Journal of Banking and Finance l0 (1986) 431-445. North-Holland

W E A K - F O R M E F F I C I E N C Y IN T H E K U A L A L U M P U R A N D S I N G A P O R E S T O C K M A R K E T S

Mar t in M. L A U R E N C E *

The William Paterson College of New Jersey, Wayne, NJ 07470, USA

Received October 1984, final version received June 1985

Previous weak-form efficiency tests of the Kuala Lumpur and Singapore stock markets have mixed findings but mostly have suggested close conformity with a random walk. Using a disparate type of sample data over a longer and diverse time period, this paper seeks to replicate the earlier investigations of these two thin markets in order to verify whether the previous results may be sample specific. The distribution of daily stock returns is also examined to determine the validity of using statistical tests based on the normality assumption. Results tend predominately to confirm independence of serial stock returns and indicate distinctly non- normal distributions.

1. Introduction

Prior published studies of weak-form market efficiency on the Stock Exchange of Singapore (SES) and the Kua la L u m p u r Stock Exchange (KLSE) have suggested surprisingly close agreement between measured and theoretically predicted behavior of c o m m o n stock returns. Using a disparate type of sample data over a longer and diverse time period, the objective of

this paper is to verify whether the previous findings are a result of the choice of data samples and time periods studied. This s tudy also provides empirical evidence on the na ture of the dis t r ibut ion of daily stock returns in these two

*The author thanks M.J. Gruber and R.G. Hawkins, New York University and L.P. Jennergren, University of Odense for helpful comments and advice. Financial support from'the Fulbright Research Abroad Program of the Office of Education, U.S. Department of Health, Education and Welfare, and the William Paterson College of New Jersey sabbatical leave and assigned research time programs permitted data collection overseas and processing in the U.S. Eswar Phadia, William Paterson College, provided:expert programming and statistical as- sistance. The author also is grateful to the Kuala Lumpur Stock Exchange and the Stock Exchange of Singapore for making data available and wishes, in particular, to thank Frances Kim, Lee Choy and Tan Thuan Keng for their help. Ng Goo Phai and Richard Chong Song Kee, United Malayan Banking Corp. Bhd., both provided research assistance through the kind cooperation of Dr. V. Kanapathy. The author also thanks an anonymous referee for helpful suggestions. Views expressed here do not necessarily reflect those of any institution or organization.

0378-4266/86/$3.50 �9 1986, Elsevier Science Publishers B.V. (North-Holland)

432 M.M. Laurence, The Kuala Lumpur and Singapore stock markets

thin markets which has an important bearing on the choice of statistical tools used to test the efficient market hypothesis.

Weak-form theory I asserts that successive returns generated by an efficient market will be independent, i.e., resemble a ' random walk'. 2 Tests on many other exchanges also have suggested rather close agreement with theory. 3 Perfect adherence to weak-form efficiency requires, among other conditions, freely available information, competition among investors and instantaneous communication. Both the SES and KLSE exist in environments where the putative conditions for weak-form efficiency are ostensibly less favorable than in most of the other markets previously investigated. A relative lack of investment data, small numbers of investors and shares, small amounts of business and financial news, no ticker tapes, little financial analysis, low degree of market regulation, and an unsophisticated communication system characterize these markets. The earlier unexpected findings, therefore, may be a result of the types of sample data or test methodologies used.

The first published study of weak-form efficiency on the SES, by Ang and Pohlman (1978), used weekly data from small samples over approximately two and one-half years and inferred that the SES is efficient in the weak sense. Hong (1978a, b) studied weekly market index data and weekly share price data, unadjusted for dividends, on a sample of randomly selected firms from the SES. Hong's (1978a, b) results-are mixed, and he concluded that the random walk hypothesis cannot be rejected for the SES. D'Ambrosio (1980) tested daily closing prices of six major indices of SES for weak-form conformity with the efficient markets hypothesis and found that successive changes in some SES indices have a non-random character. In the same year an unpublished study by Lim (1980) on monthly data from very small sectoral samples of the KLSE indicated efficiency.

None of the prior studies of the KLSE or SES used daily closing prices adjusted for cash and stock dividends, splits or rights issues, for a large sample of stocks, over long observation periods. Some used index data; and as Fama (1965, footnote 3) pointed out, use of market index data in random walk tests may lead to a false perception of price change dependence even when price changes of individual shares represented by the index are independent. This spurious dependence comes from the persistence of the

~Stock market efficiency implies that in equilibrium stock prices fully reflect all available information. Weak-form efficiency assumes that the only information of interest in the price forming mechanism is past prices. See Fama (1965) for additional detailed definitions of market efficiency and weak form test characteristics. ~ :

2Random walk theory assumes the current pried 6f a security reflects all available information. Only the arrival of new information will cause the price to change. More formally, a random walk model assumes that successive one-period price changes are both independent and identically distributed. See Fama (1970, pp. 383-390).

3See Conrad and Jfittner (1973), D'Ambrosio (1980), Dryden (1970), Fama (1965,1970), Granger (1975), Jennergren and Korsveld (1975), Kemp and Reid (1971), Praetz (1969) and Solnik (1973).

M.AI. Laurence, The Kuala Lumpur and Singapore stock markets 433

effect of the market factor on stocks not trading coincidentally. Logically, in thin markets this tendency may be exacerbated and may account for some of the dependence suggested by one of the other studies of the SES which used index data. On the other hand, weekly or monthly prices are more likely to reflect adjustment to new information than daily prices and thus may explain previous findings resembling market efficiency in the SES and KLSE by other researchers.

All of these previous studies used conventional methodologies which assume a normal distribution; however none of them investigated the nature of the distribution of daily returns. The shape of the distribution determines the proper types of statistical tests and the interpretation of findings. Early tests in other markets predicted normal distributions where the number of transactions per unit of time is large and transactions are spread approxi- mately uniformly over time; but empirical results even under such con- ditions deviated from normality. Later weak-form market efficiency research suggested 'fat tails'; and, indeed, such distributions were discovered. [See Fama (1970, pp. 399-400).] In the KLSE and SES even the most actively traded stocks do not trade every trading day, and trading tends to 'bunch'; therefore one would expect to find non-normal shaped distributions of returns. Tests assuming normality when it in fact does not exist may account for some of the mixed findings of earlier investigators of the KLSE and SES. This paper, using daily closing prices adjusted for cash and stock dividends, splits and rights issues, of 40 individual stocks over approximately 1500 consecutive trading days, explicitly examines the shape of the distribution of returns.

2. Background of the Kuala Lumpur Stock Exchange (KLSE) and the Stock Exchange of Singapore (SES) and study data

2.1. Historical and institutional background

While early Malayan share trading activities can be traced to 1910 'barroom' transactions among brokers in Singapore, today tl~e KLSE and SES constitute formally organized equity markets in the respective indepen- dent republics of Malaysia and Singapore.

From 1960 to May 24, 1973, as a consequence of their historical relationships, the two countries shared one market (exchange) for common stocks. Telephone lines linked two trading rooms approximately 250 miles apart, one in Kuala Lumpur and one in Sihgapore. However, in May 1973 the two governments terminated the interchangeability of currencies which simultaneously led to the individual incorporation of the KLSE and SES. Completely separate exchange operations commenced on June 4, 1973. 4

4For more detailed and earlier historical origins see: Fact Book 78 (Stock Exchange of Singapore, Ltd., Singapore, 1978) pp. 16-18; and (Dr.) Tan Pheng Teng (1978).

434 M.M. Laurence, The Kuala Lumpur and Singapore stock markets

Transaction costs on the SES are scaled according to share prices and differ from 'ready' contracts to 'time bargain' contracts. 5 The major propor- tion of trading is on a 'ready' basis and most prices for industrials are greater t h a n SS1 . 6 For shares trading at or over SS1, for ready settlement, a brokerage commission of I ~ is payable by both buyer and seller. (Minimum brokerage per transaction is S S5.) In addition there is a stamp duty of 20 cents for each S SI00 or fractional part transacted. 7

Transactions costs on the KLSE resemble those in the SES. Brokerage commissions are scaled according to share price to a maximum of 1~ on 'ready' contracts payable by both buyer and seller, a Minimum brokerage is MS5. 9 Stamp duty of MS1 for every certificate transferred is payable by transferee, and MS1 for every MS1000 (or fractional part) contracted, is payable by both buyer and seller. 1~

On both exchanges trading is by auctioning, but direct business is also permitted, t~ Traders on these exchanges are trading room clerks representing brokers who are exchange members. There were 20 member brokerage firms on the SES in 1979. t2 KLSE had 34 member brokerage firms in 1979.13 Brokerage firms may not trade for their own accounts. ~4

Approximately 260 firms' stocks are listed on the SES. Of that total about 150 are industrials; the balance are distributed rather evenly in finance, hotel, property, oil palm, tin and rubber sectors. ~5 Comparable breakdowns for the KLSE are a total of approximately 250 firms with about 135 industrials and the rest distributed nearly evenly across the same sectors. ~6 Shares of many firms are traded simultaneously on both exchanges. Total stock trading volume for 1978 on the SES was 3387 million Singapore dollars, 17 while on the KLSE total stock trading volume was 2539 million Malaysian dollars. ~8

5'Ready delivery" is for all contracts to be delivered on the second market day following the date of contract. 'Time bargain' (Settlement) is for contracts on the 1000 lot board due for delivery on the last trading day of each month or for contracts on the 'Big Board' (2,000 share lot) due for delivery at mid month on dates specified by the SES committee: Fact Book 78, op. cir., p. 18, 20.

6Stock Exchange of Singapore Journal, Vol. 7, No. 2, pp. 24, 27-80. 7Fact Book 78, op. cir., p. 70. 8No 'settlement' or 'time bargain contracts' are allowed on the KLSE. 9Rule 6, Brokerage, 'Rules For Trading By Member Firms And Member Companies,' The

Knala Lumpur Stock Exchange, pp. 72-73. ~~ Rule I l, Section (4), p. 95. t qbid., Rule 14, Section (8), p. 98. t2The Singapore Stock Exchange Journal, Vol. 7, No. 4 (April, 1979) p. 67. laThe Kuala Lumpur Stocg Exchange Gazette, Vol. 7, No. 3 (March, 1979) pp. 30-32. t4Rule 7; Section (6), 'Rules for Trading', op. cit., p. 45. t51977 Companies llandbook of the Stock E'xchange of Singapore, Ltd., Vol. XI (Stock"

Exchange of Singapore Ltd., Singapore, June 30, 1977) pp. vii-x{. 16Annual Companies llandbook, Vol. IV, The Kuala Lumpur Stock Exchange (Kuala Lumpur,

1978) table of contents. tTThe Singapore Stock Exchange Journal, Vol. 7, No. 2, February 1979, p. 26. Exchange rates

for 1978: S Sl =0.4343 SU.S.; M $1 =0.4432 SU.S. �9 laThe Kuala Lumpur Stock Exchange Gazette, Vol. 7, No. 2, Feb., 1979, p. 57.

M.M. Ltntrem'e. The Kuala Lumpur aml Singapore stock markets 435

Debentures, preferred stocks, bonds and government securities also trade on both exchanges, t9 In 1977, SES instituted the first organized options trading market in Asia. 2~

2.2. Sample data selection

In selecting sample firms the primary factor considered was homogeneity of both market sector and trading activity.

For the SES the industrial sector comprises nearly 70~ of the total paid-in capital and 50~ of the total number of listed shares. 21 In the KLSE the industrial sector embodies over 50~ of the paid-in capital and over 50~ of the total number of listed shares. 22 On both exchanges industrials account for nearly 60~ of total trading turnover measured in terms of either number of shares or market value. 23 The relative importance of the industrial sector in both exchanges, therefore, dictated the use of only industrials in the two s.'imples of stocks generated for this study. 24

In order to establish samples containing stocks with trading activity levels as homogeneous as possible, the most actively traded industrial stocks from both exchanges were sought. The desired samples would have contained only stocks that had at least one trade every trading day in order to obtain a number of series of closing prices of uniform length.

The first attempt to discern consistently traded stocks by ranking them by number of shares traded over the period June 1977 to August 1978 failed. This is to say, stocks with the highest trading volumes arc not necessarily stocks that are consistently traded every day or nearly every day.

Therefore, with the assistance of experienced staff of the two exchanges, lists of firms were drawn up - 24 from the SES and 16 from the KLSE - of the most consistently traded industrial firms. In addition to the activity criterion preference was given to stocks listed on the exchanges during the entire period studied. 2s

Data for this study is composed of individual stock price observations from the KLSE commencing June 1, 1973 through December 31, 1978, and from the SES commencing January 1, 1973, to February 12, 1979. 26 This

t~Faet Book 78, op. cit., p. 21; Listing Manual, The Kuala Lumpur Stock Exchange (Kuala Lumpur) p. I I.

2~ Book 78., op. cir., p. 16. "-tFact Book 78, op. cit., p. 21. Z2The Kuala Lump,tr Stock Exchange Gazette, Vol. 7, No. 2, Feb., 1979, pp. 62-63. 231bid., p. 57; The Singapore Stock Exchange Journal, Vol. 7, No. 2, Feb., 1979, p. 25. 2~Concern over possible 'special case" reasons for lack of efficiency in commodity stocks, i.e.,

rubbers or tins, also dictated the elimination of these stocks from the samples. 25Suspensions did occur in a small number of firms used in the samples and two firms v,'ere

not listed on the KLSE until several months after June 1973. Z6During the period January 1, 1973 to June 3, 1973 the two exchanges still were consolidated

into one exchange.

436 M.M. Laurence, The Kmda Lumpur and Singupore stock markets

yielded 1382 trading days on the KLSE and 1525 trading days on the SES. Observations are last transaction (closing) prices on those days when a transaction occurred. Table I lists each firm selected together with the number of transaction days in the period studied.

Table I Sample stocks and number of transaction days,

No. of Stock no. Name of stock transaction days

Kuala Lumpur Stock Exchange (1382 trading days)

I Sime Darby 1368 2 ttaw Par 1062 3 General Lumber 1309 4 Sire Lim ! 139 5 Genting 1358 6 Inchcape 1287 7 Pan Electric 1359 8 Ben & Co. 1095 9 Boris ! 154

10 Taiping Textiles 1136 I1 Wearne Bros. 1240 12 Magnum 1354 13 Tan Chong 1155 14 Cold Storage 1910 15 North Borneo Timber 608 16 Esso Ordinaries 975

Stock Exchange qf Singapore (1525 trading days)

I Haw Par ll71 2 Cold Storage 1474 3 Sembawang Ship 1310 4 Wearne Bros. 1424 5 Pan Electric 1518 6 Malayawata 1171 7 Cycle & Carriage 1465 8 Inchcape 1521 9 Harimau 1362

l0 Metro 1039 11 Boris 1183 12 Sime Darby 1516 13 Genting 1417 14 General Lumber 1330 15 National Iron 1305 16 Central Sugar 1220 17 Malayan Flour 823 18 Straits Steamship 1086 19 Fraser & Neave 1421 20 F.E. Levingston 1146 21 Leong Huat 1087 22 Prima 93 l 23 Perak Carbide 788 24 Tractors Malaysia 1040

M.M. Laurence, The Kuala Lumpur aml Singapore .stock markets 437

Of the 40 KLSE and SES stocks in the sample none traded every trading day during tile periods observed in this study. Only six stocks, three from each sample, traded over 98% of the total possible trading days. The least frequently traded KLSE stock traded only 608 days or about 44% of the total trading days while the least frequently traded SES sample stock traded 788 days or about 52% of the total trading days. Therefore, the data consists of 40 chronological price series of differing lengths and differing trading gaps. Any trading days in which there was no trading in a stock are simply omitted from its sequence.

Before using the data for statistical tests, they were transformed and screened for large errors in the following manner: First they were adjusted for cash and stock dividends, splits, and rights issues; then log price differences were calculated in a manner consistent with prior random walk tests; e.g. l o g P t - l o g P t _ t, following Fama (1965), where Pt includes the value of cash dividends or rights as well as the observed price adjusted for stock dividends or splits. 27 From these differences means and standard deviations were calculated for each stock. Any observations greater than three standard deviations from the mean were flagged for !nvestigation~

Adjustments for cash dividends and stock dividends also are consistent with prior tests. 2s Rights issue adjustment assumed the value of a right,

R = ( P , - P , ) / ( n + I), (1)

where

Pt = closing price on last trading day before ex-rights day, P, = subscription price, and n = number of rights required to buy one new share.

3. Tests of dependence and distributional statistics

3.1. R a n d o m walk tests - Serial correlat ions arid rults

Serial correlations and runs tests are commonly used to determine whether there are dependencies in successive values of log price differences. Because these tests are well known, very little attention will be given to discussing them. The reader is directed to the references for technical details.

27Logarithms of price differences have been used in past random walk tests because firstly, there is evidence to suggest that variance in price changes is a function of price level, and, secondly, because log P~-P~_ t is approximately the rate of return from continuous compound- ing over the time period t - 1 to t.

28Fama (1965, p. 46). The adjustment for cash dividends used the full pre-tax value awarded to shareholders.

43g M.M. Laurence, The Kuala Lumpur and Singapore stock markets

3.2. Serial correlations

This test is simply a computation of the correlation coefficients between price changes lagged 1, 2, 3, etc., time periods. [See Kendall (1948, p. 412.)-I

Serial correlation tests were made on the 40KLSE and SES stocks' log price differences between consecutive transaction days (differencing interval 1) for lags 1-30. Results for lags !, 2, 3, 5 and 10 are shown in table 2. While for lag 1 the serial correlation coefficients are generally positive, ten out of 40, or one-quarter, are negative, However, of the ten negative values only two are statistically significant at better than the 5~ level; and both of these are from the SES sample.

Of the 40 serial correlation coefficients calculated for lag I, only 16 are non-significant. In the SES sample 13 of the 24 stocks have serial correlation values for lag 1 significant at lower than the 1~ level. In addition six other stocks' serial correlation values are significant at the 5~ level. The KLSE sample contains five out of 16 stocks with serial correlation coefficients for lag ! significant at lower than 5~ level. (Two of the five are significant at the 1'~ levcl.)

The largest coefficient in absolute value is 0.185; while the mean absolute serial correlation for the KLSE and SES samples, respectively, is 0.041 and 0.078.

For lag 2 nearly all serial correlation coefficients are negative (31 of 40 ) . Eight are statistically significant at at least the 5~ level. While the absolute values tend to become smaller as the lag increases, no distinct patterns emerge from serial correlation coefficients for lags greater than two. Consider- able fluctuation in signs and magnitudes occur across the complete range of lags. 29

3.3. Rims tests

A run is defined as a price change sequence of the same sign, e.g., + + + - - 0 0 + w o u l d constitute four runs where ' + ' represents a price increase, ' - ' a price decrease and '0' no change. Assuming price change independence, the total expected number of runs of all three types, M, is calculated by

[ M = N ( N + I ) - ~ n N, i = 1

(2)

where N=to t a i number of price changes and hi=total number of price

-'gSerial correlation coefficients for differencing intervals greater than one were not calculated as prior studies indicated that they were unlikely to yield significant information.

M.M. Laurence, The Kuala Lumpur and Si gapore stock markets 439

T a b l e 2

Ser ia l c o r r e l a t i o n coef f ic ien ts {d i f fe renc ing i n t e r v a l I, l ags 1-10).

L a g s

F i r m I 2 3 5 lO

Kuala Lumpur Stock Exchange

I 0 .008 - 0.048 0.081 b 0.0554 0.062 ~

2 0 .060 ~' 0.023 0.089 b 0 .015 0 .036

3 - 0 . 0 0 6 - 0 . 0 1 9 0.016 0.041 0 .010

4 0 .027 - 0 . 1 1 4 b 0.028 0.0604 0.003

5 0.041 - 0 .030 - 0 .004 0 .034 0.049

6 0 .014 0.018 0.042 0 .018 0 .000

7 - 0 .008 - 0 .044 0.021 0.013 0.0738

8 0.033 - 0.097 ~' 0,059 ~ 0.003 0.005

9 0.031 - 0.065 ~ 0 .032 0 .034 0.002

I 0 - 0,000 - 0.038 - 0.007 0 .027 0.003

I I 0.0714 - 0 .026 0.029 0 .057 ~ 0.034

12 0 ,044 - 0 . 1 1 5 b 0 .006 0 .004 0.047

13 0,0584 - 0.022 - 0.058 ~ 0 .020 0.023

14 0.04 1 0.0644 0.054 0.005 - 0.006

15 0.107 b - 0 . 0 2 2 - 0 . 0 5 9 - 0 . 0 1 3 0.018

16 0.109 b 0 .036 - 0 . 0 0 1 - 0 . 0 2 1 0.048

Stock Exchange of Singapore

I 0 .062 ~ 0.026 0.085 b 0 .014 0.033

2 0 .095 b 0.032 0.086 b 0 .014 0 .006

3 0.071 u - 0.073 b - 0.003 0.015 0.055 ~

4 0 .185 u 0 .046 0 .046 - 0.024 0 .044 5 - 0 ,077 b - 0.045 0 .002 13.141 b 0.053 ~

6 - 0 .080 h - 0.009 - 0.008 - 0 .016 - 0 .002

7 0 .136 b - 0.013 0.059 ~ 0 .022 - 0 .072 b

8 0.0898 - 0.053 ~ 0 .062 ~ - 0 .036 0.051 a

9 - 0.018 - 0.028 0 .056 a - 0 .006 0,047

I 0 0.097 b -- 0.023 0.063 ~ 0 .003 0.0754

I I -- 0 .000 -- 0.021 0.003 0.033 -- 0.0624

12 0.062 ~ -- 0.012 0.049 0.003 0 ,062 ~

13 0 . 0 6 6 ~ - - 0 . 0 1 0 0 . 0 1 6 - - 0 . 0 1 6 0.000

14 -- 0.005 0.006 -- 0 .040 0 .017 0.009

15 0 .080 b -- 0.023 0.059 J 0.005 0.008

16 0.091 b - -0 .034 0 .016 - -0 .014 0.015

17 -- 0 .054 -- 0 .026 0 .080 J -- 0 .049 0.033

18 O. 104 b -- 0 .019 0.0644 0 .040 0.019

19 -- 0 .023 -- 0.043 0 .064 ~ 0 .040 0 .027

20 0 .059 ~ -- 0.038 0.053 -- 0 .080 b 0.018

21 0 .129 u 0 .052 0 .029 0 .015 -- 0 .004 22 0.0734 -- 0.003 0 .024 0 .067 ~ 0.001

23 0.081" -- 0 .092 b 0 .009 0 .013 0.073 a 24 0.145 b -- 0 .020 0.087 b 0 .026 0.055

4Reject H o, p = 0 at 5~o leve l o f s ign i f i cance .

bReject Ho, p = 0 a t I~/o leve l o f s ign i f i cance .

440 AI.,%I. Laurence. The Kuala Lumpur and Singapore .stock markets

changes of each sign. The standard error of M is

E ,t, E -2N E S , = Li =, Li = l i= t

�9 N 2 ( N - !) (3)

Fortt, nately for large N, the sampling distribution of /%1 is approximately normal. [See Wallis and Roberts (1956, pp. 569-572).-I Tests of statistical significance are, therefore, straightforward comparisons of the number of observed runs versus the number of expected runs using a standardized variable,

K = (d - M + �89 M, (4)

where J = the total observed number of runs of all types and tile sign of the discontinuity adjustment is plus if J < 3,1 and minus otherwise.

Following Fama (1965) runs tests were calculated for the 40 KLSE and SES stocks for differencing intervals 1, 2, 3, 5, 7 and 10, i.e., for price changes in each stock occurring between 1, 2, 3, 5, 7 and 10 sequential trading days on which there actually was a trade in the stock. The results for differencing interval I arc reported in table 3. All but two stocks, one in the KLSE and one in the SES, have negative standardized variables indicating that 38 of 40 firms have less actual than expected runs. However, the significance levels of the standardized variables are mixed. Only 23 of the 40 stocks have standardized variables as small as - 2 . In the KLSE sample three stocks have standardized variables smaller than - 3 and an additional three are smaller than - 2 ; while for the SES sample ten stocks have standardized variables smaller than - 3 and an additional seven are smaller than - 2 . (Five stocks have standardized variables smaller than - 4 , and one is smaller than -6 . ) The mean absolute standardized variable for the KLSE sample is 1.72 while the same statistic for the SES sample is 2.64.

For differencing intervals greater than one, most standardized variables are smaller than two in absolute value and of varying signs. 3~ The mean absolute variables tend to decrease as differencing intervals increase reflecting share price adjustment predicted by efficient markets theory.

The high proportion of positive serial correlation coefficients found earlier agrees with the nearly total negative standardized variables reported here. Negative standardized variables indicate fewer observed than expected runs which are also anticipated by the positive serial correlation coefficients.

S~ for differencing intervals greater than one are not tabulated here but are available upon request from the author.

M.M. L,:urence. Tile Kuala l.umpur and Singapore stock marketx 441

Table 3

Stock no. Total no. Expected no. Standard Standard KLSE of runs (JJ of runs (M) error (S . ) variable (K)

Kt.:h: Lumpur Stock Exchunge I 823 844.580 17.195 - t.226 2 635 640.585 15.142 -0.336 3 773 771.705 16.732 -0.048 4 685 720.394 15.675 -2.226 5 828 833.027 17.162 -0.264 6 748 775.515 16.579 - I . 629 7 813 814.685 17.125 -0.069 8 660 668.940 15.260 -0.553 9 706 718.044 15.711 -0.735

I0 716 745.201 15.753 -1.822 II 696 770.763 16.355 -4.541 12 781 838.663 17.116 -3.340 13 669 711.518 15.820 -2.656 14 545 567.271 13.988 --1.556 15 348 391.500 11.470 -3.749 16 598 640.294 14.615 -2.860

Stock Exchange of Singapore Stock no. SES

I 698 709.121 15.89 -0.668 2 393 441.579 12.52 --3.839 3 833 861.321 16.93 --I.643 4 803 875.131 17.54 -4.084 5 890 898.022 18.15 --0.414 6 653 715.332 15.90 --3.888 7 820 904.455 17.82 --4.712 8 854. 908.833 18.11 --3.001 9 855 849.633 17.15 --0.284

10 624 659.335 15.00 --2.323 11 729 764.785 15.94 -1.085 12 889 927.213 18.06 -2.088 13 834 $73.812 17.52 -2.244 14 768 790.926 16.84 -1.331 15 794 844.811 16.86 -2.984 16 723 756.455 16.21 -2.033 17 231 254.324 9.42 -2.423 18 638 704.071 15.36 -4.270 19 836 917.728 17.58 -4.620 20 650 707.173 1534 -3.601 21 643 679.308 15.20 -2.026 22 545 599.037 14.21 -3.766 23 470 473.076 12.93 -0.199 24 577 674.525 15.00 -6.470

442 M.M. Laurem'e, The Kuala Lnmpur am/Sit gapore .st,wk market.~

Some consis tency exists between the s ta t is t ical ly significant s t andard ized wlr iables and serial cor re la t ion coefficients. In the K L S E sample, of seven possible pairs of significant s tat is t ics there are four ac tual matchcd pairs while in the SES sample there are 15 actual ma tched pairs of a possible 21 pairs.

Tables 4 and 5 summar i ze the results of these two stat is t ical tests on the SES and K L S E and add F a m a ' s NYSE findings as a benchmark . Toge the r the results suggest only sl ightly greater devia t ion from perfect weak-form efficiency on the two smal ler exchanges. Whe the r the differences in weak- form efficiency are s ta t is t ical ly significant canno t be de termined.

Table 4 Serial correlation comparisons {differencing interval I, lag I).

Mean absolute Reject Ho, p=O: serial

correlation At 5'!,, level At I". level Signs coefficient Reference

,~hda)'.,6a 16 Stocks (KLSE)

U.S. 30 Stocks (NYSEI

Singal,ore 24 Stocks (SESI

5/16 2/16 + 13/16 0.041

11/30 No pattern 0.048

19/24 13/24 + 17/24 0.078

Table 2

l"am a 11965}

Table 2

Table 5 Runs test comparisons (differencing interval I, lag I}.

Standardized variables

Minimum < - 2 < - 3 Positive value MASV" Reference

U.S. 30 Stocks (NYSE) 8/30

Malaysia 16 Stocks (KLSE) 6,'16

Singapore 24 Stocks

�9 (SES) 17/24

4/30 -4.23 1.53 Fama (1965)

3/16 1/16 -4.54 1.73 Table 3

10/24 1/24 -6.47 2.67 Table 3

~Mean absolute standard variable,

.ll.M. Laurence, The Kilahl Llonptlr and Singapore stock markets 443

3.4. Di.s'trihlttional statistics

In o rder to es tabl ish a basis for descr ib ing the empir ica l d i s t r ibu t ions of s tock price changes, means and s t anda rd devia t ions of the empir ical distr i- bu t ions of log price differences, differencing interval 1, were calculated. Of the K L S E stocks, 1 ! have negat ive means; and 15 of the 24 SES stocks also have negat ive means indica t ing some possible d o w n w a r d drift in prices. All of the means , however, are close to zero, i.e., none is s tat is t ical ly significantly different from zero at the 570 level.

Tab le 6 i l lustrates a c o m p a r i s o n of the average empir ica l d is t r ibut ions for the 40 K LSE and SES s tocks with the normal d i s t r ibu t ion and the average empir ica l d i s t r ibu t ion found by F a m a (1965).

Table 6 Average empirical distributions.

.r .~___I .~+I ~ , .'~ 4- 2 .~+2~ .~+3 .'~+4 .'~+5 S.D. S.D. S.D. S.D. S.D. S.D. S.D. S.D.

Normal 0.3830 0 .6826 0 .8664 0 .9545 0 .9876 0 .9973 0.99994 0.9999 Fama. U.S. 0.4667 0 .7459 0 .8847 0 .9478 0 .9756 0 .9886 0 .9970 0.9988 KLSE, 16 0.5609 0 .7967 0 .8995 0 .9462 0 .9710 0 .9833 0 .9943 0.9970 SES. 24 0.5814 0 .8085 (I.9056 0 .9487 0.9691 0 .9820 0 .9926 0.9963

Each cell in the table represents the cumula t ive average p ropo r t i on of observed log price differences falling into the pa r t i cu la r s t anda rd devia t ion interval specified for the row sample indicated. F r o m one-ha l f s t anda rd dev ia t ion upwards to one and one-ha l f s t anda rd devia t ions a larger p ropo r - t ion of obse rva t ions is found in SES and K L S E samples. At the two s t a n d a r d devia t ion level the p ropo r t i on of obse rva t ions is a pp rox ima te ly the same in all cases. Then a shift takes place from 2�89 up to 5 s t anda rd dev ia t ions so that the K L S E and SES tend to have smal ler p ropor t i ons of obse rva t ions in those intervals. This indicates relat ively ' fat ' tails combined with peakedness , or leptokur tos is . 31

This may mean the log price differences in these marke t s have infinite var iance, and cau t ion should be exercised in using s t anda rd stat is t ical m e t h o d o l o g y to make inferences abou t weak- form efficiency. 32

3~The usual measure of kurtosis (peakedness), a,, ,is the mean of fourth powers of the deviations from the mean divided by the fourth power of the standard deviation. It is customary to call a distribution leptokurtic if its value of a ,>3. See Freund and Williams (1969, pp. 107- 108). For the 40 firms in the two samples only one firm had a.t<3 and that was a borderline case of a.~ = 2.94.

S-'Researchers are also interested in the distribution of share price changes over time because one part of the random walk model specifies identical distribution of share price changes; however, because conclusive tests to prove identical distribution are difficult to design and because the information is less interesting economically, most studies are only concerned with describing the distribution of the sample average as in this paper.

444 M.AI. Laurem'e, The Kuala Lumpur and Singapore stock market.~

4. Conclusions

Serial correlat ion coefficients, runs tests and distributional statistics have provided evidence of the character of successive daily price changes for some of the most actively traded stocks in the industria! sectors of the KLSE and SES - two of the world 's smaller stock markets.

The two independence tests manifest mixed behavior. Some sample stocks exhibit r andom walk behavior while others - particularly many of those from the SES - ' a p p e a r to deviate from a random walk. This finding is consistent with Granger ' s (1975, p. 11) comment that the random walk hypothesis is ' . . . clearly only an "average" kind of law, and may not hold true for all securities at all times'. Even though statistical measures of weak-form efficiency of the K L S E and SES indicate some small deviations from perfect independence, the question of whether the deviations are large enough to exploit profitably remains open and to be answered by future filter studies.

Average empirical distributions o f successive price changes over time on the KLSE and SES resemble reported findings in other markets, i.e., leptokurtic and distinctly non-normal , This means that statistical tests of significance based on the normali ty assumption may be inappropriate.

Weak-form efficiency characteristics of the SES and KLSE parallel closely those found in the NYSE. This suggests that differences in relevant infor- mat ion sets may be more apparent than real, i.e., in small markets price- forming information may be disseminated very rapidly without sophisticated communica t ions technology, hordes of analysts, large numbers of business journals and intensive market regulation.

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