seasonalities and the 1987 crash: the international evidence

Seasonalities and the 1987 Crash:

The International Evidence

BOB G. WOOD, JR.

This paper examines several seasonal regularities in stock returns before and after the international crash of

October 1987. The analysis investigates the day of tire week, pre- and post-holiday, turn of the year, turn of the

month, and month of the year effects in Pacific Rim and U.S. equity markets. The incidence of return regularities

decreases significantly in the period following the crash. We posit that an alteration of the returns generating

process in these markets is the most likely cause of the change in the trading patterns.

I. INTRODUCTION

The persistent and pervasive nature of calendar trading anomalies has intrigued financial

economists for many years. First documented by Wachtel (1942), seasonal regularities are the subject of intense scrutiny for the last two decades. Trading patterns documented include days of the week, exchange holidays, times of the year, times of the month, and months of the year.

Return regularities are present in the financial markets of North American, European, and

Pacific Rim countries through bull and bear markets and diverse economic conditions. This

study’s purpose is to learn if the international crash of October 1987 had an effect on the

seasonalities in Pacific Rim and U.S. equity markets. The crash of 1987 was unprecedented in severity and scope. The most commonly ascribed

precipitants of the crash include the federal budget and trade deficits, computerized trading

programs, and speculative bubbles (Malliaris & Urrutia, 1992). After evaluation of these potential causes, Roll (1988) finds no single causative factor that precipitated the crash. Shiller,

Kon-Ya, and Tsutsui (1991), in a survey of institutional investors, report that price movement

feedback rather than exogenous news reports was primarily responsible for crash transmission. A striking increase in bidirectional and unidirectional causality feedback occurred between geographically diverse equity markets during the crash (Mall&is & Urrutia, 1992). Investor psychology and behavioral activities leading to a generalized market panic best explain the

intensity and extensiveness of the crash according to some observers (Leland & Rubinstein

(1988), Shiller (1989)).

This research is important for the following reasons.

Bob G. Wood, Jr. l College of Business, Arkansas State University, State University, AR 72467

International Review of Financial Analysis, Vol. 3, No. 1,1994, pp. 65-91.

Copyright 0 1994 by JAI Press, Inc., All rights of reproduction in any form reserved.

ISSN: 1057-5219

65

66 INTERNATiONAL REVIEW OF FINANCIAL ANALYSIS /Vol. 3(1 f

1. Seasonal “anomalies” that do not persist over time may simply be artifacts of the sample periods of earlier studies.

2. Seasonalities that do persist may provide clues for the development of more descriptive models of asset pricing.

3. A comprehensive global asset pricing model must account for common seasonalities found in different markets.

4. Difirences in seasonalities suggest that alternate market structures have an influence on the returns generating process (as argued in Amihud and MendeIson, 1987).

The next section of the paper describes the data and markets used in the study. Subsequent sections examine day of the week, holiday, turn of the year, turn of the month, and month of the year effects in Pacific Rim and U.S. equity markets in the period preceding and following the 1987 crash. The paper closes with a discussion of our results and a brief summary.

II. DATA

The presence of seasonal regularities in Pacific Rim and U. S. equity markets is examined using the daily closing prices of the Nikkei Stock Average (Japan), the Weighted Stock Index (Taiwan), the Hang Seng Index (‘Hung Kong), the A~~ Ordinaries Index (Austr~ia}, the Strait Times Index (Singapore), and the St~~rd and Fours 500 Composite Irzdex (United States) from January 1, 198 1 through December 3 1, 1991. Sources of the data are The Wall Street Jo~~ffZ (Eastern Edition), The Times of London, the Taiwan Stock Exchange, HSI Services, Inc. of Hong Kong, the Australian Stock Exchange, the Stock Exchange of Singapore Ltd., and the Center for Research in Security Prices (CRSP).

The Nikkei Stock Average is a price weighted average containing 225 stocks. These stocks represent 60 percent of the capitalization of the First Section of the Tokyo Stock Exchange. The

Taiwan Weighted Stock Index is a value-weighted index of essentially all stocks traded on the Taiwan Stock Exchange. Hong Kong’s Hung Seng Index represents approximately 70 percent of the Stock Exchange of Hong Kong’s total market capitalization. Over 320 companies’ common shares make up the All Ordinaries Index of Australia. The Strait Times Index of the Stock ~chunge of Singapore is a narrow-based, capitali~tion weighted index of 30 companies (Berlin, 1990). The Standard and Pours 500 Composite Zndex (S&P 500) proxies US. equity market returns.

We define the pre-crash trading period in our study as trading days occurring from January 1, 1981 through September 30, 1987 (inclusive). The post-crash trading period is defined as trading days between November 1, 1987 and December 31, 1991 (inclusive). We exclude trading days if an index price is unavailable.

III. THE DAY OF THE WElEK EFFECT

A difference in the average return of U.S. equity markets dependent on the day of the week was first reported by Cross (1973). Active trading accentuates the difference in returns (McInish & Wood, 1985). Many empirical studies find negative average returns for Monday trading in U.S. equity markets, while the last trading day of the week’s returns are positive (Cross, 1973;

Seasonalities and the 1987 Crash 67

French, 1980; Gibbons & Hess, 1981; and Lakonishok & Levi, 1982). Research using Pacific Rim equity markets finds negative Tuesday returns with positive average returns on the last trading day of the week (Aggarwal & Rivoli, 1989; Condoyanni, O’Hanlon, & Ward, 1987; Howe & Wood, 1993; Jaffe & Westerfield, 1985a, b,; and Kato, 1990). Table 1 summarizes the extant empirical examinations of the day of the week effect in U.S. and Pacific Rim equity markets.

Researchers offer many rationales as explanations for the day of the week effect. The seasonality is not simply an artifact resulting from measurement errors (Cross, 1973; Gibbons & Hess, 1981; Keim & Stambaugh, 1984; Jaffe & Westerfield, 1985a; and Smirlock & Starks, 1986). French (1980) examines trading time-clock time hypotheses as potential inducers of the effect but rejects both suppositions. Settlement date procedures are also insufficient as explanations for day of the week effects (Dyl & Martin, 1985; Gibbons & Hess, 1981; Lakonishok & Levi, 1982, 1985). Although theoretically appealing, inventory adjustments by specialists, short-sellers, and other investors seem inadequate in explaining the phenomenon’s persistence and intensity (Miller, 1988). Jacobs and Levy (1988) offer investor psychology and behavioral patterns as promising potential rationales for the day of the week effect.

As shown in Table 2, we find a significant day of the week effect in the equity markets of Japan, Taiwan, and Australia before the crash. Our findings support the existing literature on market anomalies; the average return on the last trading day of the week is positive and significant in all Pacific Rim markets. Average Tuesday returns are negative in all Pacific Rim markets except Taiwan; the returns differ significantly from zero in the markets of Japan, Hong Kong, Australia, and Singapore. Monday returns in the U.S. are less than zero but are not significant. Wednesday returns are significant and positive in all markets studied (positive but not significant in the U.S. market). Unlike previous studies of the Japanese equity market, we find no significant difference in Friday returns when Friday is followed by Saturday trading and Friday returns when Friday is not followed by Saturday trading in the period preceding the crash (see Table A3).’

The incidence of market seasonalities decreases significantly following the crash. The Hong Kong Hang Seng Index is the only average to show a significant day of the week effect in the period following the crash. Although the average return on the last trading day of the week remains positive in all markets, the returns differ significantly from zero only in the Hong Kong market. After the crash, Monday returns are positive in all markets except Taiwan; returns do not differ significantly from zero except in Japan. Wednesday returns remain positive in Japan, Hong Kong, Australia, Singapore, and the United States but are significant only in the Hong Kong and Singapore markets.

Although Friday trading returns in Japan are negative when Friday is followed by Saturday trading and positive when Friday is the last trading day of the week, the difference in returns is not significant (see Table A4).

IV. THE HOLIDAY EFFECT

Prior empirical research finds dramatically higher average returns on trading days preceding market holidays than on other trading days (Lakonishok & Smidt, 1988; Ariel, 1990; and Howe &Wood, 1993). The average return on trading days following market holidays is less than zero. Table 3 summarizes the literature on trading days around exchange holidays.

68 INTERNATIONAL REVIEW OF FINANCIAL ANALYSIS /‘Vol. 30)

Table 1 Summary of Day of the Week Effect Empirical Studies

Author Cmmy Period Major Result(s)

cross (1973)

French (1980)

Gibbons&Hess (1981)

Lakonishok & Levi (1982)

Keim & Stambaugh (1984)

United States

United States

United States

1953-1970

1953-1977

1962-1978

United States 1962-1979


Jaffe & Westerfield (19851) Japan 1970-1983

Jaffe & Westerfield (1985b)

Australia 1973-1982

Japan 197&1983

Condoyanni, O’Hanlon, and Ward ( 1987)


Lakonishok and Smidt (1988)

Aggarwal and Rivoli (1989)

Australia 1981-1984

Japan 1969-1984

Singapore 1969-1984


Hong Kong 1976-1988 Singapore 19761988

Jaffe, Westerfield, and Ma (1989) United States 193&1981

Japan 1970-1983 Australia 1973-1982

Kato (1990) Japan 1974-1987

Howe and Wood 11993) Japan 1981-1991

Taiwan 1981-1991

Hong Kong 1981-1991

Australia 1981-1991

Singapore 1981-1991

Monday Negative 39.5%, Friday Positive 62% of the Time

Monday Negative; Friday Highest

Monday Negative; Hypothesis: Equal Daily Returns Rejected

Monday Negative; Wednesday, Friday Positive

Monday Negative; Last Trading Day Highest; Hypothesis of Equal Returns for all Days Rejected

Monday Negative; Last Trading Day Positive; Tuesday Lowest;

Monday Negative; Last Trading Day Positive; Tuesday Lowest Day of the Week Effect Significant

Monday Negative; Day of the Week Effect Signi~c~t

Tuesday Negative; Friday Positive

Monday PositiveI; Tuesday Negative; Wednesday Positive; Day of the Week Effect Significant

Tuesday Negative; Wednesday, Thursday, Friday Positive;

Day of the Week Effect Significant

Monday, Tuesday Returns Below Average, Friday Above Average; Day of the Week Effect Significant in Both Markets

Negative Monday Only if Preceded by Negative Friday

Monday, Tuesday, and Thursday Returns Low; Wednesday, Friday, and Saturday Returns High Last Trading Day of the Week Positive, Wednesday Positive in all Pacific Rim Markets; Day of the Week Effect Significant in Japan, Hong Kong, Australia, and Singapore

Now 1. Condoyanni, O’Hanlon, and Ward (1987) define Monday reNm as the change from Friday’s close to Monday’s close (including Saturday returns). Jaffe and Westerfteld (1985a,b) find significant positive Saturday returns. The positive Saturday remws could explain why these findings differ from the negative Monday reNmS in the Japanese market reported by other authors.


Table 2 Summary of the Day of the Week Effect in Pacific Rim and U.S. Equity Markets Preceding and Following the Crash of 1987’

Country

Pm-Crash Post-Crash

Significant’ Days F-Test3 Country Sign$icant Days F-Test

Japan Tu, We, Fr, Sa, All Significant Japan MO

Taiwan Tu, We, Th, Sa, All Taiwan

Hong Kong We, Fr Significant Hong Kong Tu, We, Fr Significant

Australia Tu, We, Th, Fr, All Significant Australia -

Singapore We, Fr Significant Singapore We -

United States Th, All United States

Norest 1. Complete statistical results are found in Appendix Tables Al and A2.

2. Significant at the five percent level for two-tailed test.

3. The F-Value for the Ho: RetM, = Ran, = Retwe = Ret,,

Although theoretically alluring as a potential explanation of pre- and post-holiday abnormal returns, the alteration in settlement period caused by exchange holidays is not consistent with empirical results (Lakonishok & Levi, 1982). Further, increased risk on these trading days is not responsible for the abnormal average returns on days preceding exchange holidays (Ariel, 1990). Jacobs and Levy (1988) offer market psychology and investor behavior as potential explanations for the aberrant returns preceding and following exchange holidays.

Table 4 shows that average returns on the days preceding market holidays during the sample period before the crash are positive and significant in all Pacific Rim markets. These returns differ significantly from other trading day returns, however, only in the Singapore market. The returns on days following market holidays are less than zero in the equity markets of Taiwan, Singapore, and the United States but do not differ significantly from zero in any of these markets. The average return on days following exchange holidays in Taiwan differs significantly from other trading days.

Table 3 Summary of Holiday Effect Empirical Studies

Author Country

Lakonishok & Smidt (1988) United States

Ariel ( 1990) United States

Howe and Wood (1993) Japan 1981-1991 Taiwan 1981-1991

Hong Kong 1981-1991 Australia 1981-1991

Singapore 1981-1991

Period Major Result(s)

1897-1986

1963-1982

Pre-Holiday Returns 20 Times Average Returns

Pre-Holiday Returns 15 Times Average Returns; 35 Percent of Total Market Return from Pre-Holiday Trading

Australian Market Pre-Holiday Returns Differ Significantly from Other Trading Day Returns

70 INTERNATIONAL REVIEW OF FINANCIAL ANALYSIS ,’ Vol. 3(l)

Table 4 Summary of the Holiday Effect in Pacific Rim and U.S. Equity Markets Preceding and Following the Crash of 1987l

Pre-Crush Post-Crash

country Pre-Holiday T-Value2 Post-Holiday T-Value Pre-Holiday T-Value Post-Holiday T-Value

Japan Significant3 - - -

Taiwan Significant - Significant - -

Hong Kong Significant - - Signi~cant - -

Australia Signi~cant - - - - - - -

Singapore Significant Significant - - - - - -

United States - - - - - -

Notes: 1. Complete statistical results are found in Appendix Tables AS and A6

2. The T-Value is the approximate t-statistic for testing the null hypothesis that the mean of the Pre-Holiday (Post- Holiday) Trading and the mean of all other trading day groups are equal under the assumption of unequal variances


In the period following the crash, the average return on days preceding holidays remains

positive in all markets except Japan; however, the returns differ significantly from zero only in the Hong Kong market. No significant difference between the average return on days before

exchange holidays and other trading days is found. The return on days following exchange holidays does not differ signi~cantly from zero nor from other trading days in any of the markets studied in the period following the crash.

V. THE TURN OF THE YEAR EFFECT

The last trading days at the end of a year and the first trading days of the following year in U.S.

equity markets have positive abnormal returns (Howe & Wood, 1993; Lakonishok & Smidt,

1988; Roll, 1983). The effect is more pronounced in small firm stocks (Roll, 1983). Cash-flow

patterns in annual bonuses, holiday gifts, and year-end pension contributions may partially

Table 5 Summary of Turn of the Year Effect Empirical Studies

Author country

Roll (1983) United States

Jaffe and Westefield (1985b) Japan Lakonishok and Smidt (1988) United States

Howe and Wood (1993) Japan Taiwan Hong Kong Australia

Singapore

Period

1963-1980

1970-1983 1897-1986

1981-1991 1981-1991 1981-1991

1981-1991 1981-1991

Major Result(s)

Small Firm Returns Differ Significantly From Large Firm Returns During the Period

No Turn of the Year Effect in the Japanese Market High Returns From the Last Trading Day Before

Christmas Through the End of the Year Returns During the Turn of the Year Period are

Positive and Significant in Taiwan, Hong Kong, Austraha, and Singapore; Average Daily Returns During the Period Differ Signi~~~~y From Other Trading Days in Hong Kong, Australia, and Singapore

Seaso~a/;tje5 and the 1987 Crash 71

Table 6 Summary of the Turn of the Year’ Effect in Pacific Rim and U.S. Equity Markets Preceding and Following the Crash of 19872

Pre-Crash Post-Crash

country Turn Period Other Days T-Value3 Country Turn Period Other Days T-Value

Japan Significant4 Significant Japan - - Taiwan Significant Significant Taiwan -

Hong Kong Significant - Signi~c~t Hong Kong - -

Australia Signi~cant Signi~c~t Signi~c~t Australia - -

Singapore Signifkxnt - Singapore Significant Significant

United States - United States - - -

Notes: 1. The Turn of the Year Period is defined as the last five trading days of year,, and the first five trading days of year,.

2. Complete statistical results are found in Appendix Tables A7 and AS.

3. The T-Value is the approximate r-statistic for testing the null hypothesis that tbe means of the two groups are equal under the assumption of unequal variances.


explain the return seasonal at the turn of the year (Jacobs & Levy, 1988). Table 5 summarizes existing empirical studies of the turn of the year phenomenon.

We define the turn of the year period as the Iast five trading days of year t-l and the first five trading days of year t. As displayed in Table 6, the average return on trading days of the turn

of the year period is positive and differs significantly from zero in all Pacific Rim markets in

the period preceding the crash (U.S. market returns are positive but not significant). The Hong

Kong and Australian markets show a significant difference between the average returns during

the turn of the year period and the average return on other trading days. In the period following the crash, all markets continue to have positive returns during the turn

of the year period but the returns differ significantly from zero only in the Singapore market.

The turn of the year period returns in the Singapore market are also significantly different from the average return on other trading days.

VI. THE MONTHLY EFFECT

Prior research of U.S. and Pacific Rim markets shows a significant difference in the average

daily return during different times of the month (Ariel, 1987; Jaffe & Westerfield, 1989; Ogden, 1990; and Howe &Wood, 1993). The monthly effect consists of higher returns in U.S., Hong Kong, and Australian equity markets during the first one-half of the month and in the Japanese

equity market during the second one-half of the month. Table 7 summarizes this literature. Ariel (1987) considers several potential explanations for the pattern of returns but finds no explanation sufficient to completely explain the phenomenon. These hypotheses include a mismatch between calendar and trading time, a dividend effect, and a manifestation of the January effect. Ogden (1990) offers the st~d~dization of payments by institutions and individuals as an explanation for the anomaly.

Using Ariel’s (1987) de~nition of the trading month, we find positive and significant average returns during the first one-half of the month in the equity markets of Taiwan and Australia

72 INTERNATIONAL REVIEW OF FINANCIAL ANALYSIS /Vol. 3(l)

Table 7 Summary of Monthly Effect Empirical Studies

Authu~ Country Period Mujor Result{sJ

Ariei (1987)’ United States 1963-1981

Lakonishok and Smidt2 (1988) United States 1897-1986 Jaffe and Westerfield (1989) Japan 1970-1983

Australia 1973-1985 Ogden (1990) United States 1969-1986 Howe and Wood (1993) Japan 1981-1991

Taiwan 1981-1991 Hong Kong 1981-1991

Australia 1981-1991 Singapore 1981-1991

First One-Half Average Returns Positive

Equal Returns for Each One-Half of the Month

Second One-Half Average Returns Positive



First One-Half Average Returns are Positive and S~~jfic~t in Hong Kong and Australia; Second One- Half Returns are Positive and Significant in Japan; The difference between the Two Period’s Returns is Significant in Hong Kong and Australia

Notes: 1. Ariel(1987). Jaffe and Westertield (1989a), and Howe and Wood (1993) define a trading month as the last trading day of the previous month (inclusive) to the last trading day of the current month (exclusive).

2. Lakonishok and Smidt (1988) define the first one-half of a trading month as I‘. the first through the fifteenth calendar day of the month if it is a trading day, or if not, through the next trading day. The last hatf of the month consists of there- maining days”.

before the 1987 crash (see Table 8). Japan and Singapore markets have significant and positive returns during the second one-half of the month. The average returns of the two halves differ significantly in Japan and Australia.

Following the crash, no significant difference in average returns of the two trading periods is found in the Pacific Rim and U.S. equity market returns. Additionally, none of the average returns for either period differs significantly from zero in any of the markets studied.

Table 8 Summary of the Monthly’ Effect in Pacific Rim and U.S. Equity Markets Preceding and Following the Crash of 19872

Pi-e-Crash Post-Crush

First Half Second Half T-Value3 First Half Second Hdf T-Value

Japan - Significant4 Significant Japan - - -

Taiwan Significant - - Taiwan - -

Hong Kong - - - Hong Kong - - -

Australia Significant - Significant Australia - -

Singapore Significant - Singapore - -

United States - - - United States - - -

Notes: 1. A trading month is defined as the last trading day of the previous month (inclusive) to the last trading day of the current month (exclusive).

2. Complete statistical results are found in Appendix Tables A9 and AlO.

3. The T-Value is the approximate t-statistic for testing the null hypothesis that the means of the two groups are equal under the a~omptioo of unequal variances.


Seasonalities and the 7 987 Crash 73

VII. THE MONTH OF THE YEAR EFFECT

Positive abnormal returns in U.S. equity markets during January are first documented by

Wachtel (1942). Abnormal returns during January are present in the U.S. markets for most of this century (Givoly & Ovadia, 1983 and Jones, Lee, & Apenbrink, 1991). Monthly seasonality

is also present in Pacific Rim equity markets (Gultekin & Gultekin, 1983; Jaffe & Westerfield,

1985b; Kato & Schallheim, 1985; Lee, 1992; and Howe &Wood, 1993). Table 9 summarizes

previous empirical research on the monthly seasonality in Pacific Rim and U.S. equity markets.

A recoil from year-end tax loss selling induced price declines is most frequently cited as

reason for persistence of the January effect (Wachtel, 1942; Branch, 1977; Gultekin & Gultekin,

1983; and Roll, 1983). A recent study by Jones, Lee, and Apenbrink (1991) supports this

hypothesis-abnormal January returns did not occur in the U.S. market until after introduction

of a personal income tax in 1917. This hypothesis lacks universal support. High January returns

occur in the Australian equity market even though the Australian tax year ends in June (Brown,

Keim, Kleidon, & Marsh (1983)). Furthermore, the rebound strength pattern is inconsistent with

tax loss theory predictions (Chart, 1986).

Rozeff and Kinney (1976) offer an informational dissemination hypothesis as an explanation of the January effect. Similarly, Penman (1987) posits that corporate news release timing

influences the return seasonality. Another hypothesis offered as explanation of the phenomenon

is institutional investor “window dressing”-ridding their portfolio of losing issues-before

Table 9 Summary of Month of the Year Effect Empirical Studies

Author Country Period Major Result(s)

Bonin & Moses (1974)

Rozeff & Kinney (1976)

Givoly & Ovadia (1983)

Gultekin & Gultekin (1983)

Keim (1983)

Jaffe & Westerfield (1985b)


United States 19041974



Australia 19.59-1979

Singapore 1970-1979


Japan 197&1983

Kato and Schallheim (1985) Japan 19641981

Jones, Lee, and Apenbrink (1991) United States 1899-1929

Lee (1992)

Howe and Wood (1993)

Hong Kong 197C1989

Singapore 1970-1989

Taiwan 197&1989

Japan 1975-1989

Japan 1981-1991

Taiwan 1981-1991

Hong Kong 1981-1991

Australia 1981-1991

Singapore 1981-1991

Significant Seasonal Pattern

Significant Monthly Pattern

January Returns High

No Pattern in U.S. Returns; Australia and Singapore Have High January Returns

January Size Effect Significant

January Returns Significant; Significant Monthly Effect

January Effect Present

January Returns Significant in Last One-Half of Sample Period

Significant Monthly Pattern in All Markets

January Returns Significant and Positive in Japan, Taiwan, Hong Kong, and Singapore; Significant Month of the Year Effect in Taiwan, Australia, and Singapore

74 INTERNATIONAL REVIEW OF FINANCIAL ANALYSIS /Vol. 3(l)

Table 10 Summary of the Month of the Year Effect in Pacific Rim and U.S. Equity Markets Preceding and Following the Crash of 1987’

Pre-Crash Post-Crash

Countty SigniJicant2 Months F-Test3 Country Significant Months F-Test

Japan Jan, Mar, Nov, Dee, All - Japan - -

TaiWail Feb. Apr, Sep, All Taiwan Jan, Feb -

Hong Kong Jan, Apr - Hong Kong Jill -

Australia Mar, Apr, Aug, All Sjgni~cant Australia JUl -

Singapore Feb, Apr - Singapore Jan, Mar, Aug Significant

United States All United States Dee -

~oresr 1. Complete statistical results are found in Appendix Tables At 1 and A12. 2. Significant at the five percent level for two-tailed test. 3. The F-Value for the Ho: Ret,, = Re+, = RetMu = = Retkp

annual report preparation (Givoly & Ovadia, 1983; Bildersee & Kahn, 1987; and Ritter &

Chopra, 1989). Inventory adjustment by market participants may also explain the phenomenon

(Ritter, 1988). Seasonal risk patterns may be responsible for the seasonal return regularities (Tinic & West,

1984 and Corhay, Hawawini, & Michel, 1987). Admati and Pfleiderer (1988) suggest that the

timing of trades by informed and uninfo~ed traders may explain the seasonality. Year-end

cash flow patterns from bonuses, gifts, and pension plan contributions may also be responsible

for the pattern in U.S. equity market returns (Lakonishok & Smidt, 1986 and Jacobs & Levy,

1988). Kato and Schallheim (1985) find the seasonal equity in Japan mirrors semiannual bonus

payments. The decline in significance of this pattern in recent years may be due to the decrease

of arbitrage opportunities from initiation of futures trading (Maberly & Maris, 1991). Each of

these theories in and of themselves is inadequate to explain the anomaly but a combination of

these factors may explain the seasonality’s perseverance.

As shown in Table IO, the Australian market is the only market in our study to show a

significant difference in monthly returns in the period preceding the crash. January returns are

greater than zero in all markets, but differ signi~c~tly from zero only in Japan and Hong Kong.

April returns are positive and significant in Taiwan, Hong Kong, Australian, and Singapore

equity markets. The difference in monthly returns is significant only in the Singapore market following the

crash. A dramatic decrease in the number of months with average returns significantly different

from zero also occurs following the crash. January returns remain positive in all markets but

differ significantly from zero only in Taiwan and Singapore.

VIII. DISCUSSION

The incidence of calendar anomalies in Pacific Rim and U.S. equity markets decreases

dramatically following the intemational crash of 1987. Two potential explanations for this

change exist. First, the seasonal anomalies present in the period preceding the crash can simply


be artifacts of the sample period. However, it seems unlikely that “anomalies” documents in diverse economic climates and differing institutional settings are purely coincidences.

Second, the decrease may represent an alteration of the returns generating mechanism in these markets. Leland and Rubinstein (1988) document an approximate doubling of volatility in the U.S. market in the six months following the crash. In our sample period, volatility (as measured by standard deviation) is approximately twice as high in the subperiod following the crash than

it is in the subperiod preceding the crash in each market studied. ‘Ibis increased volatility is indirect evidence of a change in the returns generating mechanism of these markets. Changes in volatility may account for the decrease in the significance of return anomalies. However,

many of the patterns are altered to a degree that the increase in volatility cannot solely be responsible for a decrease in the presence of trading regularities.

In sum, the international crash of 1987 was unpr~dented in its severity and the number of geogr~hicaIly diverse markets it affected. The incidence of return seasonalities previously documented in Pacific Rim and U.S. equity markets decreases dramatically in the period following the crash. We posit that an alteration in the returns generating process in these markets is the most likely cause of the change in the trading patterns.

APPENDIX

Table Al Average Percent Returns on Country Common Stock Indexes by Day of the Week’ (January 1,198l-September 30,1987)

Monday Tuesday Wednesday Thursdffy Friday Satz~rd~ All Days

TOKYO Nikkei Stock Average

Mean 0.0314 Std. Dev. 0.7157

Observations 313 T:Mea.u=O 0.7774 F Value’

TAIWAN Weighted Stock Index

Mean 0.0280 Std. Dev. 1.3323 Observations 316 T:Mean=O 0.3731 F Value

HONG KONG Hang Seng Index

Mean -0.1581 Std. Dev. 2.2296 Observations 314 T:Mean=O -1.2568 F Value

AUSTRALIA All Ordinaries Index

Mean 0.0544 Std. Dev. 0.9400

-5.1295 0.2008 0.0796 0.1083 0.7271 0.7161 0.8173 0.7263

332 335 329 326 -3.2423** 5.1333** 1.7671 2.6922**

0.1219 0.1648 0.1296 0.0171

1.1253 1.0654 0.9392 1.1397 332 330 332 329

1.9731x 2.8101** 2X38* 1.2364

-0.0165 0.2174 0.1001 0.2240 1.6398 1.5013 1.8417 1 S988

341 337 342 332 -0.1862 2.6578** 1.0049 2.5529*

-0.0958 0.1040 0.0968 0.1901 0.0698

0.8682 0.8530 0.8357 0.7981 0.8636

0.1881 0.0737 0.5952 0.7337

217 1852 4.6552** 4.3216**

8.694**

0.1546 0.1131 1.1048 1.1216

318 1957 2.4954* 4.4622**

0.675

0.0760 1.7782

1666 1.7437 2.726*

76 INTERNATIONAL REVIEW OF FINANCIAL ANALYSIS /‘Vol. 31)

Table Al (continued)

(January 1, 1981~September 30, 1987)

Monday Tuesday Wednesday Thursday Friday Saturday All Days

AUSTRALIA

Observations 325

T:Mean=O 1.0431

F VaIue

SINGAPORE

Strait Times Index

Mean -0.0543

Std. Dev. 1.2337

Observations 332

T:Mean=O -0.8014

F Value

UNITED STATES

Standard & Poors 500

Mean -0.0507

Std. Dev. 0.9667

Observations 327

T:Mean=O -0.9488

F Value

346 347 346 341

-2.0530* 2.2713* 2.1.552* 4.3984**

1705

3.3355**

5.132**

-0.0316 0.1441 0.0609 0.1427

1.1099 1.1206 1.1967 1.0919

335 343 338 328

-0.5209 2.3811* 0.9359 2.3672*

0.0526

1.1536

1676

1.8681

2.209*

0.0491 0.0807 0.1100 0.0792

0.9778 0.8422 0.8477 0.8190

350 349 342 338

0.9388 1.7891 2.3996* 1.7782

0.0546

0.8936

1706

2.5234*

1.608

Nofes.- 1. Returns am computed as r, = ((q - v,_t)fv,_l) x 100, where v, is the value of the index at end of day t.

2. The F-Value for the Ho: Re& = Re&= Reiwe = Ret,

* Significant at five percent level for hvo-tailed test.

**Significant at one percent level for two-tailed test.

Table A2 Average Percent Returns on Country Common Stock Indexes by Day of the Week’ (November 1,1987-December 31,199l)

Monday Tuesday Wednesday Thursday Friday Saturday All Days

TOKYO

Nikkei Stock Average

Mean

Std. Dev.

Obseffations T:Mean=O

F Value2 TAIWAN

Weighted Stock Index

Mean

Std. Dev. Observations

T:Mean=O F Value

HONG KONG

Hang Seng Index Mean Std. Dev.

Observations T:Mean=O

F Value

-0.2315 0.1135

1.5683 1.4375

197 207

-2.0720* 1.1360

0.0305 0.0153 0.0850

1.4604 1.4586 1.1823

210 205 204 0.3031 O.lSOO 1.5273

0.0023 0.0046

0.8107 1.4137

32 105s

0.0164 0.1058 1.491

0.1044 0.0637 -0.2012 -0.1427 0.1372

2.7681 2.5964 2.7141 2.8381 2.6631 199 206 204 204 206

0.5322 0.3520 -1 .OS88 -0.7180 0.7392

0.3097 0.0801 2.4595 2.6427

190 1186

1.7354 1.0443

0.918

-0.3194 0.2160 0.1909 0.0772 0.1831

2.4065 1.5147 1.2128 1.3401 1.2366 19s 211 210 211 204 -1.8530 2.0713* 2.28&t* 0.8371 2.1147*

0.0747 1.6010

1031 I .4983

3.918**

Seaso~al~t~es and the 1987 Crash 77

Table A2 (continued)

Tuesday We~es~y Thursaky Friday S&M-day All Days


Mean Std. Dev. Observations T:Mean=O F Value

SINGAPORE Strait Times Index


UNITED STATES Standard & Poors 500


1.2419

198 -0.2652

-0.1001 -0.0118 0.1753 0.1147 0.1186 1.6716 1.1390 1.0078 1.1362 0.9867

202 206 210 211 207 -5.8511 -0.1482 2.5202* 1.4669 1.7297

0.0799 0.0930 0.1004 -0.0726 0.0639 1.1059 0.8648 0.8594 0.9939 1.1663

201 215 215 211 211 1.0244 1.5772 1.7125 -1.0615 0.7961

0.0655 0.0238 0.0286 0.0227 0.9088 0.9339 0.9791 0.9360

211 213 214 209 1.0465 0.3719 0.4269 0.3505

0.0240 1.0026

1045 0.7746 0.202

0.0607 1.2126

1036 1.6123 1.769

0.0530 1.0039

1053 1.7130 1.074

Noies: I. Rehuns are computed as rr = ((v, - v,-t)/v,-t) x 100, where v, is the value of the index at end of day t. 2. The F-Value for the HO: Ret,, = Re+,,= Re& . = Rat,, * Significant at five percent level for two-tailed test. **Significant at one percent level for two-tailed test.

Table A3 Friday Mean Returns in the Japanese Equity Market witb and without Saturday Trading (January I, 198l-September 30,1987)

Friday Trading Followed by Saturday Trading’

Friday Trading not Followed by Saturday Trading T- V&e2


Mean 0.1187 0.0841 Standard Deviation 0.7365 0.7003 T: Mean=0 2.4503* 1.1773 Observations 231 96 T-Value 0.3924

Notes: 1. The Japanese market closed on the second Saturday of the month through July, 1986 and the second and third Saturdays each month from August, 1986 through January, 1989. Saturday uading was suspended in February, 1989.

2. The T-Value is the approximate ~-statistic for testing the null hypothesis that the means of the two groups are equal under the ~sumption of unequal variances.

*Significant at five percent level for two-tailed test. **Significant at one percent level for two-tailed test.

78 INTERNATIONAL REVIEW OF FINANCIAL ANALYSIS / Vol. 3(l)

Table A4 Friday Mean Returns in the Japanese Equity Market with and without Saturday Trading (November 1,1987-December 31,1992)

Friday Trading Followed by Saturday Trading’

Friday Trading not Followed by Saturday Trading T-Value2

TOKYO


Mean -0.1220 0.1221

Standard Deviation 0.6414 1.2526

T: Mean=0 -1.0584 1.2823

Observations 31 173

T-Value -1.059

Notes: 1. The Japanese market closed on the second Saturday of the month through July, 1986 and the second and third Saturdays each month from August, 1986 through January, 1989. Saturday trading was suspended in February, 1989.

2. The T-Value is the approximate r-statistic for testing the null hypothesis that the means of the two groups are equal under the assumption of unequal variances. ‘Significant at five percent level for two-tailed test.


Table A5 The Holiday Effect in Pacific Rim and U.S. Stock Markets (January 1,198l-September 30,1987)

TOKYO

Nikkei Stock Index

Mean

Standard Deviation

T: Mean=0

Observations

T-Value3

TAIWAN


Mean

Standard Deviation

T: Mean=0

Observations

T-Value

HONG KONG

Hang Seng Index

Mean

Standard Deviation

T: Mean=0

Observations

T-Value

AUSTRALIA

All Ordinaries Index

Mean

Standard Deviation

T: Mean=0

Pre-Holiday’ Trading

0.2120

0.6077

3.0810**

78

0.2693

0.9015

2.8809**

93

All Other Trading Days

0.0681

0.7384

3.8832**

1775

1.696

0.1059

1.1311

4.0422**

1865

1.380

Post-Holiday2 Trading

0.1818

0.8404

1.9224

79

a.1196

1.3054

Xl.8885

94


0.0693

0.7286

4.0075**

1774

1.334

0.1254

1.1106

4.8747**

1864

-2.068*

0.0609 0.2328 0.0706

1.7809 2.5488 1.7379

1.3661 0.7641 1.6232

1598 70 1597

1.828 0.747

Observations

T-Value

0.4603

1.6911

2.2612*

69

0.2783

0.4708

3.6917**

0.0649 0.1060 0.0689

0.8699 0.9950 0.8602 3.0440 0.6734 3.2675**

39 1641 40 1666

1 S27 0.269



Pm-Holiday ’ Trading

All &her Trading Days

Post-Holiday2 Truding

AI1 Other Trading DW

SINGAPORE Strait Times tndex

Mean Standard Deviation T: Mean=0 Observations T-Value



0.4178 1.0255 3.2oso**

62

0.1577 0.6232 1.8248

52

0.0386 1.1562 1.3416

1614 2.549’

0.0513 0.9007 2.3186*

1654 0.845

-o.oQm 2.1880

-0.0319 63

-0.0625 1.0864

-0.4191 53

0.0550 1.0947 2.0192*

1613 -0.431

0.0583 0.8868 2.6749

1653 -0.969

Nom: 1. Pre-Holiday Trading is defined as the last trading day before a scheduled exchange holiday. 2. Post-Holiday Trading is defined as the first trading day after a scheduled exchange holiday. 3. The T-Value is the approximate r-statistic for testing the null hypothesis that the means of the two groups are equal un- $5 the assumption of unequal variances. l significant at five percent level for two-tailed test.

Significant at one percent level for two-tailed test.

Table A6 The Holiday Effect in Pacific Rim and U.S. Stock Markets (November 1,1987-December 31,199l)

Pre-Holiday’ Trading

At1 Other Trading Days

Post-Holiday* Trading


TOKYO Nikkei Stock Index

Mean Standard Deviation T: Mean=0 Observations T-Value3

TAIWAN Weighted Stock Index




-0.0010 1.3617

-0.0052 45

0.3479 2.6975 1.0714

69

0.3825 1.0836 2.2325*

40

0.0049 1.4167 0.1089

1010 -0.027

0.0655 2.6393 0.8301

1118 0.861

0.0623 1.6176 1.2122

991 1.240

0.0084 1.5246 0.0364

44

0.2884 3.3281 0.7198

69

0.4188 I .4336 1.8242

39

0.0044

1.4095

0.1002 1011

0.018

0.0692 2.5954 0.8914

1118 0.669

0.0612 1.6064 1.1996

992 1.369

80 INTERNATIONAL REVIEW OF FINANCIAL ANALYSIS /‘Vol. 3(?)


Pre-Holiday’ All Other Trading Trading Days

Post-Holiday2 Trading


AUSTRALIA


MeFIn

Standard Deviation

T: Mean=0

Obse~ations

T-Value

SINGAPORE

Strait Times Index

Mean

Standard Deviation

T: Mean=0

Observations

T-Value

UNITED STATES


Mean

Standard Deviation

T: Mean=0

Obse~ations

T-Value

0.3037

0.8378

1.9857

30

0.2081

0.6869

1.8673

38

0.1995

0.7551

1.5629

35

0.0158

1.0062

0.4990

1015

1.551

0.0551 1.2280

1.4182

998

0.764

0.0480 1.0112 1.5131

1018

0.878

0.0484

1.0084

0.2587

29

0.2318

1.1797

1.1953

37

0.0978

1.3151

0.4337

34

0.0233

1.0029

0.7414

1016

0.135

0.0544 1.2139

1.4166

999

0.874

0.0515

0.9926

I .6562

1019

0.264

Nores: 1. Pre-Holiday Trading is defined as the last trading day before a scheduled exchange holiday.

2. Post-Holiday Trading is defined as the first trading day after a scheduled exchange holiday.

3. The T-Value is the approximate r-statistic for testing the null hypothesis that the means of the two groups are equal under the assumption of unequal variances. *Significant at five percent level for two-tailed test.


Table A7 Turn of the Year’ Effect in Pacific Rim and U.S. Stock Markets (January 1,198l-September 30,1987)

Turn qf the Year Period All Other Day


Mean

Standard Deviation

T: Mean=0

Observations

T-Value

TAIWAN


Mean

Standard Deviation

T: Mean=0

Observations

T-Value

0.2120 0.0688

0.5275 0.7403

3.2395** 3.9230**

65 1’784

0.3058 0.1065

0.7666 1.1314

3.2157** 4.0951**

65 1892

1.545

1.409

Seasonalities and the I987 Crash


81

Turn of the Year Period AI1 Other Days T-V&S2


Mean 0.6753 0.0516 Standard Deviation 1.2712 1.7918 T: Mean=0 4.2a27** 1.1530

Observations 65 1601

T-Value 2.778** AUSTRALIA

All Ordinaries Index MCWl 0.3123 0.0601 Standard Deviation 0.7366 0.8670 T: Mean=0 3.4178** 2X093** Observations 65 1640 T-Value 2.312*


Mean 0.3161 0.0420 Standard Deviation 0.8836 1.1621 T: Mean=0 2.8844** I .4509 Observations 65 1604 T-Value 1.880


Mean 0.0984 0.0529 Standard Deviation 1.0083 0.8890 T: Mean=0 0.7867 2.4085 Observations 65 1641 T-Value 0.403

Nom: 1. Turn of the year is defined as the first five trading days of yea13 and the last five trading days of ye*,_, 2. The T-Value is the approximate t-statistic for testing the null hypothesis that the means of the two groups are equal under the assumption of unequal variances. ‘Significant at five percent level for two-tailed test. “Significant at one percent level for two-tailed test.

Table A8 Turn of the Year’ Effect in Pacific Rim and U.S. Stock Markets (November 1,1987-December 31,199l)

Turn ofthe Year Period AU Other Days T-Value2


MetUl Standard Deviation T: Mean=0 Observations

T-Value

0.0577 0.0022 1.4853 1.4112 0.2604 0.0505

45 1010

0.258



Turn of ihe Year Period All Other Days T-Value2

TAIWAN


Mean

Standard Deviation

T: Mean=0

Observations T-Value

HONG KONG

Hang Seng Index

Mean

Standard Deviation T: Mean=0

Observations

T-Value

AUSTRALIA


Mean

Standard Deviation

T: Mean=0

Observations

T-Value

SINGAPORE

Strait Times Index

Mean


Observations

T-Value

UNITED STATES


Mean Standard Deviation

T: Mean=0

Observations

T-Value

0.5888 0.0601

3.0639 2.6243

1.2891 0.7733

45 1141

0.2223 0.0680

1.3358 1.6123 1.1164 1.3238

45 984

0.1289 0.0193

0.8645 1.0085

0.9998 0.6054

45 1588

0.5398 0.0390

1.2897 1.2052

2.8077** 1.0184

45 984

0.0084 0.0550

1.4734 0.9787

0.0382 1.7837

45 1008

1.317

0.632

0.717

2.7174**

a.305

Notes; 1. Turn of the Year is defined as the first five trading days of year, and the last five trading days of Y=kl. 2. The T-Value is the approximate t-statistic for testing the null hypothesis that the means of the two groups are equal under the assumption of unequal variances. *Significant at five percent level for two-tailed test. **Significant at one percent level for two-tailed test.


Table A9 The Monthly’ Effect in Pacific Rim and U.S. Stock Markets (January 1,198lSeptember 30,1987)

First Nine Tradig Days ht Nine Trading Days T-Value2

TOKYO


Mean 0.0430 0.1183 Standard Deviation 0.6813 0.7521 T: Mean=0 1.7066 4.2427** Observations 729 729 T-Value -2.003*

TAIWAN


Mean 0.1221 0.1042 Standard Deviation 1 BY29 1.1420 T: Mean=0 3.0095** 2.4610 Observations 729 729 T-Value 0.306

HONG KONG

Hang Seng Index

Mean 0.0795 -0.0117 Standard Deviation 1.9028 1.7034 T: Mean=0 1.1262 -0.1844 Observations 729 729 T-Value 0.964


Mean 0.1342 0.0154 Standard Deviation 0.9126 0.8370 T: Mean=0 3.9710** 0.4979 Observations 729 729 T-Value 2.590**

SINGAPORE

Strait Times Index

Mean 0.0425 0.0862 Standard Deviation 1.2371 1.1103 T: Mean=0 0.9230 2.0869* Observations 729 729 T-Value -0.710

UNITED STATES


Mean 0.0605 0.0418 Standard Deviation 0.9115 0.8819 T: Mean=0 1.7907 1.2805 Observations 729 729 T-Value 0.398

Notes: 1. A trading month is defined as the last trading day of the previous month (inclusive) to the last trading day of the current month (exclusive). 2. The T-Value is the approximate f-statistic for testing the null hypothesis that the means of the two groups are equal under the assumption of unequal variances. ‘Significant at five percent level for two-tailed test. “Significant at 1 percent level for two-tailed test.


Table A10 The Monthly’ Effect in Pacific Rim and U.S. Stock Markets (November 1,1987-December 31,199l)

First Nine Truding Days Last Nine Trading Days T-Value2

TOKYO

Nikkei Stock Average Mean

Standard Deviation

T: Mean=0

Observations

T-Value

TAIWAN

Weighted Stock Index Mean

Standard Deviation

T: Mean=0

Observations

T-Value


Mean


Observations

T-Value

AUSTRALIA


Mean

Standard Deviation

T: Mean=0

Observations

T-Value


Mean

Standard Deviation

T: Mean=0

Observations

T-Value UNITED STATES


Mean

Standard Deviation

T: Mean=0

Observations

T-Value

-0.0144 a.0340

1.6371 1.2241

4.1868 4.5899

450 450

0.203

0.0783 0.0780 2.6704 2.6503 0.6216 0.6228

450 450

0.002

0.1583 ~0444 1.7287 1.543 1

1.9334 -0.6093

450 450

1.856

0.0016 0.0121

0.9985 0.9006 0.0336 0.2849

450 450

-0.166

0.0573 0.0522 1.2099 1.1417

1.0030 0.9694 450 450

-0.710

0.0770 -0.0056

1.0125 0.9375 1.6129 -0.1258

450 450

1.270

Nores: 1. A trading month is defined as the last trading day of the previous month (inclusive) to the last trading day of the cumznt month (exclusive).

2. The T-Value is the approximate ~-statistic for testing the null hypothesis that the means of the two groups are equal under the assumption of unequal variances. ‘Significant at five percent level for two-tailed test.

*‘Significant at one percent level for two-tailed test.

Tab

le

All

Ave

rage

P

erce

nt

Dai

ly

Ret

urns

on

Cou

ntry

C

omm

on

Stoc

k In

dexe

s by

Mon

th

of t

he Y

ear’

All

2 4

Jan.

Fe

b.

Mar

. A

pr.

May

Ju

ne

July

A

ug.

Sep.

O

ct.

Nov

. D

ec.

Mon

ths

3 fn

(Jan

uar

y 1, 1

981-

Sep

tem

ber

30,1

987)

g

TO

KY

O

Nik

kei

Sto

ck A

vera

ge

Mea

n

0.13

08

0.01

51

0.18

81

0.10

05

0.04

63

a.07

06

-0.0

246

0.11

83

-0.0

511

0.03

77

0.12

96

0.12

03

Std

. Dev

. 0.

5533

0.

5502

0.

7731

0.

7820

0.

9110

0.

6505

0.

8286

0.

7309

0.

7121

0.

9739

0.

5579

0.

5528

0.

7337

O

bser

vati

ons

155

148

172

161

153

171

171

170

146

147

131

127

1852

T

:Mea

n=

O

2.94

36**

0.

3346

3.

1924

**

1.63

00

0.62

81

1.41

93

a.38

80

2.11

12

-0.8

674

0.46

92

2.65

76**

2.

4523

* 4.

3220

**

F V

alu

e’

1.46

3 T

AIW

AN

W

eigh

ted

Sto

ck A

vera

ee

Mea

n

Std

. Dev

. O

bser

vati

ons

T:M

ean

=O

F

Val

ue

HO

NG

KO

NG

H

ang

Sen

g In

dex

Mea

n

Std

. Dev

. O

bser

vati

ons

T:M

ean

=O

F

Val

ue

AU

ST

RA

LIA

” 0.

1218

0.

2427

0.

1436

0.

2046

a.

0524

0.

0174

0.

0230

0.

1465

0.

3348

0.

0587

0.

0044

0.

1314

0.

1131

0.

7920

0.

9397

1.

1395

1.

3207

1.

2679

1.

1959

1.

1184

1.

1658

1.

3995

1.

0587

0.

9112

0.

7771

1.

1216

14

8 14

1 17

8 17

4 18

5 17

1 17

9 18

3 16

6 14

3 14

3 14

6 19

57

1.87

10

3.06

68**

1.

6813

2.

0439

* -0

.562

5 0.

1902

0.

2749

1.

7005

3.

0823

**

0.67

63

0.05

76

2.04

34

4.46

22**

1.

657

0.37

38

0.07

91

4.19

09

0.27

38

0.10

48

0.01

69

0.09

35

a.00

30

-0.2

980

0.13

04

0.20

18

0.19

67

0.07

47

1.58

89

1.50

18

1.85

38

1.54

80

1.46

58

1.55

12

1.65

00

1.94

19

1.94

45

2.65

56

1.85

66

1.47

25

1.77

80

142

129

154

132

152

140

150

144

147

123

128

124

1665

2.

8037

**

0.59

81

-1.2

778

2.03

22*

0.88

12

0.12

86

0.69

37

a.01

85

-1.8

579

0.54

47

1.22

99

1.48

75

1.71

44

1.63

3

All

Ord

inar

ies I

nde

x M

ean

0.

0573

-0

.123

3 0.

1659

0.

2751

a.

0257

4.

1222

0.

1315

0.

1823

0.

0938

0.

0401

0.

0649

0.

0817

0.

0697

S

td. D

ev.

0.80

06

0.89

56

0.94

20

0.90

84

0.93

69

0.79

40

0.90

18

0.82

06

0.83

07

0.93

82

0.83

64

0.59

40

0.86

33

Obs

erva

tion

s 13

8 14

0 15

2 13

9 15

3 14

2 15

7 15

3 15

1 13

3 12

7 12

1 17

06

T:M

ean

=O

0.

8400

-1

.628

3 2.

1720

* 3.

5701

**4.

3389

-1

.835

3 1.

8277

2.

7475

**

1.38

83

0.49

25

0.87

43

1.51

25

3.33

60**

F

Val

ue

2.70

0**

E

Tab

le

All

(con

tinu

ed)

JaJl

. Fe

b.

Mar

. A

pr.

May

Ju

ne

July

A

ug.

Sep.

O

ct.

Nov

. D

ec.

All

M

onth

s

SIN

GA

PO

RE

S

trai

t Tim

es I

nde

x M

ean

0.

1795

0.

2380

a.

0390

S

td. D

ev.

1.10

95

1.16

83

0.97

92

Obs

erva

tion

s 14

1 12

5 15

3 T

:Mea

n=

O

1.92

08

2.27

76*

-0.4

924

F V

alu

e U

NIT

ED

ST

AT

ES

S

tan

dard

& P

oors

500

M

ean

0.

0981

0.

0533

0.

8993

S

td. D

ev.

0.97

56

0.89

76

0.84

14

Obs

erva

tion

s 14

6 13

4 15

3 T

:Mea

n=

O

1.21

48

0.68

77

1.32

20

F V

alu

e

0.16

17

0.11

35

0.09

09

-0.1

121

a.03

53

0.00

29

0.04

61

0.75

43

1.00

38

1.05

95

1.22

37

1.48

29

1.20

77

1.06

64

146

141

147

140

158

149

130

2.59

00*

1.34

26

1.03

97

-1.0

843

-0.2

989

0.02

96

0.49

3 1

0.06

12

0.01

07

0.05

50

-0.0

585

0.14

86

-0.1

047

0.15

55

0.87

78

0.78

14

0.77

46

0.78

16

1.02

16

1.01

62

0.94

41

146

146

150

150

153

143

134

0.84

21

0.16

49

0.86

95

XI.

9160

1.

7987

-1

.232

0 1.

9066

0.01

93

-0.0

039

0.05

32

1.15

54

1.46

51

1.15

37

125

120

1675

0.

1863

-0

.029

0 1.

8884

1.

110

0.12

55

0.03

12

0.05

46

0.93

97

0.82

71

0.89

36

122

129

1706

1.

4757

0.

4285

2.

5234

* 1.

105

Nor

es:

I.

A t

radi

ng m

onth

is

defi

ned

as t

he p

erio

d fr

om t

he l

ast

trad

ing

day

of t

he p

revi

ous

mon

th

(inc

lusi

ve)

thro

ugh

the

last

tra

ding

da

y of

the

pre

sent

mon

th

(exc

lusi

ve).

2.

The

F-V

alue

fo

r th

e H

o: R

et,,

= R

erFC

b = R

erM

, =

= R

e&

‘Sig

nifi

cant

at

riv

e pe

rcen

t le

vel

for

two-

taile

d te

st.

“Sig

nifi

cant

at

one

per

cent

lev

el

for

two-

taile

d te

st.

3 k 0

Tab

le

Al2

2

Ave

rage

P

erce

nt

Dai

ly

Ret

urns

on

Cou

ntry

C

omm

on

Stoc

k In

dexe

s by

Mon

th

of t

he Y

ear

3 z s A

ll

Jan.

Fe

b.

Mar

. A

pr.

MaY

Ju

ne

July

A

ug.

Sep.

O

ct.

Nov

. Q

D

ec.

Mon

th

3 CD

(N

ovem

ber

1, 1

987-

Dec

embe

r 31

, 19

91)

TO

KY

O

:

Nik

kei

Sto

ck A

vera

ge

Mea

n

0.13

42

0.11

29

-0.0

226

0.03

05

; 0.

1283

-0

.146

1 0.

0313

a.

2774

-0

.038

8 0.

2344

4.

1318

0.

0549

0.

0046

Std

. Dev

. 1.

4987

1.

0511

1.

1996

2.

2037

0.

7272

0.

8377

1.

0401

1.

7947

1.

2807

1.

9022

1.

3564

1.

2892

1.

4137

9

Obs

erva

tion

s 81

77

87

84

83

87

90

93

80

88

10

2 10

3 10

55

T:M

ean

=O

0.

8063

0.

9425

-0

.175

5 0.

1267

1.

608

1 -1

.626

9 0.

2858

-1

.490

7 a.

2706

1.

1558

-0

.981

7 0.

4322

0.

1058

F

Val

ue’

0.

911

TA

IWA

N

Wei

ghte

d S

tock

Ave

rage

M

ean

0.

6685

0.

6123

-0

.010

0 0.

3933

-0

.051

3 -0

.180

2 0.

0405

-0

.293

1 0.

0257

-0

.166

8 0.

3154

a.

3902

0.

0788

Std

. Dev

. 3.

0917

2.

2195

1.

9428

2.

0977

2.

5514

2.

7779

1.

0146

3.

0143

2.

4431

3.

0062

2.

5853

2.

8005

2.

6420

Obs

erva

tion

s 88

77

10

3 95

10

5 96

16

1 10

7 90

91

12

3 11

3 11

87

T:M

ean

=O

2.

0285

* 2.

4206

* a.

0524

1.

8276

X

J.20

61

-0.6

357

0.50

64

-1.0

060

0.09

99

a.52

94

1.35

32

-1.4

811

1.02

81

F V

alu

e 1.

623

HO

NG

KO

NG

H

ang

Sen

g In

dex

Mea

n

0.22

27

0.20

03

0.16

86

-0.0

096

a.05

81

-0.0

820

0.29

96

a.22

78

-0.0

240

0.18

35

0.04

23

0.17

53

0.07

41

Std

. Dev

. 1.

2699

1.

3553

1.

4415

1.

0745

2.

1277

2.

8893

0.

8959

1.

8678

0.

8676

1.

3333

1.

5851

1.

4140

1.

6010

Obs

erva

tion

s 84

72

86

76

90

79

87

86

81

84

10

7 99

10

31

T:M

ean

=O

1.

6071

1.

2539

1.

0844

a.

0782

-0

.258

9 4.

2522

3.

1195

** -

1.13

08

X1.

2485

1.

2616

0.

2758

1.

2338

1.

4983

F V

alu

e 0.

795

AU

ST

RA

LIA

A

ll O

rdin

arie

s In

dex

Mea

n

0.08

56

-0.1

079

0.17

74

0.06

06

0.10

61

0.00

13

0.21

35

0.02

34

4.14

51

0.00

13

-0.0

773

-0.0

333

0.02

40

Std

. Dev

. 0.

996

1 1.

0885

0.

9232

0.

8314

0.

8463

0.

7141

0.

6810

1.

0297

0.

7546

1.

3207

1.

4882

0.

8562

1.

0026

Obs

erva

tion

s 81

80

86

75

90

81

87

91

83

88

10

6 97

10

45

T:M

ean

=O

0.

7735

-0

.886

4 1.

7818

0.

6314

1.

1891

0.

0160

2.

9238

**

0.21

63

-1.7

472

0.00

91

-0.5

346

a.38

29

0.77

46

F V

alu

e 1.

033

e

Tab

le

Al2

(c

onti

nued

)

Jan

Feb

M

ar

Apr

M

aY

Jun

Jul

At%

se

p O

tt

Nov

D

ee

All

M

onth

s

SIN

GA

PO

RE

S

trai

t Tim

es I

nde

x M

ean

0.

3543

S

td. D

ev.

1.57

06

Obs

erva

tion

s 84

T

:Mea

n=

O

2.06

77*

F V

alu

e U

NIT

ED

ST

AT

ES

Sta

nda

rd &

Poo

rs 5

00

Mea

n

0.04

47

Std

. Dev

. 1.

3623

O

bser

vati

ons

85

T:M

ean

=O

0.

3026

F

Val

ue

0.16

71

0.19

29

0.07

85

0.11

47

0.09

52

0.09

33

-0.4

288

a.15

08

0.04

14

1.05

31

0.79

46

0.80

19

0.71

80

0.93

64

0.90

64

1.87

63

0.81

99

1.60

83

75

87

80

82

84

82

87

83

88

1.37

39

2.26

42*

0.87

60

1.44

62

0.93

17

0.93

19

-2.1

313*

-1

.675

8 0.

2417

0.14

60

0.06

21

0.04

69

0.14

28

0.03

61

0.09

44

a.07

43

-0.0

631

0.01

49

0.93

82

0.81

30

0.95

88

0.77

77

0.93

77

0.76

49

1.10

88

0.71

37

1.22

20

77

87

82

87

85

83

91

80

88

1.36

55

0.71

29

0.44

32

1.71

32

0.03

61

1.12

43

X1.

6390

a.

7904

0.

1143

0.02

64

0.16

08

0.06

07

1.23

47

1.32

32

1.21

26

105

99

1036

0.

2189

1.

2094

1.

6123

2.

241*

-0.0

412

0.21

82

0.05

30

1.06

04

1.11

23

1.00

39

103

105

1053

a.

3941

2.

0101

* 1.

7130

0.

720

Noz

es:

1.

A t

radi

ng m

onth

is

defi

ned

as t

he p

erio

d fr

om t

he l

ast

trad

ing

day

of t

he p

revi

ous

mon

th

(inc

lusi

ve)

thro

ugh

the

last

tra

ding

da

y of

the

pre

sent

mon

th (

excl

usiv

e),

2.

The

F-V

alue

fo

r th

e H

o: R

et,,

= R

etpe

b = R

e&,

=

= R

q,,

*Sig

nifi

cant

at

fiv

e pe

rcen

t le

vel

for

two-

taile

d te

st.

“Sig

nifi

cant

at

one

per

cent

lev

el

for

two-

taile

d te

st.

~easo~alities and the 7 987 Crash 89

NOTE

1. Supporting numbers that are not consequential part of the text here appear in the Appendix of this paper and are in a collection of tables numbered Al-Af2.

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