L in et al.
(1994),
L ongin and Solnik(2001),
Ang andChen
2002),
and Connolly and Wang(2003)
have proven that during bull and bear markets, the level of correlation between two assets are inconsistent, especially during the initial and end periods, and extreme bull and extreme bear periods of bull (or bear) market, where volatilities are greater than the entire period. Hence, the test of interaction between the two variables using traditional correlation methods fails to consider the differences in the level of volatility between the two variables during different periods.Hence, using correlation coefficient to measure the level of interaction will lead to error. Hence, the correlation coefficient must be adjusted according to the volatility of the variables during the two periods to ensure greater objectivity in the test. Hence, the author shall use the heteroscedasticity biases based on correlation coefficients (Forbes and Rigobon
2002)
Based on Forbes and Rigobon
(2002)
equation for adjusting heteroscedasticity bias, the correlation coefficient is adjusted to equation(1):
p* p
CY
!
is the volatility of a particular variable during a period of higher volatility in two different periodsCY
�
is the volatility of a particular variable during a period of lower volatility in two different periodsHence, this paper defines PI as the stock buying and selling correlation coefficient during a specific period (including the initial periods, end periods, extreme bull and extreme bear periods in bull (bear) markets) as, and P2 as the institutional investors' buying and selling correlation coefficient during the entire period. If the level of coefficient of institutional investors' buying and selling activities between specific time periods increases significantly as compared to entire periods, and if such correlation coefficient is positive, it implies that synchronous trading will occur between two institutional investors; if the level of correlation is significantly reduced
and the correlation coefficient is negative, it implies that contrarian trading will occur between two institutional investors.
Usually, Fisher's z-test is used for testing two sets of correlation coefficients. Hence, the P values of the two sets of correlation coefficient must be transformed into Zy values before testing can take place. The test assumptions and z values are as follows:
. < => . < two institutional investors during a specific period (including the initial periods, end periods, extreme bull periods and extreme bear periods)
P2. Correlation coefficient of stock buying and selling by two institutional investors during the entire period
Z : Fisher's z coefficient transformed from PI
r,
Z : Fisher's z coefficient transformed from P2
r,
E( Zr, zr, _ ) : Expected value of the difference between two Fisher's z coefficients after transformation
V(z - Z ) : Variance of the difference between two r1 r2
Fisher's z coefficients after transformation
nl No. of days during a specific period (including the categories of institutional investors was observed. Apparent contrarian trading was seen only during extreme down periods in bull markets.
Table
1
Correlations of buying and selling activities for three categories of institutional investors in bull markets foreign VSEntire average 7.64 -0.39
period Correlation 0.149
Initial Daily average 14.37 0.63 periods of Correlation 0.371
bull Z value 4.223***
markets Activities (synchronous buying)
Extreme average 22.48 1.45
bulls Correlation 0.216
in Z value 1.429*
bull Activities (synchronous
markets buying)
Extreme average 8.87 -6.88
bears Correlation -0.283
in Z value -2.156***
bull Activities ( contrarian
markets trading)
End average 10.19 0.83
periods of Correlation 0.004
bull Z value -2.509
markets Activities synchronous buying
( contrarian (synchronous trading) selling)
Note 2: The symbol () of activities represents achieving significant level in statistics.
All in all, all the three categories of institutional market). However, this trait was not apparent. Also, there investors exhibited synchronous selling in bear markets, was no contrarian trading between the three institutional and only synchronously bought high between themselves investors in bear markets.
during rebound in a bear market (extreme bull in a bear
Table 2 Correlations of buying and selling activities for three categories of institutional investors in bear markets foreign VS foreign VS foreign VS investment trusts investment trusts securities dealers local VS securities
dealers foreign trusts foreign dealers foreign local trusts dealers
Entire average 7.64 -0.39 7.64 0.15 7.64 -0.24 -0.39 0.15
period Correlation 0.149 0.341 0.286 0.382
Initial average -12.26 -1.52 -12.26 -3.28 -12.26 -4.80 -1.52 -3.28
periods Correlation 0.247 0.389 0.370 0.543
of bear Z value 1.761** 0.969 1.645* * 3.577***
markets Activities (synchronous synchronous (synchronous (synchronous
selling} selling selling} selling}
Extreme average 20.67 5.87 20.67 4.03 20.67 9.89 5.87 4.03
bulls Correlation 0.212 0.041 0.161 0.283
in Z value 0.646 -3.1ll -l.301 -1.103
bear Activities synchronous synchronous synchronous synchronous
markets buying buying buying buying
Extreme average -18.03 -l.05 -18.03 -2.42 -18.03 -3.47 -l.05 -2.42
bears Correlation 0.138 0.392 0.314 0.396
III Z value -0.238 1.264 0.669 0.334
bear Activities synchronous synchronous synchronous synchronous
markets selling selling selling selling
End average -13.06 -0.13 -13.06 -1.12 -13.06 -1.24 -0.13 -1.12
periods Correlation 0.223 0.338 0.335 0.409
of bear Z value l.300* -0.038 0.933 0.551
markets Activities (synchronous synchronous synchronous synchronous
selling} selling selling selling
Note 1: * significant at 10% level (2-tailed), ** significant at 5% level (2-tailed), *** significant at 1 % level (2-tailed).
Note 2: The symbol () of activities represents achieving significant level in statistics.
V . CONCLUSIONS
In most cases, institutional investors exhibit synchronous buying in a bull market. Contrarian trading between institutional investors was apparent only when rapid correction occurred during extreme down periods in bull markets. This implies that during the initial periods in bull markets, after stock prices have fallen sharply and when undershooting have occurred for most stocks, long term investment funds would flow into the stock market.
Hence, synchronous buying by institutional investors was observed. Many studies have found that institutional investors would engaging in buying and buy high when extreme bull occurred in a bull market, thus, synchronous buying would occur frequently. When stock prices rise to a high level, institutional investors would profit.
Over-optimism would cause institutional investors to synchronously buy at high prices. In a bull market, foreign and local institutional investors would engage in contrarian trading only when rapid correction of stock prices occurred.
Under such circumstances, foreign investors would tend to buy low, and local institutional investors would choose to take profit.
In a bear market, synchronous selling was often seen in institutional investors. Synchronous buying at high prices between institutional investors would occur only when the market rebounded and an extreme bull market took place in a bear market. However, this phenomenon was not apparent.
Also, no contrarian trading occurred between institutional investors during a bear period. This implies that during the initial period of a bear market, when stock prices fall from a high level, institutional investors would sell their stock holdings to close their positions and take profit. Hence, synchronous selling was often seen among institutional investors. Panic selling often followed an extreme bear market, and massive redemption would occur among fund investors, resulting in selling low, therefore, synchronous selling among institutional investors. When correction took place, even when stock prices were low, institutional investors would often be over pessimistic, leading to synchronous selling at low prices. In a bear market, even when stock prices rebound rapidly, although institutional investors would buy low in anticipation of a rebound, they did not engage in active synchronous buying, as rebound was thought to be transient.
REFERENCES
[I] Ang, A., & Chen, J. (2002). Asymmetric correlations of equity portfolio, Journal of Financial Economics 63(3), 443-494.
[2] Cao, H. H., & Brennan, M. J. (1997). International portfolio investment flows, Journal of Finance 52(5),1851-1880.
[3] Carhart, M. M., Kaniel, R, Musto, D. K., & Reed, A. V. (2002).
Leaning for the tape: evidence of gaming behavior in equity mutual funds, Journal of Finance 57(2), 661-693.
[4] Connolly, R A., & Wang, F. A. (2003). International equity market co-movements: economic fundamentals or contagion, Pacific Basin Finance Journalll(1), 23-43.
[5] Covring, V., Lau, S. T., & Ng, L. (2006). Do domestic and foreign fund managers have similar preferences for stock characteristics? a cross-country analysis, Journal of International Business Studies 37(3), 407-429
[6] Fabozzi, F. J., & Francis, J. J. (1979). Mutual fund systematic risk for bull and bear markets: an empirical examination, Journal of Finance 34(5),1243-1250.
[7] Falkenstein, E. G. (1996). Preferences for stock characteristics as revealed by mutual fund portfolio holdings, Journal of Finance 51(1), 111-135.
[8] Forbes, K. 1, & Rigobon, R (2002). No contagion, only interdependence: measuring stock market co-movements, Journal of Finance 57(5), 2223-2261.
[9] Jegadeesh, N., & Titaman, S. (1993). Returns to buying winners and selling losers implications for stock market efficiency, Journal of Finance 48(1), 65-91.
[10] Lakonishok, J., Shleifer, A., & Vishny, R W. (1992). The impact of institutional trading on stock prices, Journal of Financial Economics 32(1),23-43.
[11] Lin, W-L., Engle, R F., & Ito, T. (1994). Do bulls and bears move across borders? international transmission of stock returns and volatility, Review of Financial Studies 7(3), 507-538.
[12] Lindahl-Stevens, M. (1980). Redefining bull and bear markets, Financial Analysts Journal 36(6), 76-93.
[13] Longin, F., & Solnik, B. (2001). Extreme correlation of international equity markets, Journal of Finance 56(2), 649-676.
[14] Scharfstein, D. S., & Stein, 1 C (1990). Herd behavior and investment, American Economic Review, 80(3),465-479.
[15] Scharfstein, D. S., Stein, 1 C, & Froot, K. A. (1992). Herd on the street: informational inefficiencies in a market with short-term speculation, Journal of Finance 47(4), 1461-1484.
[16] Thaler, R., & De Bondt, W. F. M. (1985). Does the stock market overreact, Journal of Finance 40(3), 793-805.
[17] Wermers, R (1999) Mutual fund herding and impact on stock price, Journal of Finance 54(2), 581-622.