess how factors affect market returns when viewed from another country perspective. The monthly returns would need to be translated into the home currency of investors in the country perspective of concern. The market betas would be derived using the home market of the investors as the independent variable. It is possible that the risk-return relationship specified by the CAPM and/or the size effect may be empirically supported when the markets are assessed from a different country perspective. This topic deserves consideration in future research.
REFERENCES Aggarwal, R., Rao, RI’., & Hiraki, T. (1990). Regularities in Tokyo exchange security returns: P/E, size, and seasonal influences. Journal of Financial Research, 13, 249-263. Banz, R.W. (1981). The relationship between return and market value of common stocks. Journal of Financial Economics, 9, 3-18. Basu, S. (1983). The relationship between earnings, market value, and return for NYSE common stocks: Further evidence. Journal of Financial Economics, 12, 129-156. Black, F., Jensen, M.C., & Scholes, M. (1972). The capital asset pricing model: Some empirical tests. in M. Jensen, (Ed.), Studies in the theory of capital markets. Praeger. Chan, K.C. & Chen, N.F. (1991). Structural and return characteristics of small and large firms. Journal of Finance, 46, 1467-1484. Chan, L., Chan, K.C., Hamao, Y., & Lakonishok, J. (1991). Fundamentals and stock returns in Japan. Journal of Finance, 46, 1739-1764. Fama, E.F. & French, K.R. (1992). The cross-section of expected stock returns. Journal of Finance, 47, 427-465.
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& MacBeth, J. (1973). Risk, return and equilibrium: Empirical tests. Journal of Political Economy, 81, 607-636. Lakonishok, J. & Shapiro, A.C. (1986). Systematic risk, total risk, and size as determinants of stock market returns. Journal of Banking and Finance, IO, 115-132. Lintner, J. (2965). The valuation of risk assets and the selection of risky investments in stock portfolios and capital budgets. Review of Economics and Statistics, 47, 1337. Reinganum, M.R. (1981). A new empirical perspective on the CAPM. Journal of Financial and Quantitative Analysis, 16, 439462. Rosenberg, B., Reid, K., & Lanstein, R. (1985). Persuasive evidence of market inefficiency. Journal of Portfolio Management, 11, 9-17. Sharpe, W.F. (1964). Capital asset-prices: A theory of market equilibrium under conditions of risk. Journal of Finance, 29, 425442. Thornton, W.M. (1988). Differential information, estimation risk, and the returns to small firms: Public utilities as a test case. Working Paper. Harvard University.
-I
ABSTRACT Complementing recent research on the factors explaining differences in mean returns across stocks within the U.S. (Fama & French, 1992) and Japanese (Chan, Hamio, & Lakonishok, 1991) markets, this article reports the results of an investigation of factors hypothesized to explain differences in mean returns across entire national stock markets. Unlike most studies focused solely on U.S. stocks, this study does not find a beta or size effect in the assessment of national stock market movements. The most relevant factor for explaining disparate returns across markets is country risk.
Under perfect market conditions, the risk and return characteristics of national stock markets would not depend on features unique to each country. Although the risk levels of firms could differ according to firm-specific characteristics, country characteristics that inhibit cross-border investing would be non-existent. Country markets would be integrated, essentially allowing for a single unified stock market. That is, stock markets would only be distinguished by location and not by unique restrictions. In reality, stock markets are somewhat segmented because of various imperfections, with each market exhibiting unique characteristics that distinguish it from other markets. The disparity in characteristics may explain differences in returns across markets. The objective of this paper is to determine whether market-specific characteristics affect the returns of stock markets. Results of this analysis imply whether differences in stock returns of firms around the world
Jeff Madura, Florida Atlantic University, Florida Atlantic University. Global Finance Journal, S(1): l-14 ISSN: 1044-0283
Alan L. Tucker,
Pace University,
and Marilyn
Wiley,
Copyright 0 1997 by JAI Press Inc. All rights of reproduction in any form reserved.
2
GLOBAL FINANCE JOURNAL
8(l), 1997
are attributed to market-specific risk characteristics as well as firm-specific risk characteristics. Such findings would suggest that the firm’s required rate of return is dependent on a market-specific risk characteristic beyond its control and may explain why some firms in high-risk markets list their stocks on other national exchanges. First, literature directly related to this objective is reviewed. Then hypotheses on factors that affect returns across markets are formulated. Next, a methodology is developed to test whether market returns are cross-sectionally related to these factors. Finally, results of the analysis are disclosed, along with implications.
I.
RELATED
RESEARCH
According to Sharpe (1964) and Lintner (1965), the expected returns on securities are a positive and linear function of their betas. Black, Jensen, and Scholes (1972) and Fama and MacBeth (1973) empirically confirmed a positive relationship between mean return and beta across firms. However, Reinganum (1981) found that the cross-sectional relationship between mean returns and betas of firms was not significant over the 1964-1979 period. Lakonishok and Shapiro (1986) report similar results. Recent research by Fama and French (1992) determined that the relationship between mean returns and betas of firms over the fifty-year period from 1941 to 1990 is weak. There is some evidence that factors other than beta may be related to mean returns across firms. Banz (1981) found that the size of the firm (as measured by market value of the firm’s equity) was inversely related to mean returns across firms over the 1936-1977 period, after controlling for beta. Thus, low capitalization stocks experienced excess risk-adjusted returns over this period. The size effect appeared to be about as strong as the beta effect. Rosenberg, Reid, and Lanstein (1985) found a positive and significant relationship between the book value of equity in proportion to the market value of equity and mean returns across firms. Recent research by Fama and French documents this relationship over the 1963-1990 period. Basu (1983) found that earnings-price ratios contribute to explaining cross-sectional variation in mean returns after controlling for the beta and size of each firm. In addition, the earnings-price ratios are positively related to mean returns across firms. Fama and French (1992) state that these additional variables scale stock prices and offer information about risk and expected returns. One dimension of risk is measured by the size of the firm, while another dimension is measured by book value/market value and earnings/price ratios (also see Chan & Chen, 1991). Aggarwal, Rao, and Hiraki (1990) assessed whether there were E/P and size effects on securities listed on the Tokyo Stock Exchange (TSE). They confirmed the existence of E/P and size effects for TSE-listed securities that were similar to the effects documented for firms listed on U.S. exchanges. Furthermore, they found that the E/P effect interacted with the size effect, as it was more pro-
3
Factors Affecting Returns
nounced for smaller firms. Related research by Chan, Hamao, and Lakonishok (1991) also found evidence of a size effect for stocks listed on the TSE.
II.
HYPOTHESES
FOR MARKETS
The size effect found for individual firms may be partially explained by transaction costs. Small firm stocks are generally not as liquid, which could result in higher bid-ask spreads. Thus, the excess returns for low capitalization stocks are necessary when considering the relatively large transaction costs associated with trading such stocks. An alternative explanation is that low capitalization stocks are monitored less by investment analysts. Consequently, there may be more uncertainty about these stocks, and the uncertainty may not be completely captured by the firm’s beta. (See Thornton, 1988 for a modified CAPM which incorporates prior uncertainty about the distribution of returns into the traditional CAPM framework.) Similar arguments could be used to suggest that mean returns across markets in a given period may be partially attributed to capitalization. Markets with a low capitalization may be less liquid and therefore require higher transaction costs. In addition, these markets are probably monitored less than the more established and larger markets. To the extent that less monitoring creates more uncertainty, one would expect the markets with lower capitalization to exhibit relatively high returns. The earnings/price ratio and capitalization levels of firms are somewhat related. In fact, Basu (1983) and Reinganum (1981) view these two variables as imperfect substitutes for each other. Market capitalization may serve as an adequate proxy for the size of a stock market, and therefore can be employed to test for a size effect. However, if the returns of markets vary because of differences in market liquidity, they will not necessarily be related to the market capitalization measure. Thus, the relationship between the value of shares traded per period and the mean returns across markets is also tested as value traded measures the volume of trading within each market. The value of shares traded in proportion to the number of listed companies is assessed since some markets may be viewed as active when viewed on a per firm basis even if the volume of trading is small. A final variable to be considered is country risk. This variable reflects an additional risk dimension that is not necessarily captured by the other factors described above. Country risk may be priced in a return generating process if investors require higher returns to compensate for a higher level of country risk. Given that U.S. investors have a choice of markets to invest in, the country risk proxy should be positively related to mean returns across markets. An exception would be markets that are dominated by local investors who have restricted investment opportunities; country risk may not necessarily be influential in this case, because all possible investments available to those investors may exhibit country risk. To the extent that outside investors affect stock prices, the country risk should be significantly related to returns across countries. Country risk is not completely measured by the market’s beta, because it reflects a degree of under-
GLOBAL FINANCE JOURNAL
8(l), 1997
Table 1 Descriptive Statistics
Marmots
Period
pr Year
Year
Australia
0.0770
S4W42.2
$37.2010
29~7-~~~92 -_-_II-1,241.4
Belgium
0.0470
0.826
62,332.2
7,244.0
39.3370
184.0
Canada
-0.0313
0.772
252‘163.8
76,2%0.2
67.3362
1,133.6
France
0.1112
0.818
299,502.O
-0.2028
0.693
3320,594.2
Germany
101,621.4
137.241%
735.2
634,908.8
1,017.2788
612.0 291.8
1.093
82,268.g
36,648.4
125.6776
Italy
-0.0357
0.688
145,459.2
37,779.%
161.2734
240.0
Japan
0.1810
0.569
3‘430,154.O
2,008,776.6
1,004,9819
2,015.2
0.809
135~085.8
Hong Kong
0.0651
Netherlands
0.028%
South Africa
-0.1477
-0.016
64,263.4
235.1400
267.4
129,467.4
7,563.g
9.9095
761.6 140.4
0.0461
1.173
31,970.o
12,6%0.4
87.8112
-0.0190
0.807
157,088.6
68,836.O
378.2198
U.K.
0.1808
0.976
%29,X61.6
377,557.%
185.879%
2,025.o
U.S.
0.4020
11.000
300.8148
6,7%5.8
Singapore Switzerland
Emergiq M~rk~fs
_..“““..” .-
?,231,650.0
-l.-.l.“-..~
-..~..--._.--
.~._
~_..__._
0.7525%
0.574
Brazil
0.2567
0.530
30,506.O
Chile
0.3167
0.629
12681.2
Colombia
0.3117
0.230
1,797.6
98.2
1.1603
85.4
Greece
0.3175
0.572
X,694.2
1,534.0
11.4993
125.0 6,059.g
Argenti na
-
$5‘909.2
2,045,760.0
173.6
$1,6%7.2
$9.5309
1%4.6
12,664.O
21.6440
584.4
932.4
4.3374
212.6
India
0.0125
-0.047
30,858.h
16511.8
2.672%
Jordan
0.0050
0.156
2,310.2
449.6
4.3284
103.8
Korea
0.1225
0.434
94,%49.2
77,355.2
130.7220
574.4
Malaysia
0.1250
1.039
37,785.8
6973.6
25.3433
264.8
Mexico
0.4250
1.562
35,121.6
14,20.6
70.7901
200.8
Nigeria
0.1517
0.0605
0.2092
1,238.6 33,410.6
7.2
Pakistan
0.146 0.077
281.6
0.5937
117.2 450.4
Philippines
0.1875
0.907
7,063.4
1,506.2
10.2574
147.4
Portugal
0.230%
0.767
9,092.2
10.5480
171.4
Taiwan
0.345%
0.591
126,247.4
481,162.6
2,573.%480
181.0
Thailand
0.2642
0.973
19,931.0
15333.2
73.926%
186.2 78.8
1,%14.2
Turkey
(I.7542
-0.113
9,181.4
3,0%5.2
27.4685
Venezue la
0.365%
-0.179
5028.2
l,lSh.%
17.8976
72.4
Zimbabwe
0.1842
-0.159
1,269.6
45.2
0.8029
555.4
Factors Affecting Returns
5
lying uncertainty about economic and political conditions within the market’s stock movements.
III.
DESCRIPTIVE
STATISTICS
that is not captured
ON MARKETS
Monthly price data on stock indexes of all countries whose data were consistently available were compiled over the 1987-1991 period from The Wall Street Journal. Stock price information on emerging stock markets was drawn from the Emerging Stock Markets Factbook: 1992. In aggregate, the data base includes 33 countries. Summary statistics of the mean returns and betas for each country are disclosed in Table 1. The model developed by Fama and French used the U.S. market as a basis for empirical tests, so that betas derived in that study were measured from a U.S. investor perspective. Since the foreign country markets are assessed from the perspective of the U.S. investor the U.S. market is also used as the independent variable to derive the betas of the national markets. To the extent that U.S. investors use the U.S. market when deriving betas for individual U.S. securities or portfolios of U.S. securities, they are likely to use a similar approach when deriving the betas from a portfolio of foreign securities. The mean monthly return accounts for exchange rate movements relative to the U.S. dollar since all markets are viewed from a U.S. perspective. The exchange rate data were also drawn from The Wall Street Journal and the Emergitig Stock Markets Factbook: 1992. Each market is treated as a portfolio of securities. Twenty-nine of the 33 betas were significantly different from zero at the .05 level, implying a significant relationship between the foreign market and U.S. market returns. The betas of the South Africa, India, Jordan, and Pakistan markets were not significant. Since the beta of a foreign market reflects the sensitivity of a large portfolio of stocks to the U.S. market it is not necessarily representative of every individual stock in that market. The focus of this research is on a return-risk relationship across markets rather than on the selection of individual foreign stocks. The implications from this cross-market analysis provide important insights into optimal asset allocation decisions for U.S. based investors, and focus on whether the return from foreign market investing is conditioned on systematic risk from the U.S. perspective. The information on market capitalization, number of shares traded, and the proportion of shares traded to the number of firms was drawn from the Emerging Stock Markets F&book: 1992 for all countries.
IV.
METHODOLOGY
For the five-year period extending from 1987 through 1991, the cross-sectional relationship between the market characteristics just described and returns of the foreign market is assessed, using the following model:
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GLOBAL FINANCE JOURNAL
rj = ~0 + ~1 BETAj + ~$n(MCAI’)j + vsln(VALUE)j WsEMERGj + cj
8(l), 1997
+ v,Jn(VALFIRM)j
+ (1)
where:
9 BETAj MCAI’j VALUEi VALFIRMj
EMERGj
ej wo, -.w5
= mean monthly return of the jth market over the 1987-1991 period less exchange rate gains or losses = beta, or systematic risk of the jth market over the 1987-1991 period = mean market capitalization of the jth market over the 1987-1991 period = mean value of shares traded per year in the jth market over the five-year period = mean value of shares traded per year in proportion to the number of firms listed per year for the jth market over the five-year period = 1.0 for markets considered to be emerging, zero otherwise (since emerging markets tend to have a higher level of country risk than other markets, the EMERG variable serves as a proxy for country risk) = error term = parameters.
Ordinary least squares regression analysis is employed to test the model described above. This model is analogous to the cross-sectional model used by Fama and French in that it captures risk and size proxies. However, since the objective of this study is to explain the cross-sectional variation in market returns rather than firm returns, a country risk proxy is also incorporated. The independent variables were averaged over a five-year period that begins one year before the five-year period used to measure returns. This procedure captures the lagged relationship between the variables and returns. Fama and French also use data for variables in the year before the returns they model. In addition to a five-year analysis, the relationship between market-specific variables and mean returns is assessed on an annual basis. Each year from 1987 through 1991, the cross-sectional relationship between the variables described earlier and returns of the market is assessed by applying least squares regression analysis to the following model: rjt = h + hlln(MCAP)j,,_l
+ hzln(VALUE)j,,_l 3LhEMERGj + Uj,t
+ h31n(VALFIRM)i,t_1 + (2)
where: rjJ
MCAPj,,_l VALUEj,,l
= mean monthly return of the jth market in year t = market capitalization of the jth market in the previous year = value of the shares traded for the jth market in the previous year
Factors Ajfecting Returns
VALFIRMj,,_l EMERGj,t
7
= value of the shares traded in proportion to the number listed firms for the jth firm in the previous year = 1.0 for emerging markets, zero otherwise = error term = parameters.
Each country’s systematic risk was not included short time horizon per observation.
V.
of
in this model because of the
RESULTS
Correlation coefficients between the variables used in the two models are displayed in Table 2. The correlation coefficients in the top matrix of Table 2 are based on the five-year model, while the coefficients in the lower matrix are based on the annual model. The VALUE and VALFIRh4 variables are highly correlated, which suggests that markets with a relatively large value of outstanding shares traded per year also have a relatively large value of shares traded per year when adjusted for the number of firms. Both variables are highly correlated with market capitalization, which suggests that the larger markets (in terms of capitalization) experience the most trading. All three variables exhibit a negative correlation with mean returns across markets. The correlation coefficients between variables are somewhat similar for the five-year and one-year time horizons. Given the high correlations among independent variables, multicollinearity may present a serious bias in the tests of statistical significance on regression coefficients. For this reason, the model was revised by systematically removing one of the correlated independent variables. Models excluding combinations of correlated variables were also applied; these results are not shown, as the significance status of each variable remaining in the model was unaffected.
Correlation
Table 2 Coefficients for Variables in Model Five-Year Period
r Y
Beta ln(MCAP) ln(VALUE) ln(VALFIR M)
BETA
/n(MCAPj
h(VALUE)
ln(VALFIR M)
1.00 .95 .82
1.00 .92
1.00
1.00
-.09
1.00
-.28
.48
-.15 -.19
.55 .50
One-Year Period Y
In(M;AI’) ln(VALUE) ln(VALFIRM)
-.55 1.00 -.52 -.49
ln(MCAP)
ln(VALUE)
ln(VALFIRM)
1.00 .90 .79
1.00 .92
1.00
Notes:
‘S@ificant 2Significant
.33000
-.32437 .02130 .04650 -.02381 -.02791
at the 45 level. at the .lO level.
Number of cases
EMERG R2 Adj. R2 F-Value
BETA ln(MCAP) ln(VALSHARE) ln(VALNUM)
Constant
Coefficient
33
.3250 .2000 2.60
Model 1
2.73l
-.71 .23 .58 .52 -.41
t-value -
.27978
-.08920 .02681 .00893 .00815
Coefficient
33
.3164 .2188 3.242
3.34l
.24 .27
-.42 .30
t-value
.30815
p.26609 .03462 .02346 .00148
Coefficient
33
.3182 ,220s 3.272
2.76l
-.61 .40 .36 .04
t-value
Period
Model 3
Table 3 Analysis Over the 1987-1991
Model 2
Results of Cross-Sectional
.30515
p.21305 .02570 .01767 .00862 -
Coefficient
33
.3209 .2238 3.312
Model 4
3.02l
-.59 .28 .51 .33 -
t-value
Note:
The Goldfeld-Quandt confidence level.
Number of cases
F-Value
ln(MCAP) ln(VALSHARE) ln(VALNUM) EMERG R2 Adj. R2
Constant
161
test and White’s test for heteroskedasticity
were applied
to the data series/ Neither
-.41 .09 -1.22 .0094 -.0096 .50
-.04032 .01046 -.35196
-.47 -.Ol 0.00 -1.30 .0108
-.05679 -.00107 .00041 -.40483
161
1.21144 -.05743 -.00036 -.40472
1.32
.91267
1.29
1.21199
-.0146 .43
Coefficient
t-value
Coefficient
t-value
CoefjCicierzt
Model 2
test showed
161
,010s -.OOSl .57
evidence
1.30 -.63 -0.00 -1.31
t-value
Period
Model 3
Analysis Over the 1987-1991
Model 2
Results of Cross-Sectional
Table 4
of heteroskedasticity
161 even at the 10%
-1.31 .OlOS -.OOSl .57 -.40481
t-value 1.37 -.48 -.Ol
Model 4 1.21097 -.05686 .0007
Coefficient
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GLOBAL FINANCE JOURNAL
8(l), 1997
Results of the cross-sectional analysis over the 1987-1991 period are disclosed in Table 3. The results are shown for four different models. The first model includes all independent variables, while each of the remaining models excludes one of the correlated independent variables. The general results for each variable are somewhat similar, regardless of the model used. The betas and mean returns across markets are positively related, as hypothesized. However, the relationship is not statistically significant. The next three independent variables reflect a “size effect,” since mean returns may be larger for markets that are not as capitalized or are characterized as having thin trading. These variables are not significant in any model, which suggests no evidence of a “size effect” across global stock markets. The EMERG variable distinguishes between markets that are emerging (set equal to one) versus those that are well developed (set equal to zero). This variable was positive and highly significant in all models, implying that the mean return for emerging markets is significantly above that of the well developed markets after controlling for other market-specific characteristics. The higher returns for emerging markets do not appear to be due to differences in beta, market capitalization, or trading volume since these variables were not found to be significant. Results of the cross-sectional analysis using annual observations are disclosed in Table 4. The mean monthly returns per year per country are regressed against the annual values of the independent variables. Given 33 countries and five years per country, there are 165 observations. Since there are missing data on 4 observations, 161 observations are used. Table 4 reports results for four models, each of which excludes one of the independent variables. None of these models are significant in explaining cross-sectional variation in the returns across countries. It appears from these results that either the cross-sectional variation in market returns cannot be explained or that an annual period is insufficient to capture any relationships. The results suggest no significant relationship between the market capitalization or market trading volume variables and mean returns across markets. Furthermore, the EMERG variable is not significant in this model. Thus, the disparate annual returns across markets is not attributed to some markets’ being more developed than others. While the EMERG dummy variable distinguishes between the emerging and well developed markets, it does not distinguish among emerging markets or among well developed markets. An alternative measurement of each country’s status is its perceived degree of country risk by country risk analysts. Therefore, the EMERG variable is replaced with RISK, which represents the country risk rating in each year for each country (as quoted in Instittltional Investor) based on a survey of country risk analysts. Results from applying this revised model are disclosed in Table 5. When applied to the five-year period, the country risk rating was negative and significant, implying that mean returns are higher for countries with a lower country risk rating (i.e., a higher level of country risk.) Thus, it appears that country risk can be a relevant factor in the global market return generating process.
11
Factors Ajjfecting Returns
Table 5 Results of Cross-Sectional Analysis Incorporating the Country Risk Rating Variable Five-Year Period Coeficient
Constant BETA ln(MCAP) ln(VALSHARE) ln(VALNUM) RISK
.52146
1.90
-.04758 .01036 .04747 -.00551
-.73 .22 .45 -2.08’
X2
26
Adj. X2 F-Value
.12
Number of cases N&s:
VI.
Annual Observations
t-value
Coefficient 44603
t-value
.02606 -.02604 -.01891
.27 -.23 -.14 -.lO .92
.67
-.01221
.00730 ,013 -.02
1.87
.22
33
161
The Goldfeld-Quandt test and White’s test for heteroskedasticity were applied to the data series. Neither test showed evidence of heteroskedasticity even at the 10% confidence level. ‘Significant at the .05 level.
COMPLEMENTARY
ANALYSIS
OVER A LONGER TIME PERIOD
Since the results previously obtained may be time dependent the tests are repeated using weekly market indexes for 11 countries over the 1976-1989 time period. Data were collected from the Federal Reserve’s Macro Data Tape to compare the effects observed in the more recent time period to the longer time horizon of returns. Data for smaller markets were not available for these earlier periods, since many of the emerging markets had no active participation in the early part of the period. For the 1976-1989 period, 9 of 11 stock markets had betas which were significantly different from zero. The Canadian and German markets exhibited insignificant betas over this period. When replicating the cross-sectional model derived from Fama and French (1992), beta is again shown not to be a significant determinant of returns, but country risk rating is. To isolate the possible impact of the 1987 stock market crash the tests are repeated adding a dummy variable with a value of 1 in 1987 and zero in other years. The coefficient on this variable is insignificant, indicating there was no impact from the U.S. market crash. Given the longer time period used for these complementary tests, it is possible that the regression coefficients are intertemporally unstable, and may be conditioned on time. Therefore the data were tested to determine whether aggregation across time periods was obscuring the effects of the relationships among variables. A random effects model was used incorporating BETA and RISK as the independent variables to allow for the tendency of the error term to be higher for some countries than others and higher for some time periods than others. This model requires a two-stage process. In the first step OLS is used to estimate
12
GLOBAL FINANCE JOURNAL
rjt = ~0 + WlBETAj, + v~RISK~, + ejt
8(l), 1997
(3)
where: = annual return of the jth market over the tth period less exchange rate gains or losses BETAj, = beta, or systematic risk of the jth market over the tth year RISKj, = the risk rating for country j in year t = error term ejt wo, ...w2 = parameters. rjt
The residuals from this regression are saved and decomposed into a time effect, an individual (country) effect, and a random effect. The decomposition is
where:
5
I4 rljt
=individual (country) effect, = time effect =purely random effect
The model is reestimated using generalized least squares using the structure imposed by the error decomposition. Table 6 shows the result of this test. As before beta does not contribute to market returns, but country risk is a significant explanatory variable. Since this model allows for error variance to change over time, the general results remain even after accounting for the existence of heteroscedasticity. VII.
SUMMARY
This analysis addresses whether the returns (from a U.S. perspective) across stock markets are related to the market’s beta (sensitivity of returns to U.S. market returns), the market’s capitalization, the annual value of shares traded in that market, the mean value of shares traded per firm, and the market’s country risk. The results suggest that over the five-year period, the most relevant variable for explaining disparate returns across markets is country risk. The risk-return relationship specified for individual stocks by the capital asset pricing model does not seem to apply to entire markets. That is, the higher returns of some markets are not significantly related to the systematic risk of these markets. The riskreturn relationship may depend on the definition of risk; for this analysis the sensitivity of foreign market returns to the home investor’s market was used. It should also be mentioned that these empirical results are ex post, while the riskreturn relationship specified by the CAPM is ex ante. The three variables that serve as proxies for the market’s size effect were not significantly related to mean returns across markets. Thus even though other
13
Factors Aflecfing Returns
Table 6 Long-Term Analysis Thirteen-Year
Constant Beta
Coefiicienf 0.01109 -0.00034 -0.00010
t-value
2.56951’ XI.26984 -1.98798l .06 .04 2.21
R2 Rating Adj. R2 F-value Number of Cases Note:
Period
143
‘Significant at the .05 level
studies have documented a significant inverse relation between size and returns within a market, there does not appear to be any empirical support for a size effect in explaining disparate mean returns across markets. The methodology used for this analysis could be applied to assess how factors affect market returns when viewed from another country perspective. The monthly returns would need to be translated into the home currency of investors in the country perspective of concern. The market betas would be derived using the home market of the investors as the independent variable. It is possible that the risk-return relationship specified by the CAPM and/or the size effect may be empirically supported when the markets are assessed from a different country perspective. This topic deserves consideration in future research.
REFERENCES Aggarwal, R., Rao, RI’., & Hiraki, T. (1990). Regularities in Tokyo exchange security returns: P/E, size, and seasonal influences. Journal of Financial Research, 13, 249-263. Banz, R.W. (1981). The relationship between return and market value of common stocks. Journal of Financial Economics, 9, 3-18. Basu, S. (1983). The relationship between earnings, market value, and return for NYSE common stocks: Further evidence. Journal of Financial Economics, 12, 129-156. Black, F., Jensen, M.C., & Scholes, M. (1972). The capital asset pricing model: Some empirical tests. in M. Jensen, (Ed.), Studies in the theory of capital markets. Praeger. Chan, K.C. & Chen, N.F. (1991). Structural and return characteristics of small and large firms. Journal of Finance, 46, 1467-1484. Chan, L., Chan, K.C., Hamao, Y., & Lakonishok, J. (1991). Fundamentals and stock returns in Japan. Journal of Finance, 46, 1739-1764. Fama, E.F. & French, K.R. (1992). The cross-section of expected stock returns. Journal of Finance, 47, 427-465.
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GLOBAL FINANCE JOURNAL
S(l), 1997
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