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Risk, return, and equilibrium in the emerging markets: Evidence from the Korean stock market
J ECOBUSN
353
1991; 43:353-362
Risk, Return, and Equilibrium in the Emerging Markets: Evidence from the Korean Stock Market Hee-Kyung K. Bark
This study examines, with the methodology of Fama and MacBeth (Journal of Political Economy 71: 607-636, 1973), whether the capital asset pricing model (CAPM) is applicable to the Korean stock market, which is small and relatively underdeveloped in comparison with the U.S. and other advanced nation stock markets. Our empirical findings indicate that the Sharpe-Lintner-Mossin CAPM paradigm is not adequate in the Korean stock market. First, the critical condition of the CAPM, a positive trade-off between market risk and return, is rejected. Second, we find that residual risk played an important role in pricing risky assets. The inadequacy of the CAPM in the Korean stock market may be attributed to market inefficiency and the highly undiversified portfolios held by the Korean investors.
I. Introduction The Korean stock market has emerged as one of the fastest-growing capital markets in the world. The major driving forces behind this growth have been the excellent performance of the Korean economy and the expected internationalization of the Korean securities market. Recently, foreign interest in the Korean stock market has greatly increased, with the Korean government's disclosure of its plan to liberalize the Korean stock market starting January 1, 1992. The process of internationalization holds many implications for both Korean and international investors. Hence, this study attempts to empirically investigate the risk-return relationship for assets in the Korean stock market. In modem portfolio theory, the mean variance capital asset pricing model (CAPM) has become the major analytic tool for explaining the relationship between the expected return and risk. The main implication of the CAPM is that expected return should be linearly related to an asset's covariance with the return on the market portfolio (i.e., beta risk). The principle of risk compensation that higher beta risk is associated with
Address reprint requests to Hee-Kyung K. Bark, c/o Dr. Tae-ho Bark, Korea International for International Economic Policy, IN3 Box 1906, Young-Dong, Seoul 135-169, Korea.
Journal of Economicsand Business © 1991 Temple University
0148-6195/91/$03.50
3.54
H.-K. K. Bark higher return has been established empirically. 1 The empirical results obtained by Fama and MacBeth (1973) represent the most widely cited and respected evidence supporting the CAPM. The objective of this study is to test empirically how well the market equilibrium model of the CAPM, which was developed in the United States and other advanced nations, can explain the pricing of assets in the emerging Korean stock market, which is not yet fully developed. The risk-return structure of Korean stocks is analyzed by testing the CAPM with Fama and MacBeth's two-stage approach, a combination of both time-series and cross-section estimation. Hence, this study attempts to determine whether the CAPM is applicable to the Korean Stock Exchange (KSE), to assess the extent of diversification of Korean investors' portfolios, and to suggest portfolio management strategies that utilize controlled risk exposure and efficient diversification. The remainder of this article is organized as follows. Section 2 describes the data, and Section 3 discusses the methodology. Section 4 presents the empirical results. Finally, Section 5 offers a summary and concluding remarks.
II. D a t a The data used in this study are the monthly returns for all common stocks traded on the Korean Stock Exchange except stocks in the banking and finance industry. The data were obtained from the Daewoo-Yonsei database. 2 The monthly returns include dividends and capital gains, with appropriate adjustments for capital changes such as stock splits and dividends. The return for month t is calculated as follows:
D. + (p. - p._, ) R. =
,
(I)
Pit- 1 where Dit --- dividend per share paid from the end of month t - 1 to the end of month t; Pit- l = price per share at the end of month t - 1, and Pit = market value at the end of month t of one share purchased at the end of month t - 1. This study covers the time period from January 1980 to December 1987. The eight years were divided into five overlapping intervals of four years each. The first interval is January 1980 to December 1983, the second January 1981 to December 1984, the third January 1982 to December 1985, the fourtli January 1983 to December 1986, and the last period January 1984 to December 1987. For each interval, firms on the Korean Stock Exchange were ranked according to market value at the end of the third year. The market value of the firm was obtained by multiplying the number of shares of the firm's common stock by the closing price per share at the end of the third year. The data for number of shares outstanding and the closing price were available in the daily returns file of the Korea Securities Computer Corporation. 3 Twenty portfolios were then
1For more details, see Black, Jensen, and Scholes (1972), and Fama and MacBeth (1973). 2 In Korea, large securities companiesusually have their own research database. Among these databases, the Daewoo-Yonsei database is the most reliable and accurate, as it is jointly provided by the Daewoo Securities Company, the biggest domestic securities company with the largest capital stock, and Yonsei University, one of the most prestigious universities in Korea. 3 The Korea Sccurities Computer Corporation (KOSCOM) is a subsidiary firm of the Korea Stock Exchange (KSE). KOSCOM provides automatic computing services to securities institutions, securities companies, and other corporations. It is responsiblefor the automaticquotation systemof the stock exchange and for the developmentof the securities mechanizationproject.
Risk and Return in Emerging Markets
355
formed on the basis of ranked value with equal weight of individual securities. These portfolios were arranged in order of increasing firm size, each containing roughly the same number of securities. That is, portfolio 1 contains the smallest firms, and portfolio 20 contains the largest firms. We then conducted our testing in the fourth year of the interval. Thus, we have five nonoverlapping years of testing from 1983 to 1987.
III. Methodology
After ranking the portfolios according to firm size, the Farna-MacBeth (1973) method was used to test the capital asset of pricing model in the Korean Stock Market. 4 The procedure is as follows.
Step 1: A time series regression is run for each stock to estimate the beta over the previous three years. The first-pass regression equation is (2)
Rit = ~o -t- ~igmt "-I-eit,
where Rit and Rmt are the rates of return on stock i and the market portfolio M in month t. Using the beta and residual standard deviation obtained in Equation (2) for each stock, we calculate the beta and residual standard deviation for each portfolio as: 1 N
~p = -~r E 13i, zv i=l
1 N
S(ep) =
E S(ei). -N i=l
Here, two market returns are computed. One assumes an equally weighted market portfolio, its monthly return being the equally weighted average of rates of return on all available stocks in the sample for that month. The other assumes a value-weighted portfolio using as weights the market values of each stock at the end of the preceding year.
Step 2: Cross-sectional regressions, using the returns from the 20 portfolios, are performed on the obtained estimates, /~p, B~, and S(ep), month by month for the fourth year of the interval. Here, the term /3p 2 is used to investigate the linearity of the risk--return relationship. 5 The second-pass regression equation is ^
^
2
Rpt = rot + rlt~pt-i + r2t~pt-i + r3tS(ept-1) + Ilpt,
(3)
where
Rpt = return on portfolio p in month t, /~m- ~ = average of the estimated beta coefficients of the stocks in portfolio p as of the beginning of the month for which the return is calculated, 4 See Fama and MacBeth, (1973: 614-618) 5 Tinic and West (1986) found that the relationship between stock returns and systematic risk contains important nonlinearitiesduring 1935-1982. Thesenonlinearitiescannotbe ascribedto previouslydocumented anomalies related to firm size or January seasonality.
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H.-K. K. Bark
32pt- 1 = average of the squared values of the beta coefficients of the securities in portfolio p as of the beginning of month t, S(ept-1) = average of the estimated unsystematic risks of the securities in portfolio p as of the beginning of month t, u~,t = a random error term, and rot, f~t r2t, and r3t --" regression coefficients in month t. 2 1, and S(ept_ 1), Here, the subscript t - 1 on the explanatory variables, 13pt_l, Butis to indicate that they are computed from a period prior to the month of the returns (Rpt). Hence, we examine the relationships between returns for month t and estimates of risk measures that were available at the beginning of the month in computing the least squares of the rjt in Equation (3). Also, in order to see which factor, 3v or S(ep), has more explanatory power in versions of Equation (3), two modified cross-sectional regression equations are run as follows:
Apt = rot + rltBpt-i + ~lpt, and
(3A)
Apt = rot + rlt~pt-i + r3tS(ept-1) + ~lpt.
(3B)
Step 3: Step 1 and Step 2 are repeated for each interval. The above procedure produces a time series of estimates associated with each of the r coefficients. Since the coefficients may vary form one month to another, the mean of estimated coefficients is calculated as N ~rjt ~ j = t=l
( j = 0, 1,2,3)
N where N is the number of months in the testing period from January 1983 to December 1987. The t statistics for testing the hypothesis ?j = 0 is as follows: =
In this study, testable hypotheses regarding the CAMP are as follows: HI: Beta should be the only factor that explains the rate of return on a risky asset. Hence, residual risk does not affect return (i.e., E(r3t ) = 0). 1-12: The relationship between the expected return and risk is linear. That is, there are no nonlinearities in security market line (i.e., E(~2t ) = 0). H3: There is a positive price of risk in the capital market. In other words, there is a positive relationship between return and risk (i.e., E(~lt) > 0).
IV. Empirical Results Using the computed value-weighted market index, Table 1 provides summary descriptions, including beta coefficients, explanatory powers of the market model (R2), average monthly returns, and standard deviations on the 20 portfolios for the entire sampling period from January 1980 to December 1987. First, Table 1 shows that the sensitivity of portfolio returns to the value-weighted market index (beta) declines with
357
Risk and Return in Emerging Markets Table 1. Sensitivity and Explanatory Power for the Market Model Entire Period (January 1980-December 1987) Portfolio
Beta
Average
SD
number
coefficient
R2
return [ Rp]
[o (R p)]
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
0.8757 0.8355 0.7551 0.8737 0.8333 1.0567 0.7778 0.7399 0.7681 0.8109 0.8892 0.8004 0.9041 0.8918 0.8831 0.9454 0.9715 0.9017 1.1105 1.1915
0.3334 0.4696 0.4198 0.4966 0.5820 0.6740 0.4838 0.4577 0.5128 0.6048 0.6367 0.5857 0.6884 0.7450 0.7397 0.8130 0.8263 0.7613 0.8365 0.8572
0.036120 0.032093 0.031284 0.024355 0.025332 0.025098 0.025202 0.026965 0.023688 0.022995 0.017262 0.025748 0.022839 0.022653 0.019915 0.021140 0.020972 0.018586 0.010685 0.017550
0.0995022 0.079804 0.076465 0.081344 0.071669 0.084450 0.073370 0.071759 0.070369 0.068410 0.073114 0.068618 0,071492 0.067788 0.067371 0.068792 0.070120 0.067803 0.079666 0.084432
Note: Estimated with monthly data and based on the value-weighted market index.
size, contrary to expectations, since beta is usually considered a measure of risk. For U.S. data, the beta coefficient increases as size decreases. Thus, smaller finns are viewed as having greater risk. For Korean data, the reverse is true, smaller firms having much lower betas than the larger finns. Second, Table 1 shows that return is negatively related to size. The difference between the return on the smallest and largest finns is 1.857 percent per month. The smaller beta as size decreases, along with an increase in average return, means that smaller finns provide a higher return as well as a lower beta. Thus, this evidence suggests that beta is not a sufficient measure for risk in the Korean stock market. For direct testing of the CAPM, three different versions of the cross-sectional regression Equation (3) were run on the 20 portfolios. The results are presented for three different versions of the risk-return regression Equation 3: whereas in Tables 2 and 3, one or more of the variables in Equation (3) is suppressed, Table 4 is based on Equation (3) itself. The results are reported for six periods: the overall period 1983-1987 and five one-year testing periods, which were generated from five overlapping intervals. For each period and model, the tables show _ri, the average of the month-by-month regression coefficient estimates, rjt; and ~2, the average of the month-by-month coefficients of determination. The t statistics for testing the hypothesis that ?j = 0 are presented in parentheses. Finally, the results are presented for two computed market indexes: the equally weighted market index (EWI) and the valueweighted market index (VWI). The empirical results are as follows. First, the average coefficient for systematic risk, 71, is negative in a consistent manner for all models and both market indexes. Specifically, the rl in Tables 2 and 3
H . - K . K. B a r k
358
Table 2. Average V a l u e s o f Estimated Coefficients o f the Cross-sectional Regression
gpt = rot + rlt~pt-I ~" ~pt Market index VWI
(3A)
Period
N
ro
rl
~2
Total period (1983-1987)
60
0.04524 a (3.275)
- 0.02025 ( - 1.665)
0.204
1st interval
12
0.05009 a (2.945)
-0.04536 a ( - 2.472)
12
0.02496 (0.935)
- 0.00860 (-.311)
3rd interval (1985)
12
0.02009 (1.020)
- 0.00909 (-0.426)
4th interval
12
0.02831 (1.668)
0.01205 (0.471)
12
0.10276 (1.871)
- 0.05023 ( - 1.296)
60
0.04652 a (4.136) 0.05648 ° (3.071) 0.02948 (0.998) 0.04319 a (3.852) 0.03527 b (2.022) 0.06816 (1.672)
- 0.01719 b ( - 1.676) - 0.04320 a ( - 2.336) - 0.01049 (-0.399) - 0.03154 a ( - 3.368) 0.00111 (0.059) - 0.00181 ( - 0.052)
0.313 (1983)
0.182
2rid interval (1984)
0.143
0.240 0986)
0.142
5th interval (1987) EWI
Total period (1983-1987) 1st interval (1983) 2nd interval (1984) 3rd interval (1985) 4th interval (1986) 5th interval (1987)
12 12 12 12 12
0.143 0.284 0.149 0.049 0.076 0.156
Note: T-statistics are presented in parentheses. a Significant at the 0.05 level. b Significant at the 0.10 level.
are significantly negative at the I0 percent level based on the equally weighted market index, and ~1 in table 4 is significantly negative at the 5 percent level based on the value-weighted market index. This finding, the negative sign of the estimated market premium, is contrary to our prior belief about the CAPM, because the critical condition of the CAPM is that there is, on average, a positive trade-off between market risk and return. 6 The negative sign of the estimated market premium, which implies that firms with higher market beta would have lower expected returns, suggests that beta risk is not a valid measure of risk in the Korean stock market. Hence, the results of this test seem to coincide with the summary descriptions in Table 1.
6 With the same cross-sectional regression equation as the above Equation 3A, the negative sign of the estimated market risk premium, r I = - 0 . 0 0 6 8 9 , was also empirically found in the Spanish stock market. For more details, see Palacios, (1975:114-149).
359
Risk and Return in Emerging Markets Table 3. Average Values of Estimated Coefficients of the Cross-sectional Regression
Apt
= rot -I-
Market index VWI
EWI
rlt~pt-i
q- r3tS(ept-l)
"~" ~lpt (3B)
Period
N
?0
?l
?3
~2
Total period (1983-1987) 1st interval (1983) 2nd interval (1984) 3rd interval (1985) 4th interval (1986) 5th interval (1987)
60
0.01764 (1.174) 0.02295 (0.785) 0.07741 (1.797) -0.02640 (-0.769) - 0.01611 ( - 0.684) 0.03038 (0.965)
-0.01882 ( - 1.632) -0.05158 ~ ( - 2.810) -0.01423 (-0.479) -0.00891 (-0.427) 0.01640 (0.645) -0.03578 ( - 1.123)
0.25992 a (1.705) 0.31951 (1.328) -0.49433 a (- 1.997) -0.48134 (1.238) 0.42737 (1.408) 0.56573 (1.286)
0.343
Total period (1983-1987) 1st interval (1983) 2nd interval (1984) 3rd interval (1985) 4th interval (1986) 5th interval (1987)
60
0.2781 a (1.909) 0.03761 (1.283) 0.08053 (1.706) -0.00277 ( - 0.081) -0.00587 ( - 0.266) 0.02952 (1.328)
- 0.02003 a ( - 1.823) - 0.05209 b ( - 2.909) - 0.01308 (-0.475) -0.03602 b ( - 3.443) -0.00430 ( - 0.179) 0.00532 (0.149)
0.22224 (1.438) 0.27666 (1.102) - 0.50099 a ( - 1.895) 0.53077 (1.496) 0.48888 (1.481) 0.31591 (0.691)
0.276
12 12 12 12 12
12 12 12 12 12
0.419 0.284 0.327 0.382 0.303
0.390 0.257 0.218 0.236 0.280
Note: T-statistics are presented in parentheses. a Significant at the 0.10 level. b Significant at the 0.05 level.
Second, in Table 3, the average of the monthly estimated coefficients for residual risk, ~3, is statistically significant and positive at the 10 percent level using the value-weighted market index. Also, when the variable of residual risk, S(ept_ ~), is included in Equations (3B), the average of the monthly coefficients of determination, ~2, increases considerably compared with that in Equation (3A). According to the CAPM, since investors hold the efficient market portfolio and diversify in many assets, residual risk (i.e., nonsystematic risk) should have no impact on the risk-return relationship. Therefore, the findings contradict the CAPM and suggest that residual risk plays an important role in price determination and that investors may hold undiversified portfolios. Interestingly, the empirical result that residual risk is significantly priced may corroborate actually observed Korean investor behavior that investors hold a small number of stocks in their portfolios. Third, in Table 4, neither the data for the overall period nor those for any of the one-year testing periods show a statistically significant nonlinear relationship between returns and systematic risk. In sum, our empirical results indicate that the CAPM doesn't hold true in the Korean stock market for the entire period under study. One would expect the CAPM to yield poor empirical results with Korean data,
H.-K. K. Bark
360
Table 4. Average Values of Estimated Coefficients of the Cross-sectional Regression ^ ~ 2 R p t = rot + rli[~pt-I "~" 2tf~pt-I -[" r3tS(ept-I ) q- ~ipt (3) Market index VWI
EWI
Period
N
Total period (1983-1987) 1st interval (1983) 2nd interval (1984) 3rd interval (1985) 4th interval (1986) 5th interval (1987)
60
Total period (1983-1987) 1st interval (1983) 2nd interval (1984) 3rd interval (1985) 4th interval (1986) 5th interval (1987)
60
12 12 12 12 12
12 12 12 12 12
ro
rl
r2
r3
~2
0.03781 a -0.05381 b (1.996) (-2.049) 0 . 0 1 9 1 7 -0.04450 (0.691) ( - 1.149) 0 . 1 0 1 4 9 -0.04889 (1.584) (-0.701) 0 . 0 0 1 5 1 -0.05950 (0.035) ( - 1.725) - 0.01225 0.00325 ( - 0.747) (0.068) 0.07916 a - 0.19942 (1.895) ( - 1.338)
0.02008 0 . 1 6 5 4 6 0.385 (1.609) (1.041) -0.00303 0 . 3 2 8 1 6 0.457 (-0.164) (1.531) 0.02405 -0.63819 0.316 (0.707) ( - 1.749) 0.02976 0 . 3 0 8 2 2 0.387 (1.519) (0.693) 0.01020 0 . 3 9 9 5 6 0.418 (0.488) (1.458) 0.04309 0 . 4 2 9 5 7 0.347 (0.947) (1.108)
0.03243 - 0.03007 (1.529) ( - 1.171) 0 . 0 4 7 7 3 -0.06569 (1.486) ( - 1.652) 0.06356 0.01305 (0.906) (0.201) 0 . 0 2 0 1 2 -0.07126 b (0.671) (-2.89) -0.03866 0.02347 (-0.916) (0.3671) 0.06946 - 0.04993 (1.329) (-0.631)
0.00630 0 . 1 9 9 4 8 0.335 (0.622) (1.288) 0.00904 0 . 1 8 3 6 8 0.431 (0.542) (0.792) -0.01303 -0.41356 0.314 ( - 0.591) ( - 1.088) 0.02012 0 . 3 7 4 5 2 0.271 (1.396) (1.221) -0.01440 0.75908 ° 0.328 (-0.603) (2.127) 0.02980 0 . 0 9 3 6 7 0.329 (0.909) (0.237)
Note: T-statisticsare presented in parentheses.
*Significantat the 0.10 level. b Significantat the 0.05 level.
because the Korean stock market is small and relatively underdeveloped in comparison with the security markets in the United States. The empirical results of this test support this prior expectation. The main reasons why the CAPM paradigm is inadequate for the Korean stock market can be suggested as follows: First, the Korean stock market is inefficient because of information barriers and other prevailing inadequacies in the infrastructure. The market equilibrium models, such as the C A P M , are primarily based on the assumption of market efficiency; hence, the model may not be appropriate if the assets are inefficiently priced. Mainly, the inefficiency in the Korean stock market is due to the maximum upper and lower limits allowed in daily price movements and transactions by large shareholders. The daily price limits, which may suppress the daily movements of individual stock prices, can engender truncated returns and delay the effects of new information on individual stock prices. 7 Also, the influence of large shareholders, who reputedly trade on monopolistic
7 In the advancedstock markets, for example, the U.S. and U.K. stock markets, there are no daily price change limits. Although daily price change limits exist in the Japanese stock market, they do not actually affect the daily stock price movementsand bring about market inefficiencybecause the maximumupper and lower limits are about three times as large as those in the Korean stock market.
Risk and Return in Emerging Markets
361
information with a large capital base, is considered to be a major impediment to market efficiency. Second, the most typical investors in the Korean stock market hold highly undiversifled portfolios with a small number of stocks. Individual investors constitute the largest holding group in the stock market, and institutional investors are fairly underdeveloped relative to the U.S. market. Therefore, one of the basic assumptions of the CAPM, that investors hold large diversified portfolios, is not applicable to the Korean stock market. This phenomenon is supported by the empirical finding that the risk premium associated with residual risk (unsystematic risk) is statistically significant and positive. In short, our empirical results seem to suggest that the main implications of the CAPM are not supported in the Korean stock market.
V. Summary and Concluding Remarks This study empirically examines the CAPM in the Korean stock market, which is thin and relatively underdeveloped in comparison with the U.S. and other advanced nation stock markets. Our empirical findings indicate that the Sharpe-Lintuer-Mossin CAPM paradigm is not adequate in the Korean stock market. First, the critical condition of the CAPM--a positive trade-off between market risk and return--is rejected. For the entire period of the study, an unexpected negative sign in the estimated market premium is observed. Second, residual risk plays an important role in pricing risky assets. This discovery forces us to discredit the CAPM as a predictive model in the Korean context. The inadequacy of the CAPM in the Korean stock market might be attributed to market inefficiency and to the highly undiversified portfolios held by Korean investors. Finally, this study suffers from a short observation period. However, the evidence presented here provides guidance for future research as new data become available. The issues are certainly worth further exploration. In addition, although the study uses monthly data, further research to take into account the statistical bias induced by infrequent trading of small firms would be desirable.
References Banz, R. W. March 1981. The relationship between return and market value of common stocks. Journal of Financial Economics 9:3-18. Black, F., Jensen, M., and Scholes, M. 1972. The capital asset pricing model: Some empirical tests. In Studies in the Theory of Capital Markets (M. Jensen, ed.). New York: Praeger, pp. 79-121. Blume, M., and Friend, I. May 1975. The asset structure of individual portfolios and some implications for utility functions. Journal of Finance 30:585-603. Dimson, E. June 1979. Risk measurement when shares are subject to infrequent trading. Journal of Financial Economics 7:197-216. Elton, E., and Gruber, M. 1987. Modern Portfolio Theory and Investment Analysis (3rd ed.). New York: John Wiley. Elton, E., and Gruber, M. 1990. A multi-index risk model of the Japanese stock market. In Japanese Capital Markets (E. Elton and M. Gruber, eds.). New York: Harper & Row, pp. 127-153. Fama, E. F. May 1970. Efficient capital markets: A review of theory and empirical work. Journal of Finance 25:383-417. Fama, E. F. 1976. Foundation of Finance. New York: Basic Books.
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Fama, E. F., and MacBeth, J. D. May/June 1973. Risk, return, and equilibrium: Empirical tests. Journal o f Political Economy 71:607-636. Gibbons, M. R., and Ferson, W. June 1985. Testing asset pricing models with changing expectations and an unobservable market portfolio. Journal o f Financial Economics 14:271-236. Korea Listed Companies Association 1980-1987. Annual Report o f Listed Companies. Seoul: KLCA. Korea Securities Dealers Association 1988. Securities Market in Korea. Seoul: KSDA. Korea Securities Dealers Association 1980-1987. Securities Market Shinmun (dally securities newspaper). Korea Stock Exchange 1987. Introduction to the Korean Securities Market. Seoul: KSE. Korean Stock Exchange 1980-1987. Stock (monthly magazine). Levy, H. September 1978. Equilibrium in an imperfect market: A constraint on the number of securities in the portfolio. American Economic Review 68:867-882. Levy, H. September 1980. The capital asset pricing model, inflation, and investment horizon: The Israeli experience. Journal of Financial and Quantitative Analysis 15:561-593. Palacios, J. A. 1975. The stock market in Spain: Test of efficiency of market theory. In International CapitalMarkets (E. J. Elton and M. J. Gruber, eds.). Amsterdam: North-Holland. Reinganum, M. March 1981. Misspecification of capital asset pricing: Empirical anomalies based on earnings yields and market values. Journal o f Financial Economics 9:19-46. Roll, R. March 1977. A Critique of the Asset Pricing Theory's Tests. Journal o f Financial Economics 4:129-176. Roll, R. September 1978. Ambiguity when performance is measured by the securities market line. Journal o f Finance 33:1051-1069. Sehwert, G. March 1983. Size and stock returns, and other empirical regularities. Journal o f Financial Economics 12:3-12. Sharpe, W. September 1964. Capital asset prices: A theory of market equilibrium under conditions of risk. Journal o f Finance 19:425-442. Tinic, S. M., and West, R. R. February 1986. Risk, return, and equilibrium: A revisit. Journal o f Political Economy 94:126-147.
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Risk, Return, and Equilibrium in the Emerging Markets: Evidence from the Korean Stock Market Hee-Kyung K. Bark
This study examines, with the methodology of Fama and MacBeth (Journal of Political Economy 71: 607-636, 1973), whether the capital asset pricing model (CAPM) is applicable to the Korean stock market, which is small and relatively underdeveloped in comparison with the U.S. and other advanced nation stock markets. Our empirical findings indicate that the Sharpe-Lintner-Mossin CAPM paradigm is not adequate in the Korean stock market. First, the critical condition of the CAPM, a positive trade-off between market risk and return, is rejected. Second, we find that residual risk played an important role in pricing risky assets. The inadequacy of the CAPM in the Korean stock market may be attributed to market inefficiency and the highly undiversified portfolios held by the Korean investors.
I. Introduction The Korean stock market has emerged as one of the fastest-growing capital markets in the world. The major driving forces behind this growth have been the excellent performance of the Korean economy and the expected internationalization of the Korean securities market. Recently, foreign interest in the Korean stock market has greatly increased, with the Korean government's disclosure of its plan to liberalize the Korean stock market starting January 1, 1992. The process of internationalization holds many implications for both Korean and international investors. Hence, this study attempts to empirically investigate the risk-return relationship for assets in the Korean stock market. In modem portfolio theory, the mean variance capital asset pricing model (CAPM) has become the major analytic tool for explaining the relationship between the expected return and risk. The main implication of the CAPM is that expected return should be linearly related to an asset's covariance with the return on the market portfolio (i.e., beta risk). The principle of risk compensation that higher beta risk is associated with
Address reprint requests to Hee-Kyung K. Bark, c/o Dr. Tae-ho Bark, Korea International for International Economic Policy, IN3 Box 1906, Young-Dong, Seoul 135-169, Korea.
Journal of Economicsand Business © 1991 Temple University
0148-6195/91/$03.50
3.54
H.-K. K. Bark higher return has been established empirically. 1 The empirical results obtained by Fama and MacBeth (1973) represent the most widely cited and respected evidence supporting the CAPM. The objective of this study is to test empirically how well the market equilibrium model of the CAPM, which was developed in the United States and other advanced nations, can explain the pricing of assets in the emerging Korean stock market, which is not yet fully developed. The risk-return structure of Korean stocks is analyzed by testing the CAPM with Fama and MacBeth's two-stage approach, a combination of both time-series and cross-section estimation. Hence, this study attempts to determine whether the CAPM is applicable to the Korean Stock Exchange (KSE), to assess the extent of diversification of Korean investors' portfolios, and to suggest portfolio management strategies that utilize controlled risk exposure and efficient diversification. The remainder of this article is organized as follows. Section 2 describes the data, and Section 3 discusses the methodology. Section 4 presents the empirical results. Finally, Section 5 offers a summary and concluding remarks.
II. D a t a The data used in this study are the monthly returns for all common stocks traded on the Korean Stock Exchange except stocks in the banking and finance industry. The data were obtained from the Daewoo-Yonsei database. 2 The monthly returns include dividends and capital gains, with appropriate adjustments for capital changes such as stock splits and dividends. The return for month t is calculated as follows:
D. + (p. - p._, ) R. =
,
(I)
Pit- 1 where Dit --- dividend per share paid from the end of month t - 1 to the end of month t; Pit- l = price per share at the end of month t - 1, and Pit = market value at the end of month t of one share purchased at the end of month t - 1. This study covers the time period from January 1980 to December 1987. The eight years were divided into five overlapping intervals of four years each. The first interval is January 1980 to December 1983, the second January 1981 to December 1984, the third January 1982 to December 1985, the fourtli January 1983 to December 1986, and the last period January 1984 to December 1987. For each interval, firms on the Korean Stock Exchange were ranked according to market value at the end of the third year. The market value of the firm was obtained by multiplying the number of shares of the firm's common stock by the closing price per share at the end of the third year. The data for number of shares outstanding and the closing price were available in the daily returns file of the Korea Securities Computer Corporation. 3 Twenty portfolios were then
1For more details, see Black, Jensen, and Scholes (1972), and Fama and MacBeth (1973). 2 In Korea, large securities companiesusually have their own research database. Among these databases, the Daewoo-Yonsei database is the most reliable and accurate, as it is jointly provided by the Daewoo Securities Company, the biggest domestic securities company with the largest capital stock, and Yonsei University, one of the most prestigious universities in Korea. 3 The Korea Sccurities Computer Corporation (KOSCOM) is a subsidiary firm of the Korea Stock Exchange (KSE). KOSCOM provides automatic computing services to securities institutions, securities companies, and other corporations. It is responsiblefor the automaticquotation systemof the stock exchange and for the developmentof the securities mechanizationproject.
Risk and Return in Emerging Markets
355
formed on the basis of ranked value with equal weight of individual securities. These portfolios were arranged in order of increasing firm size, each containing roughly the same number of securities. That is, portfolio 1 contains the smallest firms, and portfolio 20 contains the largest firms. We then conducted our testing in the fourth year of the interval. Thus, we have five nonoverlapping years of testing from 1983 to 1987.
III. Methodology
After ranking the portfolios according to firm size, the Farna-MacBeth (1973) method was used to test the capital asset of pricing model in the Korean Stock Market. 4 The procedure is as follows.
Step 1: A time series regression is run for each stock to estimate the beta over the previous three years. The first-pass regression equation is (2)
Rit = ~o -t- ~igmt "-I-eit,
where Rit and Rmt are the rates of return on stock i and the market portfolio M in month t. Using the beta and residual standard deviation obtained in Equation (2) for each stock, we calculate the beta and residual standard deviation for each portfolio as: 1 N
~p = -~r E 13i, zv i=l
1 N
S(ep) =
E S(ei). -N i=l
Here, two market returns are computed. One assumes an equally weighted market portfolio, its monthly return being the equally weighted average of rates of return on all available stocks in the sample for that month. The other assumes a value-weighted portfolio using as weights the market values of each stock at the end of the preceding year.
Step 2: Cross-sectional regressions, using the returns from the 20 portfolios, are performed on the obtained estimates, /~p, B~, and S(ep), month by month for the fourth year of the interval. Here, the term /3p 2 is used to investigate the linearity of the risk--return relationship. 5 The second-pass regression equation is ^
^
2
Rpt = rot + rlt~pt-i + r2t~pt-i + r3tS(ept-1) + Ilpt,
(3)
where
Rpt = return on portfolio p in month t, /~m- ~ = average of the estimated beta coefficients of the stocks in portfolio p as of the beginning of the month for which the return is calculated, 4 See Fama and MacBeth, (1973: 614-618) 5 Tinic and West (1986) found that the relationship between stock returns and systematic risk contains important nonlinearitiesduring 1935-1982. Thesenonlinearitiescannotbe ascribedto previouslydocumented anomalies related to firm size or January seasonality.
356
H.-K. K. Bark
32pt- 1 = average of the squared values of the beta coefficients of the securities in portfolio p as of the beginning of month t, S(ept-1) = average of the estimated unsystematic risks of the securities in portfolio p as of the beginning of month t, u~,t = a random error term, and rot, f~t r2t, and r3t --" regression coefficients in month t. 2 1, and S(ept_ 1), Here, the subscript t - 1 on the explanatory variables, 13pt_l, Butis to indicate that they are computed from a period prior to the month of the returns (Rpt). Hence, we examine the relationships between returns for month t and estimates of risk measures that were available at the beginning of the month in computing the least squares of the rjt in Equation (3). Also, in order to see which factor, 3v or S(ep), has more explanatory power in versions of Equation (3), two modified cross-sectional regression equations are run as follows:
Apt = rot + rltBpt-i + ~lpt, and
(3A)
Apt = rot + rlt~pt-i + r3tS(ept-1) + ~lpt.
(3B)
Step 3: Step 1 and Step 2 are repeated for each interval. The above procedure produces a time series of estimates associated with each of the r coefficients. Since the coefficients may vary form one month to another, the mean of estimated coefficients is calculated as N ~rjt ~ j = t=l
( j = 0, 1,2,3)
N where N is the number of months in the testing period from January 1983 to December 1987. The t statistics for testing the hypothesis ?j = 0 is as follows: =
In this study, testable hypotheses regarding the CAMP are as follows: HI: Beta should be the only factor that explains the rate of return on a risky asset. Hence, residual risk does not affect return (i.e., E(r3t ) = 0). 1-12: The relationship between the expected return and risk is linear. That is, there are no nonlinearities in security market line (i.e., E(~2t ) = 0). H3: There is a positive price of risk in the capital market. In other words, there is a positive relationship between return and risk (i.e., E(~lt) > 0).
IV. Empirical Results Using the computed value-weighted market index, Table 1 provides summary descriptions, including beta coefficients, explanatory powers of the market model (R2), average monthly returns, and standard deviations on the 20 portfolios for the entire sampling period from January 1980 to December 1987. First, Table 1 shows that the sensitivity of portfolio returns to the value-weighted market index (beta) declines with
357
Risk and Return in Emerging Markets Table 1. Sensitivity and Explanatory Power for the Market Model Entire Period (January 1980-December 1987) Portfolio
Beta
Average
SD
number
coefficient
R2
return [ Rp]
[o (R p)]
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
0.8757 0.8355 0.7551 0.8737 0.8333 1.0567 0.7778 0.7399 0.7681 0.8109 0.8892 0.8004 0.9041 0.8918 0.8831 0.9454 0.9715 0.9017 1.1105 1.1915
0.3334 0.4696 0.4198 0.4966 0.5820 0.6740 0.4838 0.4577 0.5128 0.6048 0.6367 0.5857 0.6884 0.7450 0.7397 0.8130 0.8263 0.7613 0.8365 0.8572
0.036120 0.032093 0.031284 0.024355 0.025332 0.025098 0.025202 0.026965 0.023688 0.022995 0.017262 0.025748 0.022839 0.022653 0.019915 0.021140 0.020972 0.018586 0.010685 0.017550
0.0995022 0.079804 0.076465 0.081344 0.071669 0.084450 0.073370 0.071759 0.070369 0.068410 0.073114 0.068618 0,071492 0.067788 0.067371 0.068792 0.070120 0.067803 0.079666 0.084432
Note: Estimated with monthly data and based on the value-weighted market index.
size, contrary to expectations, since beta is usually considered a measure of risk. For U.S. data, the beta coefficient increases as size decreases. Thus, smaller finns are viewed as having greater risk. For Korean data, the reverse is true, smaller firms having much lower betas than the larger finns. Second, Table 1 shows that return is negatively related to size. The difference between the return on the smallest and largest finns is 1.857 percent per month. The smaller beta as size decreases, along with an increase in average return, means that smaller finns provide a higher return as well as a lower beta. Thus, this evidence suggests that beta is not a sufficient measure for risk in the Korean stock market. For direct testing of the CAPM, three different versions of the cross-sectional regression Equation (3) were run on the 20 portfolios. The results are presented for three different versions of the risk-return regression Equation 3: whereas in Tables 2 and 3, one or more of the variables in Equation (3) is suppressed, Table 4 is based on Equation (3) itself. The results are reported for six periods: the overall period 1983-1987 and five one-year testing periods, which were generated from five overlapping intervals. For each period and model, the tables show _ri, the average of the month-by-month regression coefficient estimates, rjt; and ~2, the average of the month-by-month coefficients of determination. The t statistics for testing the hypothesis that ?j = 0 are presented in parentheses. Finally, the results are presented for two computed market indexes: the equally weighted market index (EWI) and the valueweighted market index (VWI). The empirical results are as follows. First, the average coefficient for systematic risk, 71, is negative in a consistent manner for all models and both market indexes. Specifically, the rl in Tables 2 and 3
H . - K . K. B a r k
358
Table 2. Average V a l u e s o f Estimated Coefficients o f the Cross-sectional Regression
gpt = rot + rlt~pt-I ~" ~pt Market index VWI
(3A)
Period
N
ro
rl
~2
Total period (1983-1987)
60
0.04524 a (3.275)
- 0.02025 ( - 1.665)
0.204
1st interval
12
0.05009 a (2.945)
-0.04536 a ( - 2.472)
12
0.02496 (0.935)
- 0.00860 (-.311)
3rd interval (1985)
12
0.02009 (1.020)
- 0.00909 (-0.426)
4th interval
12
0.02831 (1.668)
0.01205 (0.471)
12
0.10276 (1.871)
- 0.05023 ( - 1.296)
60
0.04652 a (4.136) 0.05648 ° (3.071) 0.02948 (0.998) 0.04319 a (3.852) 0.03527 b (2.022) 0.06816 (1.672)
- 0.01719 b ( - 1.676) - 0.04320 a ( - 2.336) - 0.01049 (-0.399) - 0.03154 a ( - 3.368) 0.00111 (0.059) - 0.00181 ( - 0.052)
0.313 (1983)
0.182
2rid interval (1984)
0.143
0.240 0986)
0.142
5th interval (1987) EWI
Total period (1983-1987) 1st interval (1983) 2nd interval (1984) 3rd interval (1985) 4th interval (1986) 5th interval (1987)
12 12 12 12 12
0.143 0.284 0.149 0.049 0.076 0.156
Note: T-statistics are presented in parentheses. a Significant at the 0.05 level. b Significant at the 0.10 level.
are significantly negative at the I0 percent level based on the equally weighted market index, and ~1 in table 4 is significantly negative at the 5 percent level based on the value-weighted market index. This finding, the negative sign of the estimated market premium, is contrary to our prior belief about the CAPM, because the critical condition of the CAPM is that there is, on average, a positive trade-off between market risk and return. 6 The negative sign of the estimated market premium, which implies that firms with higher market beta would have lower expected returns, suggests that beta risk is not a valid measure of risk in the Korean stock market. Hence, the results of this test seem to coincide with the summary descriptions in Table 1.
6 With the same cross-sectional regression equation as the above Equation 3A, the negative sign of the estimated market risk premium, r I = - 0 . 0 0 6 8 9 , was also empirically found in the Spanish stock market. For more details, see Palacios, (1975:114-149).
359
Risk and Return in Emerging Markets Table 3. Average Values of Estimated Coefficients of the Cross-sectional Regression
Apt
= rot -I-
Market index VWI
EWI
rlt~pt-i
q- r3tS(ept-l)
"~" ~lpt (3B)
Period
N
?0
?l
?3
~2
Total period (1983-1987) 1st interval (1983) 2nd interval (1984) 3rd interval (1985) 4th interval (1986) 5th interval (1987)
60
0.01764 (1.174) 0.02295 (0.785) 0.07741 (1.797) -0.02640 (-0.769) - 0.01611 ( - 0.684) 0.03038 (0.965)
-0.01882 ( - 1.632) -0.05158 ~ ( - 2.810) -0.01423 (-0.479) -0.00891 (-0.427) 0.01640 (0.645) -0.03578 ( - 1.123)
0.25992 a (1.705) 0.31951 (1.328) -0.49433 a (- 1.997) -0.48134 (1.238) 0.42737 (1.408) 0.56573 (1.286)
0.343
Total period (1983-1987) 1st interval (1983) 2nd interval (1984) 3rd interval (1985) 4th interval (1986) 5th interval (1987)
60
0.2781 a (1.909) 0.03761 (1.283) 0.08053 (1.706) -0.00277 ( - 0.081) -0.00587 ( - 0.266) 0.02952 (1.328)
- 0.02003 a ( - 1.823) - 0.05209 b ( - 2.909) - 0.01308 (-0.475) -0.03602 b ( - 3.443) -0.00430 ( - 0.179) 0.00532 (0.149)
0.22224 (1.438) 0.27666 (1.102) - 0.50099 a ( - 1.895) 0.53077 (1.496) 0.48888 (1.481) 0.31591 (0.691)
0.276
12 12 12 12 12
12 12 12 12 12
0.419 0.284 0.327 0.382 0.303
0.390 0.257 0.218 0.236 0.280
Note: T-statistics are presented in parentheses. a Significant at the 0.10 level. b Significant at the 0.05 level.
Second, in Table 3, the average of the monthly estimated coefficients for residual risk, ~3, is statistically significant and positive at the 10 percent level using the value-weighted market index. Also, when the variable of residual risk, S(ept_ ~), is included in Equations (3B), the average of the monthly coefficients of determination, ~2, increases considerably compared with that in Equation (3A). According to the CAPM, since investors hold the efficient market portfolio and diversify in many assets, residual risk (i.e., nonsystematic risk) should have no impact on the risk-return relationship. Therefore, the findings contradict the CAPM and suggest that residual risk plays an important role in price determination and that investors may hold undiversified portfolios. Interestingly, the empirical result that residual risk is significantly priced may corroborate actually observed Korean investor behavior that investors hold a small number of stocks in their portfolios. Third, in Table 4, neither the data for the overall period nor those for any of the one-year testing periods show a statistically significant nonlinear relationship between returns and systematic risk. In sum, our empirical results indicate that the CAPM doesn't hold true in the Korean stock market for the entire period under study. One would expect the CAPM to yield poor empirical results with Korean data,
H.-K. K. Bark
360
Table 4. Average Values of Estimated Coefficients of the Cross-sectional Regression ^ ~ 2 R p t = rot + rli[~pt-I "~" 2tf~pt-I -[" r3tS(ept-I ) q- ~ipt (3) Market index VWI
EWI
Period
N
Total period (1983-1987) 1st interval (1983) 2nd interval (1984) 3rd interval (1985) 4th interval (1986) 5th interval (1987)
60
Total period (1983-1987) 1st interval (1983) 2nd interval (1984) 3rd interval (1985) 4th interval (1986) 5th interval (1987)
60
12 12 12 12 12
12 12 12 12 12
ro
rl
r2
r3
~2
0.03781 a -0.05381 b (1.996) (-2.049) 0 . 0 1 9 1 7 -0.04450 (0.691) ( - 1.149) 0 . 1 0 1 4 9 -0.04889 (1.584) (-0.701) 0 . 0 0 1 5 1 -0.05950 (0.035) ( - 1.725) - 0.01225 0.00325 ( - 0.747) (0.068) 0.07916 a - 0.19942 (1.895) ( - 1.338)
0.02008 0 . 1 6 5 4 6 0.385 (1.609) (1.041) -0.00303 0 . 3 2 8 1 6 0.457 (-0.164) (1.531) 0.02405 -0.63819 0.316 (0.707) ( - 1.749) 0.02976 0 . 3 0 8 2 2 0.387 (1.519) (0.693) 0.01020 0 . 3 9 9 5 6 0.418 (0.488) (1.458) 0.04309 0 . 4 2 9 5 7 0.347 (0.947) (1.108)
0.03243 - 0.03007 (1.529) ( - 1.171) 0 . 0 4 7 7 3 -0.06569 (1.486) ( - 1.652) 0.06356 0.01305 (0.906) (0.201) 0 . 0 2 0 1 2 -0.07126 b (0.671) (-2.89) -0.03866 0.02347 (-0.916) (0.3671) 0.06946 - 0.04993 (1.329) (-0.631)
0.00630 0 . 1 9 9 4 8 0.335 (0.622) (1.288) 0.00904 0 . 1 8 3 6 8 0.431 (0.542) (0.792) -0.01303 -0.41356 0.314 ( - 0.591) ( - 1.088) 0.02012 0 . 3 7 4 5 2 0.271 (1.396) (1.221) -0.01440 0.75908 ° 0.328 (-0.603) (2.127) 0.02980 0 . 0 9 3 6 7 0.329 (0.909) (0.237)
Note: T-statisticsare presented in parentheses.
*Significantat the 0.10 level. b Significantat the 0.05 level.
because the Korean stock market is small and relatively underdeveloped in comparison with the security markets in the United States. The empirical results of this test support this prior expectation. The main reasons why the CAPM paradigm is inadequate for the Korean stock market can be suggested as follows: First, the Korean stock market is inefficient because of information barriers and other prevailing inadequacies in the infrastructure. The market equilibrium models, such as the C A P M , are primarily based on the assumption of market efficiency; hence, the model may not be appropriate if the assets are inefficiently priced. Mainly, the inefficiency in the Korean stock market is due to the maximum upper and lower limits allowed in daily price movements and transactions by large shareholders. The daily price limits, which may suppress the daily movements of individual stock prices, can engender truncated returns and delay the effects of new information on individual stock prices. 7 Also, the influence of large shareholders, who reputedly trade on monopolistic
7 In the advancedstock markets, for example, the U.S. and U.K. stock markets, there are no daily price change limits. Although daily price change limits exist in the Japanese stock market, they do not actually affect the daily stock price movementsand bring about market inefficiencybecause the maximumupper and lower limits are about three times as large as those in the Korean stock market.
Risk and Return in Emerging Markets
361
information with a large capital base, is considered to be a major impediment to market efficiency. Second, the most typical investors in the Korean stock market hold highly undiversifled portfolios with a small number of stocks. Individual investors constitute the largest holding group in the stock market, and institutional investors are fairly underdeveloped relative to the U.S. market. Therefore, one of the basic assumptions of the CAPM, that investors hold large diversified portfolios, is not applicable to the Korean stock market. This phenomenon is supported by the empirical finding that the risk premium associated with residual risk (unsystematic risk) is statistically significant and positive. In short, our empirical results seem to suggest that the main implications of the CAPM are not supported in the Korean stock market.
V. Summary and Concluding Remarks This study empirically examines the CAPM in the Korean stock market, which is thin and relatively underdeveloped in comparison with the U.S. and other advanced nation stock markets. Our empirical findings indicate that the Sharpe-Lintuer-Mossin CAPM paradigm is not adequate in the Korean stock market. First, the critical condition of the CAPM--a positive trade-off between market risk and return--is rejected. For the entire period of the study, an unexpected negative sign in the estimated market premium is observed. Second, residual risk plays an important role in pricing risky assets. This discovery forces us to discredit the CAPM as a predictive model in the Korean context. The inadequacy of the CAPM in the Korean stock market might be attributed to market inefficiency and to the highly undiversified portfolios held by Korean investors. Finally, this study suffers from a short observation period. However, the evidence presented here provides guidance for future research as new data become available. The issues are certainly worth further exploration. In addition, although the study uses monthly data, further research to take into account the statistical bias induced by infrequent trading of small firms would be desirable.
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