- Email: [email protected]
Overreaction in the Hong Kong stock market
p95919$$15
02-04-:0 06:47:44
p. 223
Global Finance Journal 10:2 (1999) 223–230
Overreaction in the Hong Kong stock market Alexander Kwok-Wah Fung* Department of Finance and Decision Sciences, Hong Kong Baptist University, Kowloon Tong, Hong Kong, Peoples’ Republic of China
Abstract Overreaction reported in the equity markets of the United States, Spain, and Brazil is also observed in the Hong Kong stock market. The “loser” portfolios of the 33 stocks in the Hang Seng Index (HSI), on average, outperform the “winner” portfolios by 9.9% 1 year after the formation periods. Besides its emphasis on the importance of the Hong Kong market in international investment, this paper is unique in some special features related to the overreaction study. Hong Kong has markets for index futures and stock futures. Only three stocks are used in the portfolios. All the stocks in the HSI have large market capitalization and liquidity and can be shorted with no up-tick rule. Unlike other studies in international stock markets, the “arbitrage” portfolio of buying the loser portfolio and shorting the winner portfolio can actually be formed with minimum cost and easy execution, which makes the overreaction phenomena in this study very powerful. 2000 Elsevier Science Inc. All rights reserved. JEL classification: G14; G15 Keywords: Overreaction; Market efficiency; Hong Kong stock market
International investment has drawn a great deal of attention among academic researchers and practitioners in finance. Investors in the United States are increasing their allocations of investments to overseas markets to seek higher returns as well as diversification. Since 1990, there has been growing interest in the Hong Kong market owing to the potential market in China. As a result, many multinational investment firms are increasing their presence in Hong Kong. Hence, it is important to look at investors’ behavior in Hong Kong. It is interesting to see whether some findings about the U.S. market also hold in
* Corresponding author. Tel.: 852-23395225; Fax: 852-23395885. E-mail address: [email protected] (A.K.-W. Fung) 1044-0283/99/$ – see front matter 2000 Elsevier Science Inc. All rights reserved. PII: S1044-0283(99)00016-2
p95919$$15
224
02-04-:0 06:47:44
p. 224
A.K.-W. Fung / Global Finance Journal 10 (1999) 223–230
the Hong Kong market. Interestingly, there is no clear evidence of investors’ overreaction in the Hong Kong stock market. De Bondt and Thaler (1985) first observed the overreaction phenomena in the U.S. equity market. First, they formed the “loser” portfolios, portfolios of stocks that have the lowest returns, and the “winner” portfolios, portfolios of stocks that have the highest returns in the ranking periods. They found that the prior loser portfolios significantly outperform the prior winners in the testing periods. Some argue that the observed phenomenon is caused by the bid-ask spread (Atkins & Dyl, 1990), biases in computed return (Conrad & Kaul, 1993; Dissanaike, 1994), risk mismeasurement (Chan, 1988), and size effect (Zarowin, 1990). However, even after adjustment for all these problems, overreaction still exists in the studies of De Bondt and Thaler (1987) and Chopra, Lakonishok, and Ritter (1992). So far, it seems that overreaction exists in the U.S. equity market. In international markets, overreaction is found in the Spanish equity markets (Alonso & Rubio, 1990), the Brazilian equity market (da Costa, 1994), and the U.K. equity market (Clare & Thomas, 1995). However, there is no such reported evidence in Asian equity markets. In this paper, the overreaction hypothesis is tested by using stocks in the Hong Kong Heng Sang Index (HSI). The loser portfolios and the winner portfolios of three stocks are formed in the formation periods of 2 years. The loser portfolios are found to significantly outperform the winner portfolios by almost 10% a year in the testing period of 1 year. The difference is higher than the 7.6% found in the U.S. equity market by De Bondt and Thaler (1985), calculated from their reported 3-year return of 24.6%. However, this study differs from other studies on overreaction in international markets in the following ways. The first difference is the importance of the market. The stock market capitalization of Hong Kong ranked seventh worldwide and second in Asia at the end of 1996. It is an important market for international investment because of the high liquidity of the market, the presence of a legal system and an accounting system similar to the Western standard, and its status as an indirect way to invest in China. Hong Kong is also a leader in the mutual fund (known as unit trust in Hong Kong) industry in Asia. The second difference is due to the special institutional features in Hong Kong related to the overreaction study. In most overreaction studies, selling some of the winner portfolio short may be difficult if not impossible. In most markets, there are severe limitations in short-selling—for example, Japan and most emerging markets. Hence, it is difficult to use the overreaction phenomenon to argue against market efficiency, because it is expensive or impossible to carry out the short-selling position. However, the stocks used in this study are all stocks of large market capitalization and liquidity. They are large enough for international investors to buy. Short-selling is also permitted in Hong Kong, including all the constituent stocks in the HSI. Moreover, the up-tick rule for short-selling was abolished after 25 March 1996. Short-selling is not a problem at all. The fact that only three stocks are used to form the portfolios makes the execution simple. All of them make buying the loser portfolio and selling the winner portfolio feasible in regard to market liquidity, regulations, transaction costs, and ease of executions. Hence, the arguments against market efficiency are even more compelling.
p95919$$15
02-04-:0 06:47:44
p. 225
A.K.-W. Fung / Global Finance Journal 10 (1999) 223–230
225
1. The Hong Kong stock exchange and the Hang Seng index There were 583 companies listed on Hong Kong Stock Exchange (HKSE) at the end of 1996 with market capitalization of U.S.$445.6 billion. The average daily turnover in 1996 was U.S.$727 million. The most commonly quoted stock index in Hong Kong is the Hang Seng Index, a value-weighted index. There are thirty-three stocks in the HSI. It represents more than 70% of the total market capitalization of all stocks listed on the HKSE. All the constituent stocks in the HSI are stocks with large market capitalization and liquidity. The number of stocks eligible to be sold short was increased from 0 to 17 on 4 January 1994 and further increased to 113 on 24 March 1996. For practical purposes, all the stocks in the HSI can be sold shorted. At the end of 1996, Hong Kong had markets for HSI futures, HSI options, individual stock futures, and individual stock options. There is no restriction on foreign investment and foreign exchange. 2. Data and methodology 2.1. Data The data in this study include the monthly returns (capital gains and dividends) of all 33 constituent stocks in the HSI in Hong Kong from January 1980 to December 1993. The market return is taken as the total return of the HSI. The data are taken from Datastream and PACAP. 2.2. Methodology The cumulative return of stock j in a period of T months (CR follows: CRj,T ⫽
) is calculated as
j,T
T
兿 (1 ⫹ Rj,i) ⫽ (1 ⫹ Rj,1)(1 ⫹ Rj,2) ··· (1 ⫹ Rj,T)
(1)
i⫽1
where Rj,i is the monthly return of stock j in month i. The total returns of the stocks in the HSI are calculated for the formation periods and the testing periods. The geometric mean is employed instead of the arithmetic mean used by De Bondt and Thaler (1985), da Costa (1994), and Clare and Thomas (1995). The geometric mean is used to reduce the error caused by the bid-ask spread, as pointed out by Conrad and Kaul (1993). Essentially, these returns are just those of the buy-and-hold strategy. The excess cumulative return (market-adjusted), ECRj,T, for stock j in a period of T months is defined as: ECRj,T ⫽ CRj,T ⫺ CRm,T
(2)
where CRm,T is the total return of the market (HSI) in the corresponding period of T months. A total of 14 years of returns is used. The formation periods are 2 years (e.g., 1980–1981, 1981–1982, . . ., 1991–1992). All stocks that are continuously in the HSI in each of the formation periods are ranked on the basis of their excess cumulative return, ECRj,T. The portfolio of the three stocks with the highest prior excess cumulative
p95919$$15
226
02-04-:0 06:47:44
p. 226
A.K.-W. Fung / Global Finance Journal 10 (1999) 223–230
returns is the winner portfolio, whereas the portfolio of the three stocks with the lowest excess cumulative returns is the loser portfolio. The testing periods are 1 year (i.e., 1982, 1983, . . ., 1993). In each testing period t, the average excess returns of the winner portfolio, AECRW,t, the loser portfolio, AECRL,t, and the arbitrage portfolio, DW⫺L,t, are calculated, respectively, as follows: 1 AECRW,t ⫽ (ECRW,1,t ⫹ ECRW,2,t ⫹ ECRW,3,t) 3
(3)
1 AECRL,t ⫽ (ECRL,1,t ⫹ ECRL,2,t ⫹ ECRL,3,t) 3
(4)
DL⫺W,t ⫽ AECRL,t ⫺ AECRW,t
(5)
where ECRW,i,t is the excess return of the ith stock in the winner portfolio, ECRL,i,t is the excess return of the ith stock in the loser portfolio, and DL⫺W,t is the return of the arbitrage portfolio (i.e., the excess return of the loser portfolio over the return of the winner portfolio in testing period t). If, for any reason, a stock is taken out of the HSI in the testing period, the next winner (or loser) candidate found in the formation period will be used for the rest of the testing period. The average excess returns of the winner portfolios and loser portfolios of all n testing periods are averaged to get the grand average excess returns of the winner portfolios, GAECRW, and that of the loser portfolios, GAECRL, as follows: n
GAECRW ⫽
1 n
t⫽1
GAECRL ⫽
1 n
兺 AETRL,t
兺 AECRW,t
(6)
n
(7)
t⫽1
and DGL⫺W ⫽ GAECRL ⫺ GAECRW
(8)
where DGL⫺W is the average return of the arbitrage portfolio. The traditional t-test is used to test whether GAECRW, GAECRL, or DL⫺W is significantly less than zero, because all the testing periods are nonoverlapping. Ruback (1982) obtained the variance of the cumulative average abnormal return from the variance of the average daily returns and the covariance of the average daily returns on day t and on day t ⫹ 1 for the whole testing period. His approach is suitable for overlapping periods and increases the power of the test. However, in this paper, a test of less power but straightforward is chosen. The cumulative returns for t months in the testing periods are the buy-and-hold returns for the period of t months. Hence, only the beginning and ending prices (plus the dividend) are needed to calculate the cumulative returns. This method is consistent with Eq. (1) because the interim stock prices between time zero and t are canceled out. The 12 cumulative returns in this case are all independent.
p95919$$15
02-04-:0 06:47:44
p. 227
A.K.-W. Fung / Global Finance Journal 10 (1999) 223–230
227
Table 1 Grand average excess cumulative returns of loser portfolios, winner portfolios, and arbitrage portfolios in the testing periods GAECRL,t
GAECRW,t
DGL⫺W,t
Months in testing periods
Mean
t-statistic
Mean
t-statistic
Mean
t-statistic
1 2 3 4 5 6 7 8 9 10 11 12
⫺0.02168 ⫺0.001920 ⫺0.01349 0.01291 0.03887 0.02956 0.02009 0.04328 0.04682 0.03439 0.05459 0.05048
⫺0.8007 ⫺0.08889 ⫺0.6377 0.5638 1.0244 0.8587 0.7075 1.151 1.233 0.9165 1.283 1.089
⫺0.02329 ⫺0.02577 ⫺0.0175 ⫺0.02611 ⫺0.007690 0.010558 ⫺0.00682 ⫺0.01157 ⫺0.02029 ⫺0.02342 ⫺0.02082 ⫺0.04874
⫺1.8890* ⫺1.455 ⫺0.9849 ⫺1.324 ⫺0.3788 0.3209 ⫺0.2685 ⫺0.4172 ⫺0.8228 ⫺0.5852 ⫺0.5827 ⫺1.178
⫺0.001615 0.02385 0.004017 0.039015 0.04656 0.01901 0.02691 0.05485 0.06711 0.05781 0.07541 0.09922
0.05066 0.7213 0.1443 1.287 1.204 0.4915 0.8493 1.817* 2.686* 2.216* 2.869** 3.083**
Abbreviations: GAECRL,t, grand average excess cumulative returns of the loser portfolios t months after formation; GAECRW,t, grand average excess cumulative returns of the winner portfolios t months after formation; DGL⫺W,t, grand average excess cumulative returns of longing the loser portfolios and shorting the winner portfolios t months after formation. * Significant at 5% level. ** Significant at 1% level.
The variance of the cumulative returns is obtained from these 12 numbers rather than from the monthly return (or daily returns). The t-test can be used here. 2.3. Statistical tests In this paper, the following three hypotheses are tested: H1: GAECRW ⱖ 0 with alternative hypothesis: GAECRW ⬍ 0 H2: GAECRL ⱕ 0 with alternative hypothesis: GAECRL ⬎ 0 H3: DGL⫺W ⫽ GAECRL ⫺ GAECRW ⱕ 0 with alternative hypothesis: DGL⫺W ⬎ 0 The test statistics are given by: tW ⫽
GAECRW SW/√N
(9)
tL ⫽
GAECRL SL/√N
(10)
tD ⫽
DGL⫺W SD/√N
(11)
where SW, SL, and SD are the sample standard deviations of the returns of the winner portfolios, the loser portfolios, and the arbitrage portfolios for the 12 testing periods.
p95919$$15
228
02-04-:0 06:47:44
p. 228
A.K.-W. Fung / Global Finance Journal 10 (1999) 223–230
Fig. 1. Cumulative returns of loser portfolios, winner portfolios, and arbitrage portfolios.
3. Results and interpretation The average cumulative excess returns of the loser portfolios, the winner portfolios, and their differences in the testing periods are summarized in Table 1. In comparison with the market return, the 1-year average return of the loser portfolios is higher, whereas that of the winner portfolios is lower, although not statistically significant. Now, let’s look at the dynamics. In the first 3 months after formation, the average returns of the loser portfolios and the winner portfolios are both below the market returns. However, the winner portfolios drop more than the loser portfolios. After 4 months, the loser portfolios begin to outperform the market, whereas the winner portfolios begin to underperform the market. Looking at the returns of the arbitrage portfolios, one can conclude that the loser portfolios outperform the winner portfolios significantly after 8 months from the ranking period. The difference in return is 9.9% a year. It should be pointed out that the power of the test is very low because of small sample size. The probability of rejecting the null hypothesis is very low. That explains why the GAECRs for the winner and loser portfolios are not statistically different from zero, although their signs agree with the overreaction hypothesis. The
p95919$$15
02-04-:0 06:47:44
p. 229
A.K.-W. Fung / Global Finance Journal 10 (1999) 223–230
229
Table 2 Yearly average excess returns of loser portfolios, winner portfolios, and arbitrage portfolios in the testing Testing periods
AECRL,12
AECRW,12
DL⫺W,12
1982 1983 1984 1985 1986 1987 1988 1989 1990 1991 1992 1993 Average t-statistic
0.09440 ⫺0.07821 0.1257 0.2733 0.2664 0.1330 ⫺0.07729 0.06122 ⫺0.1583 ⫺0.2046 0.2054 ⫺0.03532 0.05048 1.089
⫺0.04212 ⫺0.1947 ⫺0.008972 0.2881 0.01829 ⫺0.005603 ⫺0.03521 ⫺0.07828 ⫺0.05916 ⫺0.2107 0.01876 ⫺0.2753 ⫺0.04874 ⫺1.178
0.1365 0.1166 0.1347 ⫺0.01483 0.2482 0.1386 ⫺0.04208 0.1395 ⫺0.09913 0.006116 0.1866 0.2399 0.09922 3.083**
Abbreviations: AECRL,12, average excess cumulative returns of the loser portfolios 12 months after formation; AECRW,12, average excess cumulative returns of the winner portfolios 12 months after formation; DL⫺W,12, average excess cumulative returns of longing the loser portfolios and shorting the winner portfolios 12 months after formation. ** Significant at 1% level.
fact that the difference in the returns of the loser portfolios and the winner portfolios is statistically different from zero even though the power of the test is very low shows that investors indeed overreact; that is, tend to react more negatively to prior losers in comparison with their positive response to prior winners. This approach of looking at the difference in returns of the loser and winner portfolios is consistent with overreaction literature. The results are also presented graphically in Fig. 1. To see the variability of the return difference between the loser portfolios and the winner portfolios, the results of the yearly returns for the 12 testing periods are summarized in Table 2. The loser portfolios outperform the winner portfolios in 9 of 12 years. The annual return difference varies from ⫹24.8% to ⫺9.9%. When the formation periods are 3 years instead of 2 years, the average return of the arbitrage portfolio is 9.5% with t-statistics of 1.916, significant at the 5% level. The results are similar to those when the formation periods are 2 years.
4. Risk consideration Chan (1988) suggests that the overreaction phenomenon observed is mostly due to the varying risk premium. The betas of the loser portfolios and the winner portfolios in the testing periods are 0.9877 and 0.9157, respectively. They are not statistically different at the 5% level of significance. Moreover, the difference in beta accounts only for a difference in return of less than 2% a year, which cannot explain all the
p95919$$15
230
02-04-:0 06:47:45
p. 230
A.K.-W. Fung / Global Finance Journal 10 (1999) 223–230
difference in returns between the loser portfolios and the winner portfolios. The overreaction on the constituent stocks in the Hong Kong Hang Seng Index is real. 5. Conclusions The overreaction phenomenon reported in the equity markets of the United States, Spain, and Brazil is also observed in the Hong Kong stock market. The loser portfolios of the 33 stocks in the Hang Seng Index, on average, outperform the winner portfolios by 9.9% 1 year after the formation period. Only three stocks are used in the portfolios. All the stocks in HSI have large market capitalization and liquidity and can be shorted. The arbitrage portfolio of buying the loser portfolio and shorting the winner portfolio can actually be formed with minimum cost and easy execution. They make the overreaction phenomena in this study very powerful. Acknowledgments The author would like to thank Hung-Wan Kot, for his excellent research assistance in data gathering, computation, and graphing, and the Hong Kong Baptist University, for its financial support. The comments from the editor, the reviewer, and Professor Kin Lam are greatly appreciated. References Alonso, A., & Rubio, G. (1990). Overreaction in the Spanish equity market. J Bank Fin 14, 469–481. Atkins, A. B., & Dyl, E. A. (1990). Price reversals, bid-ask spreads, and market efficiency. J Fin Quant Anal 25, 535–547. Chan, K. C. (1988). On the contrarian investment strategy. J Bus 61(April), 147–163. Chopra, N., Lakonishok, J., & Ritter, J. R. (1992). Measuring abnormal performance: do stocks overreact? J Fin Econ 31, 235–268. Clare, A., & Thomas, S. (1995). The overreaction hypothesis and the UK stock market. J Bus Fin Account 22, 961–973. Conrad, J., & Kaul, G. (1993). Long-term market overreaction or biases in computed returns? J Fin 48(March), 39–63. da Costa, N. C. A., Jr. (1994). Overreaction in the Brazilian stock market. J Bank Fin 18, 633–642. De Bondt, W. F. M., & Thaler, R. (1985). Does the stock market overreact? J Fin 40, 793–805. De Bondt, W. F. M., & Thaler, R. (1987). Further evidence on investor overreaction and stock market seasonality. J Fin 42, 557–581. Dissanaike, G. (1994). On the computation of returns in tests of the stock market overreaction hypothesis. J Bank Fin 18, 1083–1094. Ruback, R. S. (1982). The effect of discretionary price control decisions on equity values. J Fin Econ 10(March), 83–105. Zarowin, P. (1990). Size, seasonality, and stock market overreaction. J Fin Quant Anal 25(March), 113–125.
02-04-:0 06:47:44
p. 223
Global Finance Journal 10:2 (1999) 223–230
Overreaction in the Hong Kong stock market Alexander Kwok-Wah Fung* Department of Finance and Decision Sciences, Hong Kong Baptist University, Kowloon Tong, Hong Kong, Peoples’ Republic of China
Abstract Overreaction reported in the equity markets of the United States, Spain, and Brazil is also observed in the Hong Kong stock market. The “loser” portfolios of the 33 stocks in the Hang Seng Index (HSI), on average, outperform the “winner” portfolios by 9.9% 1 year after the formation periods. Besides its emphasis on the importance of the Hong Kong market in international investment, this paper is unique in some special features related to the overreaction study. Hong Kong has markets for index futures and stock futures. Only three stocks are used in the portfolios. All the stocks in the HSI have large market capitalization and liquidity and can be shorted with no up-tick rule. Unlike other studies in international stock markets, the “arbitrage” portfolio of buying the loser portfolio and shorting the winner portfolio can actually be formed with minimum cost and easy execution, which makes the overreaction phenomena in this study very powerful. 2000 Elsevier Science Inc. All rights reserved. JEL classification: G14; G15 Keywords: Overreaction; Market efficiency; Hong Kong stock market
International investment has drawn a great deal of attention among academic researchers and practitioners in finance. Investors in the United States are increasing their allocations of investments to overseas markets to seek higher returns as well as diversification. Since 1990, there has been growing interest in the Hong Kong market owing to the potential market in China. As a result, many multinational investment firms are increasing their presence in Hong Kong. Hence, it is important to look at investors’ behavior in Hong Kong. It is interesting to see whether some findings about the U.S. market also hold in
* Corresponding author. Tel.: 852-23395225; Fax: 852-23395885. E-mail address: [email protected] (A.K.-W. Fung) 1044-0283/99/$ – see front matter 2000 Elsevier Science Inc. All rights reserved. PII: S1044-0283(99)00016-2
p95919$$15
224
02-04-:0 06:47:44
p. 224
A.K.-W. Fung / Global Finance Journal 10 (1999) 223–230
the Hong Kong market. Interestingly, there is no clear evidence of investors’ overreaction in the Hong Kong stock market. De Bondt and Thaler (1985) first observed the overreaction phenomena in the U.S. equity market. First, they formed the “loser” portfolios, portfolios of stocks that have the lowest returns, and the “winner” portfolios, portfolios of stocks that have the highest returns in the ranking periods. They found that the prior loser portfolios significantly outperform the prior winners in the testing periods. Some argue that the observed phenomenon is caused by the bid-ask spread (Atkins & Dyl, 1990), biases in computed return (Conrad & Kaul, 1993; Dissanaike, 1994), risk mismeasurement (Chan, 1988), and size effect (Zarowin, 1990). However, even after adjustment for all these problems, overreaction still exists in the studies of De Bondt and Thaler (1987) and Chopra, Lakonishok, and Ritter (1992). So far, it seems that overreaction exists in the U.S. equity market. In international markets, overreaction is found in the Spanish equity markets (Alonso & Rubio, 1990), the Brazilian equity market (da Costa, 1994), and the U.K. equity market (Clare & Thomas, 1995). However, there is no such reported evidence in Asian equity markets. In this paper, the overreaction hypothesis is tested by using stocks in the Hong Kong Heng Sang Index (HSI). The loser portfolios and the winner portfolios of three stocks are formed in the formation periods of 2 years. The loser portfolios are found to significantly outperform the winner portfolios by almost 10% a year in the testing period of 1 year. The difference is higher than the 7.6% found in the U.S. equity market by De Bondt and Thaler (1985), calculated from their reported 3-year return of 24.6%. However, this study differs from other studies on overreaction in international markets in the following ways. The first difference is the importance of the market. The stock market capitalization of Hong Kong ranked seventh worldwide and second in Asia at the end of 1996. It is an important market for international investment because of the high liquidity of the market, the presence of a legal system and an accounting system similar to the Western standard, and its status as an indirect way to invest in China. Hong Kong is also a leader in the mutual fund (known as unit trust in Hong Kong) industry in Asia. The second difference is due to the special institutional features in Hong Kong related to the overreaction study. In most overreaction studies, selling some of the winner portfolio short may be difficult if not impossible. In most markets, there are severe limitations in short-selling—for example, Japan and most emerging markets. Hence, it is difficult to use the overreaction phenomenon to argue against market efficiency, because it is expensive or impossible to carry out the short-selling position. However, the stocks used in this study are all stocks of large market capitalization and liquidity. They are large enough for international investors to buy. Short-selling is also permitted in Hong Kong, including all the constituent stocks in the HSI. Moreover, the up-tick rule for short-selling was abolished after 25 March 1996. Short-selling is not a problem at all. The fact that only three stocks are used to form the portfolios makes the execution simple. All of them make buying the loser portfolio and selling the winner portfolio feasible in regard to market liquidity, regulations, transaction costs, and ease of executions. Hence, the arguments against market efficiency are even more compelling.
p95919$$15
02-04-:0 06:47:44
p. 225
A.K.-W. Fung / Global Finance Journal 10 (1999) 223–230
225
1. The Hong Kong stock exchange and the Hang Seng index There were 583 companies listed on Hong Kong Stock Exchange (HKSE) at the end of 1996 with market capitalization of U.S.$445.6 billion. The average daily turnover in 1996 was U.S.$727 million. The most commonly quoted stock index in Hong Kong is the Hang Seng Index, a value-weighted index. There are thirty-three stocks in the HSI. It represents more than 70% of the total market capitalization of all stocks listed on the HKSE. All the constituent stocks in the HSI are stocks with large market capitalization and liquidity. The number of stocks eligible to be sold short was increased from 0 to 17 on 4 January 1994 and further increased to 113 on 24 March 1996. For practical purposes, all the stocks in the HSI can be sold shorted. At the end of 1996, Hong Kong had markets for HSI futures, HSI options, individual stock futures, and individual stock options. There is no restriction on foreign investment and foreign exchange. 2. Data and methodology 2.1. Data The data in this study include the monthly returns (capital gains and dividends) of all 33 constituent stocks in the HSI in Hong Kong from January 1980 to December 1993. The market return is taken as the total return of the HSI. The data are taken from Datastream and PACAP. 2.2. Methodology The cumulative return of stock j in a period of T months (CR follows: CRj,T ⫽
) is calculated as
j,T
T
兿 (1 ⫹ Rj,i) ⫽ (1 ⫹ Rj,1)(1 ⫹ Rj,2) ··· (1 ⫹ Rj,T)
(1)
i⫽1
where Rj,i is the monthly return of stock j in month i. The total returns of the stocks in the HSI are calculated for the formation periods and the testing periods. The geometric mean is employed instead of the arithmetic mean used by De Bondt and Thaler (1985), da Costa (1994), and Clare and Thomas (1995). The geometric mean is used to reduce the error caused by the bid-ask spread, as pointed out by Conrad and Kaul (1993). Essentially, these returns are just those of the buy-and-hold strategy. The excess cumulative return (market-adjusted), ECRj,T, for stock j in a period of T months is defined as: ECRj,T ⫽ CRj,T ⫺ CRm,T
(2)
where CRm,T is the total return of the market (HSI) in the corresponding period of T months. A total of 14 years of returns is used. The formation periods are 2 years (e.g., 1980–1981, 1981–1982, . . ., 1991–1992). All stocks that are continuously in the HSI in each of the formation periods are ranked on the basis of their excess cumulative return, ECRj,T. The portfolio of the three stocks with the highest prior excess cumulative
p95919$$15
226
02-04-:0 06:47:44
p. 226
A.K.-W. Fung / Global Finance Journal 10 (1999) 223–230
returns is the winner portfolio, whereas the portfolio of the three stocks with the lowest excess cumulative returns is the loser portfolio. The testing periods are 1 year (i.e., 1982, 1983, . . ., 1993). In each testing period t, the average excess returns of the winner portfolio, AECRW,t, the loser portfolio, AECRL,t, and the arbitrage portfolio, DW⫺L,t, are calculated, respectively, as follows: 1 AECRW,t ⫽ (ECRW,1,t ⫹ ECRW,2,t ⫹ ECRW,3,t) 3
(3)
1 AECRL,t ⫽ (ECRL,1,t ⫹ ECRL,2,t ⫹ ECRL,3,t) 3
(4)
DL⫺W,t ⫽ AECRL,t ⫺ AECRW,t
(5)
where ECRW,i,t is the excess return of the ith stock in the winner portfolio, ECRL,i,t is the excess return of the ith stock in the loser portfolio, and DL⫺W,t is the return of the arbitrage portfolio (i.e., the excess return of the loser portfolio over the return of the winner portfolio in testing period t). If, for any reason, a stock is taken out of the HSI in the testing period, the next winner (or loser) candidate found in the formation period will be used for the rest of the testing period. The average excess returns of the winner portfolios and loser portfolios of all n testing periods are averaged to get the grand average excess returns of the winner portfolios, GAECRW, and that of the loser portfolios, GAECRL, as follows: n
GAECRW ⫽
1 n
t⫽1
GAECRL ⫽
1 n
兺 AETRL,t
兺 AECRW,t
(6)
n
(7)
t⫽1
and DGL⫺W ⫽ GAECRL ⫺ GAECRW
(8)
where DGL⫺W is the average return of the arbitrage portfolio. The traditional t-test is used to test whether GAECRW, GAECRL, or DL⫺W is significantly less than zero, because all the testing periods are nonoverlapping. Ruback (1982) obtained the variance of the cumulative average abnormal return from the variance of the average daily returns and the covariance of the average daily returns on day t and on day t ⫹ 1 for the whole testing period. His approach is suitable for overlapping periods and increases the power of the test. However, in this paper, a test of less power but straightforward is chosen. The cumulative returns for t months in the testing periods are the buy-and-hold returns for the period of t months. Hence, only the beginning and ending prices (plus the dividend) are needed to calculate the cumulative returns. This method is consistent with Eq. (1) because the interim stock prices between time zero and t are canceled out. The 12 cumulative returns in this case are all independent.
p95919$$15
02-04-:0 06:47:44
p. 227
A.K.-W. Fung / Global Finance Journal 10 (1999) 223–230
227
Table 1 Grand average excess cumulative returns of loser portfolios, winner portfolios, and arbitrage portfolios in the testing periods GAECRL,t
GAECRW,t
DGL⫺W,t
Months in testing periods
Mean
t-statistic
Mean
t-statistic
Mean
t-statistic
1 2 3 4 5 6 7 8 9 10 11 12
⫺0.02168 ⫺0.001920 ⫺0.01349 0.01291 0.03887 0.02956 0.02009 0.04328 0.04682 0.03439 0.05459 0.05048
⫺0.8007 ⫺0.08889 ⫺0.6377 0.5638 1.0244 0.8587 0.7075 1.151 1.233 0.9165 1.283 1.089
⫺0.02329 ⫺0.02577 ⫺0.0175 ⫺0.02611 ⫺0.007690 0.010558 ⫺0.00682 ⫺0.01157 ⫺0.02029 ⫺0.02342 ⫺0.02082 ⫺0.04874
⫺1.8890* ⫺1.455 ⫺0.9849 ⫺1.324 ⫺0.3788 0.3209 ⫺0.2685 ⫺0.4172 ⫺0.8228 ⫺0.5852 ⫺0.5827 ⫺1.178
⫺0.001615 0.02385 0.004017 0.039015 0.04656 0.01901 0.02691 0.05485 0.06711 0.05781 0.07541 0.09922
0.05066 0.7213 0.1443 1.287 1.204 0.4915 0.8493 1.817* 2.686* 2.216* 2.869** 3.083**
Abbreviations: GAECRL,t, grand average excess cumulative returns of the loser portfolios t months after formation; GAECRW,t, grand average excess cumulative returns of the winner portfolios t months after formation; DGL⫺W,t, grand average excess cumulative returns of longing the loser portfolios and shorting the winner portfolios t months after formation. * Significant at 5% level. ** Significant at 1% level.
The variance of the cumulative returns is obtained from these 12 numbers rather than from the monthly return (or daily returns). The t-test can be used here. 2.3. Statistical tests In this paper, the following three hypotheses are tested: H1: GAECRW ⱖ 0 with alternative hypothesis: GAECRW ⬍ 0 H2: GAECRL ⱕ 0 with alternative hypothesis: GAECRL ⬎ 0 H3: DGL⫺W ⫽ GAECRL ⫺ GAECRW ⱕ 0 with alternative hypothesis: DGL⫺W ⬎ 0 The test statistics are given by: tW ⫽
GAECRW SW/√N
(9)
tL ⫽
GAECRL SL/√N
(10)
tD ⫽
DGL⫺W SD/√N
(11)
where SW, SL, and SD are the sample standard deviations of the returns of the winner portfolios, the loser portfolios, and the arbitrage portfolios for the 12 testing periods.
p95919$$15
228
02-04-:0 06:47:44
p. 228
A.K.-W. Fung / Global Finance Journal 10 (1999) 223–230
Fig. 1. Cumulative returns of loser portfolios, winner portfolios, and arbitrage portfolios.
3. Results and interpretation The average cumulative excess returns of the loser portfolios, the winner portfolios, and their differences in the testing periods are summarized in Table 1. In comparison with the market return, the 1-year average return of the loser portfolios is higher, whereas that of the winner portfolios is lower, although not statistically significant. Now, let’s look at the dynamics. In the first 3 months after formation, the average returns of the loser portfolios and the winner portfolios are both below the market returns. However, the winner portfolios drop more than the loser portfolios. After 4 months, the loser portfolios begin to outperform the market, whereas the winner portfolios begin to underperform the market. Looking at the returns of the arbitrage portfolios, one can conclude that the loser portfolios outperform the winner portfolios significantly after 8 months from the ranking period. The difference in return is 9.9% a year. It should be pointed out that the power of the test is very low because of small sample size. The probability of rejecting the null hypothesis is very low. That explains why the GAECRs for the winner and loser portfolios are not statistically different from zero, although their signs agree with the overreaction hypothesis. The
p95919$$15
02-04-:0 06:47:44
p. 229
A.K.-W. Fung / Global Finance Journal 10 (1999) 223–230
229
Table 2 Yearly average excess returns of loser portfolios, winner portfolios, and arbitrage portfolios in the testing Testing periods
AECRL,12
AECRW,12
DL⫺W,12
1982 1983 1984 1985 1986 1987 1988 1989 1990 1991 1992 1993 Average t-statistic
0.09440 ⫺0.07821 0.1257 0.2733 0.2664 0.1330 ⫺0.07729 0.06122 ⫺0.1583 ⫺0.2046 0.2054 ⫺0.03532 0.05048 1.089
⫺0.04212 ⫺0.1947 ⫺0.008972 0.2881 0.01829 ⫺0.005603 ⫺0.03521 ⫺0.07828 ⫺0.05916 ⫺0.2107 0.01876 ⫺0.2753 ⫺0.04874 ⫺1.178
0.1365 0.1166 0.1347 ⫺0.01483 0.2482 0.1386 ⫺0.04208 0.1395 ⫺0.09913 0.006116 0.1866 0.2399 0.09922 3.083**
Abbreviations: AECRL,12, average excess cumulative returns of the loser portfolios 12 months after formation; AECRW,12, average excess cumulative returns of the winner portfolios 12 months after formation; DL⫺W,12, average excess cumulative returns of longing the loser portfolios and shorting the winner portfolios 12 months after formation. ** Significant at 1% level.
fact that the difference in the returns of the loser portfolios and the winner portfolios is statistically different from zero even though the power of the test is very low shows that investors indeed overreact; that is, tend to react more negatively to prior losers in comparison with their positive response to prior winners. This approach of looking at the difference in returns of the loser and winner portfolios is consistent with overreaction literature. The results are also presented graphically in Fig. 1. To see the variability of the return difference between the loser portfolios and the winner portfolios, the results of the yearly returns for the 12 testing periods are summarized in Table 2. The loser portfolios outperform the winner portfolios in 9 of 12 years. The annual return difference varies from ⫹24.8% to ⫺9.9%. When the formation periods are 3 years instead of 2 years, the average return of the arbitrage portfolio is 9.5% with t-statistics of 1.916, significant at the 5% level. The results are similar to those when the formation periods are 2 years.
4. Risk consideration Chan (1988) suggests that the overreaction phenomenon observed is mostly due to the varying risk premium. The betas of the loser portfolios and the winner portfolios in the testing periods are 0.9877 and 0.9157, respectively. They are not statistically different at the 5% level of significance. Moreover, the difference in beta accounts only for a difference in return of less than 2% a year, which cannot explain all the
p95919$$15
230
02-04-:0 06:47:45
p. 230
A.K.-W. Fung / Global Finance Journal 10 (1999) 223–230
difference in returns between the loser portfolios and the winner portfolios. The overreaction on the constituent stocks in the Hong Kong Hang Seng Index is real. 5. Conclusions The overreaction phenomenon reported in the equity markets of the United States, Spain, and Brazil is also observed in the Hong Kong stock market. The loser portfolios of the 33 stocks in the Hang Seng Index, on average, outperform the winner portfolios by 9.9% 1 year after the formation period. Only three stocks are used in the portfolios. All the stocks in HSI have large market capitalization and liquidity and can be shorted. The arbitrage portfolio of buying the loser portfolio and shorting the winner portfolio can actually be formed with minimum cost and easy execution. They make the overreaction phenomena in this study very powerful. Acknowledgments The author would like to thank Hung-Wan Kot, for his excellent research assistance in data gathering, computation, and graphing, and the Hong Kong Baptist University, for its financial support. The comments from the editor, the reviewer, and Professor Kin Lam are greatly appreciated. References Alonso, A., & Rubio, G. (1990). Overreaction in the Spanish equity market. J Bank Fin 14, 469–481. Atkins, A. B., & Dyl, E. A. (1990). Price reversals, bid-ask spreads, and market efficiency. J Fin Quant Anal 25, 535–547. Chan, K. C. (1988). On the contrarian investment strategy. J Bus 61(April), 147–163. Chopra, N., Lakonishok, J., & Ritter, J. R. (1992). Measuring abnormal performance: do stocks overreact? J Fin Econ 31, 235–268. Clare, A., & Thomas, S. (1995). The overreaction hypothesis and the UK stock market. J Bus Fin Account 22, 961–973. Conrad, J., & Kaul, G. (1993). Long-term market overreaction or biases in computed returns? J Fin 48(March), 39–63. da Costa, N. C. A., Jr. (1994). Overreaction in the Brazilian stock market. J Bank Fin 18, 633–642. De Bondt, W. F. M., & Thaler, R. (1985). Does the stock market overreact? J Fin 40, 793–805. De Bondt, W. F. M., & Thaler, R. (1987). Further evidence on investor overreaction and stock market seasonality. J Fin 42, 557–581. Dissanaike, G. (1994). On the computation of returns in tests of the stock market overreaction hypothesis. J Bank Fin 18, 1083–1094. Ruback, R. S. (1982). The effect of discretionary price control decisions on equity values. J Fin Econ 10(March), 83–105. Zarowin, P. (1990). Size, seasonality, and stock market overreaction. J Fin Quant Anal 25(March), 113–125.