Effect of price limits on volatility and stock returns in emerging markets: evidence from the Johannesburg stock exchange.

Ngassam, Christopher

Christopher Ngassam *

This study provides additional empirical evidence on effects of price limits on stock price volatility in emerging markets using data from the Johannesburg, South Africa (JSE), stock exchange. It is found that price limit rates of stocks on the ISE vary cross-sectionally according to stock price levels and that it is possible to control for other factors besides price limits in examining effects of price limits on stock price volatility. When return volatilities between high price limit portfolios (HPLP) and low price limit portfolios (LPLP) constructed on the basis of ranked price limit rates are compared, the results show that price limits serve to reduce stock price volatility on the JSE. Although the findings reported here hold useful policy implications for policy makers and regulators, several avenues for future research on some unanswered questions are identified.

INTRODUCTION

Capital markets are essential to preventing underutilization and waste of resources in an economy faced with declining real value of its currency. In most emerging markets today, capital markets afford the opportunity to millions of savers to invest their savings in various productive assets that act as a hedge against erosion of purchasing power. The ability to buy a claim on a fraction of a real asset and the concomitant diversification possibilities for an investor with limited resources is valuable to individuals as well as the society as a whole.

Stock price volatility in developed and emerging markets around the world has received much attention in the popular press over the last few years, especially since the stock market crash on October 19, 1987. Stock price volatility unrelated to variation in fundamental values or 'noise' is considered socially wasteful. It obscures the information in prices about resource allocation. It can increase the expected returns that investors require to hold stock, which means higher cost of capital for firms and less capital investment. Therefore, academicians and policy-makers have been much concerned with the micro-structure of the stock market to protect it from great fluctuation caused by speculative and noise tradings. Circuit breakers have been recommended as mechanisms for reducing or controlling stock price volatility. The most common and perhaps the most primitive type of circuit breakers is maximum price change limits.

Theoretically, however, it is not clear whether the imposition of price limits will bring about the desired effect of reducing stock market volatility. A commonly cited benefit ascribed to price fluctuations limits is that such measures provide a cooling--off period allowing investors to re-evaluate markey information so that investment strategies can be formulated. It also allows order imbalances to be publicized to attract value traders that could bring back equilibrium. Opponents against price fluctuation limits argue that they serve no purpose other than to slow down or delay the price change. They say that even though it can stop the rice of a share from free falling on the trading day when a shock hits, the price will continue to move in the direction towards equilibrium as new trading limits are established in subsequent trading days. According to this point of view, price limits only prolong the number of trading days for the market to adopt a disturbance.

Given the above contrasting views, the effect of price limits on stock price volatility is therefore an empirical issue to be tested. However, there is relative paucity of empirical literature on the effects of price limits in emerging stock markets. The purpose of this study is to provide additional empirical evidence on the effects of price limits on stock price volatility in emerging markets using data from the Johannesburg, South Africa (JSE), stock exchange. The remainder of this paper is organizes as follows. The next section reviews the literature on the effect of price limits on stock price volatility. Research design and data are described in the third section. The fourth section presents empirical results while section five concludes the paper with recommendations for further research.

LITERATURE ON PRICE LIMITS AND VOLATILITY

The study by Ma, Rao, and Sears (1989) focused on the effect of price limits on future prices. They found that price limits may provide a cooling-off period for the market and be accompanied by substantial reduction in volatility. Chiang, Wei, Wu (1990), Chung (1991), and Chen (1992), however, did not uncover significant evidence that price limits reduce the volatility of the stock market in Taiwan and Korea.

In examining the effect of price limits on stock price volatility empirically, it is very important to control for other variables besides price limits that may affect stock price volatility. For instance, if the effect of price limits on stock market volatility is investigated simply through comparing the volatilities as measured by the standard deviation of returns for some trading days before and after price limit moves or changes in price limit rate, it could lead to a spurious conclusion because of the time-varying property of stock market volatility. To solve such a problem, Chen (1992) tried to control for the determinants of stock market volatility by constructing a regression model with a few explanatory variables (for example, macro economic and financial volatility) to explain the sources of stock market volatility. However, since the volatilities of a variety of macro economic variables explain a relatively small part of the movements in stock market volatility, as Schwert (1989) suggests, such an approach may lead to only a partial solution to the problem.

Until recently, the minimum price change increment in the United States equity markets was 1/8th of a dollar. On June 2, 1997 and June 24, 1997, the minimum price increment was lowered from 1/8th to 1/16th of a dollar for most stocks on Nasdaq and the NYSE, respectively. To date, debate continues about the impact of further "decimalization", to 1/100th of a dollar or smaller, on order flow and transaction costs. At first blush, it seems evident that minimum price increments induce artificially wide spreads, and that bid-ask spreads of many firms (especially low-priced firms) are artificially wide. However, the empirical evidence suggests that decimalization may not improve the welfare of all market participants. Before the change in Nasdaq rules, several studies examined the effects of minimum price variations. For example, although Harris (1994) does not analyze actual reductions in market tick size, he estimates the impact of changes in minimum price variations by characterizing the relation between price l evels, spreads, depth and trading volume. His evidence suggests that a smaller tick size (relative minimum price variation) may yield narrower spreads but would also result in less depth. This follows from the argument that if the price of liquidity (the spread) is lowered all else being constant, the quantity supplied (the depth) will fall. The analysis by Harris (1994) is well supported by subsequent empirical evidence. Harris (1996, 1997a) examines the Paris Bourse and Toronto Stock Exchange and finds that smaller tick sizes discourage order exposure (the placement of limit orders) by raising the expected profits of front-running (placing an order one-tick ahead of limit orders). Bacidore (1997) and Porter and Weaver (1998) find that quoted and effective spreads generally decline after the Toronto Stock Exchange lowered the tick size on April 15, 1996. Goldstein and Kavajecz (1999) report a decrease in depth across the entire limit order book after the NYSE adopted the 1/16th minimum price increment. Final ly, Jones and Lipson (1999) analyze a sample of institutional trades and find that the move to sixteenths increased trading costs as a direct result of its adverse effect on depth. The evidence, therefore, does not unambiguously support the decimalization of prices. As always, there are tradeoffs. Although the lower price obtainable through decimalization can lower the cost of trading, particularly for small orders, the cost of executing large orders may increase, due to the adverse effect of decimalization on depth. Harris (1997b,c) provides extensive reviews of research on this topic.

A segment of previous studies on the effects of price limits on volatility examines the pros and cons of using price limits to control stock market volatility. The Brady report (1987) for example, suggested that the introduction of a circuit breaker system, including price limits, has three benefits. First, it limits credit risks and loss of financial confidence by providing a 'time-out' amid frenetic trading to settle up and ensure that everyone is solvent. Second, it facilitates price discovery by providing a 'time-out' to pause, evaluate, inhibit panic, and publicize order imbalances to attract value traders to cushion violent movements in the market. Finally, circuit breaker mechanisms counter the illusion of liquidity by formalizing the economic fact of life, so apparent in the 1987 October crash, that markets have a limited capacity to absorb massive one-sided volume. Making circuit breakers part of the contractual landscape makes it far more difficult for some market participants (pension portfolio ins urers, and aggressive mutual funds) to mislead themselves into believing that it is possible to sell huge amounts in a short period of time.

The findings by Ma, Rao and Sears (1989) is consistent with this viewpoint. Using minute-by-minute data, they compared the return volatilities between pre-limit and post-limit periods and found that price limit moves are followed by reduced volatility. However, Roll (1987) argued that the fact that price limits reduce volatility does not constitute unambiguous evidence that reduced volatility after a limit move is equally consistent with a reduction in the amount of news received relative to the pre-limit move period and the limit move period. We really need information about whether the imposition of price limits reduces overall volatility in all periods.

Fama (1987) opposed the introduction of the circuit breaker as a market rule to reduce noise or unnecessary volatility in price and doubted its usefulness. He argued that this system results in the reduction of the supply and liquidity when the demand increases. Rather, it could increase the price volatility by inciting trading in anticipation of halts. He insisted that this system can only delay the adjustment of price to changes in fundamental values. Fama's argument is consistent with the study of Roll (1987), which showed empirically that the market decline of each country during the crash of October 1987 is similar irrespective of the price limits. The result of Roll's study indicates that price limits can influence price adjustment speed, but do not have any effect on the size of the price adjustment.

A theory of price limits in futures markets developed by Brennan (1986) focus on their effectiveness in preventing futures traders from reneging on contracts. Brennan's theory predicts that price limits will disappear in futures markets that have closely correlated cash markets, a prediction more or less satisfied by the existing markets in the United States. This suggestive evidence against the proposition that price limits should be used to reduce volatility. Sholler (1981) argued that the observed volatility in stock return is excessive in the sense that it cannot be explained solely by the uncertainty of future real dividend. French and Roll (1986) formalized this argument and suggested that volatility may be related to trading motivated by public or private information, or by traders' overreaction ('noise'). Schwert (1989) showed that the estimates of standard deviation of monthly stock returns vary from two to twenty percent per month during the 1957-1987 period in the US stock market. Furthermore, test s for whether these large differences could be attributable to estimation error strongly reject the hypothesis of constant variance.

DATA AND METHODOLOGY

Do price limits reduce the volatility of the stock market? To provide a more reliable empirical answer to this question, it is very important to control for ocher factors besides price limits which may affect the volatility of the stock market. As mentioned before, the empirical results obtained simply by comparing the volatilities of the stock market for some trading days before and after changes in the price limit rate, may be contaminated by the effects of factors other that the price limit system.

To protect stock investors from abrupt fluctuations of stock price, the JSE has adopted price limits. Since the rates of price limit vary according to price levels as seen in Table 1, the price limit system of the JSE provides a rare opportunity for examining the relationship between price limits and stock price volatility.

In a cross-sectional analysis, it is not necessary to control for all other determinants of volatility that could also have changed over time. To be reliable, of course, the result of cross-sectional analysis must be adjusted to cross-sectional variations in firm specific characteristics such as beta, price level and firm size. First we construct three portfolios on the basis of the ranked price limit rates of each day to adjust cross-sectional differences besides price limits. Then we test the difference in return volatilities between high and low price limit portfolios using the modified Levene test statistic that is robust under non-normality.

Price limit rates for listed stocks vary according to the price level of each stock. The JSE price limit system allows the price of every listed stock to fluctuate in any given trading day within a pre-specified level above or below its previous day's closing price. It is possible, therefore, to examine the relationship between price limits and stock price volatility cross-sectionally. Of course, an empirical result of cross-sectional analysis is more reliable after it has been adjusted to cross-sectional variations in firm specific characteristics such as beta, price level and firm size. In this study, separately constructed portfolios are used to isolate the impact of price limits from other determinants of volatility. The specifics of the portfolio construction methods are as follows:

Step 1: For each trading day, calculate the price limit rate of each stock using the previous day's closing price and pre-specified price limit range, and then sort the price limit rates of listed stocks in descending order.

Step 2: For each trading day, construct three portfolios, composed of equal number of stocks, on the basis of ranked price limit rates and calculate the daily returns of equally weighted portfolios: high price limit portfolio (HPLP), medium price limit portfolio, and low price limit portfolio (LPLP). Since the price limit rate of stock alters according to the change of stock price the stock composition of each portfolio changes over time. This property also allows any volatility difference between three portfolios which may be caused by the cross sectional variations of variables other than price limits, to be eliminated.

Step 3: Test the equality of return volatilities between HPLP and LPLP. Even though price limits serve no purpose other than slowing down or delaying the price change, measured volatility using returns over a short enough interval (for example, one day) is bound to be affected. For example, the measured volatility is much higher when a market goes down 20 percent in one day than when a market hits a 5 percent down limit four days in a row. Hence, to remove the difference in volatilities caused only by delay effect, we test the equality of volatilities between HPLP and LPLP using the returns of several non overlapping holding intervals (1 day, 2 day, 3 day, and 5 day).

Furthermore, to see whether the results of the above experiment are reliable, it is necessary to examine whether the portfolio approach is effective in controlling for other factors besides price limits. Therefore, portfolios are constructed using residuals from the following cross-sectional regression model for each trading day. The equality of volatilities between HPLP and LPLP is tested as follows:

R (I,t) = a + b PLR (i,t) + e (i,t),

where R (I,t) and PLR (I,t) are the daily return and the price limit rate of stock I at day t, respectively. If the portfolio approach is effective in controlling for other factors besides price limits, the difference of volatilities between HPLP and LPLP, if any, would be caused only by the difference of price limits between HPLP and LPLP. Therefore, the volatility of HPLP will not be significantly different from that of LPLP when residuals from the above regression model are used to construct portfolios.

The data used in this study are described in Table 2.

The entire sample period (1990.1-1999.12) is divided into five 2-year sub periods. Each subperiod is also analyzed separately to gauge the variation of price limit effects by sample periods. To construct five portfolios on the basis of ranked price limit rates, both daily returns and closing prices are necessary. The daily return of each stock is defined as:

R (i,t) = IN [P(i,t)/P(i,t-1)],

where P (I,t) is the closing price of stock I at day t. For a small time interval such as a day, this definition is similar to the arithmetic rate of return.

EMPIRICAL RESULTS

Table 3 shows descriptive statistics on a daily return series for HPLP and LPLP.

The skewness of a distribution refers to its degree of symmetry; whereas the kurtosis of a distribution refers to its degree of symmetry; whereas the kurtosis of a distribution is influenced by the peakness and thickness of its tails. In Table 3, the skewness coefficients are positive and the kurtosis coefficients normalized to zero are higher than zero, indicating greater peaks and fatter tails than under normality. The Kolmogorov statistics for daily returns of two portfolios also reject the hypothesis that the distribution of daily returns is normal at the one percent significance level. These results imply that some traditional test results concerning stock returns, which assume the normality of stock returns, may be misleading. For the hypothesis testing of equal variance, Brown and Forsythe (1974) showed that if the data have fatter tails than in the case of normal distribution, the F-statistic rejects the null hypothesis too frequently. However, the modified Levene statistic proposed by Brown and Forsy the (1994) is not sensitive to departure from normality. Hence we use the modified led Levene statistic to test the equality of return volatilities between HPLP and LPLP. To test the null hypothesis of equal variance between HPLP and LPLP, the modified Levene statistic is computed as:

L = n [[([Z.sub.H] - Z).sup.2] + [(Z.sub.L] - Z).sup.2]]/[summation over (n/t = 1)] ([Z.sub.h,t] - [Z.sub.H] + [summation over (n/t = 1)] ([Z.sub.L,t] - [Z.sub.L])]/(2n - 2)

where [Z.sub.H,t]=\[[blank].sup.r][H.sub.,t] - [[blank].sup.r]H\, t=1, ..., n

[Z.sub.L,t] = \[[blank].sup.r][L.sup.,t] - [[blank].sup.r]L\, t=1, ..., n

[Z.sub.H] = [summation over (n/t=1)] [Z.sub.H,t]/n, [Z.sub.L] = [summation over(n/t=1)] [Z.sub.L,t]/n,

Z = [[summation over (n/t =1)] [Z.sub.H,t] + [summation over (n/t = 1)] [Z.sub.L,t]]/2n,

[r.sub.H] and [r.sub.L] are the daily returns of HPLP and LPLP, respectively, and [r.sub.H] and [r.sub.L] are 10% trimmed means of HPLP and LPLP, respectively. Under the null hypothesis, the modified Levene statistic is asymptotically distributed as F (1 ,2n).

Table 4 shows the comparison of return volatilities between LPLP and HPLP.

For the full sample period, the modified Levene statistics show that the volatilities of HPLP are significantly higher than those of LPLP regardless of the length of holding interval. Even when the 5-day holding returns are used, the difference in volatilities between LPLP and HPLP is still significant at the five percent level. These results indicate that price limit do not only slow down price changes but also have a positive effect on reducing stock price volatility. However, as shown in Table 4, the effect of price limits on stock price volatility appears to be different across the sample periods. Generally, over subperiods 1, 2, and 3, the volatility of HPLP is not significantly different from that of LPLP for most of the holding intervals, whereas the difference is significant over subperiods 4 and 5 regardless of holding intervals. Why does the effect of price limits on stock price volatility appear to be different according to the sample periods? Tables 5 and 6 may provide an answer to this question.

Price limits do not always reduce stock price volatility. Price limits become binding constraints to reduce stock price volatility when stock prices go up or down beyond the price limits.

Table 5 shows the average number of trading days per listed stock effect by price limits for each subperiod, and table 6 represents the average price limit rates of both HPLP and LPLP for each subperiod. For subperiods 1, 2, and 3, the numbers of average trading days per stock affected by price limits are much smaller than those for subperiods 4 and 5. This is because the average price limit rates for subperiods 1, 2 and 3 are higher than those for subperiods 4 and 5. This may help explain why differences in volatilities between HPLP and LPLP are not significant for subperiods 1, 2, and 3.

Next we examine whether previous results are caused only by price limits or by factors other than price limits. As mentioned above, if differences in volatilities between HPLP and LPLP are eliminated when residuals from the regression model are used to construct HPLP and LPLP, it would indicate that the above results are influenced by the effect of price limits. Surprisingly, Table 7 shows that the difference in return volatilities between LPLP and HPLP are mostly insignificant regardless of the holding intervals and sample periods.

We can therefore conclude that the difference in volatilities between LPLP and HPLP is caused by price limits.

CONCLUSIONS AND RECOMMENDATIONS

Since price limit rates of stocks vary cross-sectionally according to stock price levels, it is possible to control for other factors besides price limits in examining the effect of price limits on stock price volatility. We compare the return volatilities between high price limit portfolio (HPLP) and low price limit portfolio (LPLP) constructed on the basis of ranked price limit rates. The results show that price limits serve to reduce stock price volatility.

Some very basic questions remain unanswered that future research needs to address. For example, 1) Do price limits change the character of prices around limits? 2) If price limits change price behavior, do they do so in a way detrimental to the integrity of the market? If so, is it because price limits are too tight or too loose? 3) Do price limits affect liquidity? What happens to bid/ask spread immediately before and after a limit? What happens to volume? Are there big orders on one side that are broken up into smaller orders to be executed? 4) Do local traders get out of the market and let customers trade with other customers? Do hedgers lose because they cannot establish positions, and do speculators win? In particular, who is rationed out of the market, and do they subsequently lose money because of this rationing? No one has yet examined who is affected by limits. This is an important issue for establishing policy. 5) Assuming price limits can be useful, what is the optimal strategy for setting them so as to obtain the most effective outcome? 6) When should exchanges change limits? How can they be proactive and anticipate an optimal time to do so? 7) Do price limits lower default risk? How many defaults have occurred in markets without limits versus those with limits, when other factors are controlled?

APPENDIX

The Johannesburg Stock Exchange, South Africa: Brief Background.

The Johannesburg Stock Exchange (JSE) in South Africa was established in November 1887. It is the largest and most developed tock exchange in the African continent. During 1997 and 1998, 154 firms went public. With $13.2 billion in market capitalization, the JSE is the tenth largest market in the world, ahead of, for example, Italy and Australia. There are 759 listed companies issuing a variety of securities from common stocks to preferred stocks. Debentures, mutual funds, government and municipal securities, financial futures, commodities futures, options as well as money market instruments are traded on the JSE. Of the companies quoted on the JSE, over 150 have dual listings on foreign stock exchanges, including the New York Stock Exchange.

Trading is done using an electronic on-line real time trading system that combines order-and quote-driven systems. The system is known as the JSE Equities Trading (JET) System. The capacity of the JSE system is 500,000 trades per day. Trading time runs from 9:00 a.m. to 4:00 p.m. All settlements are executed through a clearinghouse. The exchange conducts surveillance on price limits and position monitoring through the Johannesburg Stock Exchange Committee, a regulatory body that comprises fifteen stockbrokers elected annually and the Registrar of Financial Institutions as a government-appointed member. Full financial disclosure is required of all listed companies.

Margins are levied at 28% for delivery trades and 35% for other transactions. Counter-party risk management is facilitated by a trade guarantee fund. In 1998, the JSE introduced an internet-based support system to match suppliers and demanders of capital in conjunction with a stock exchange news service (SENS) to disseminate listed companies news. The average number of daily deals for the past five years (1995-1999) is 264,387.

Table 1

Price Limit on Different Sock Price Levels in the JSE

(As of December 1999)

Stock Price (Rand) (a) Price Limit Price Limit Rate
 %

 - 30 10 -3.33
 30 - 50 20 6.67-4.00
 50 - 70 30 6.00-4.29
 70 - 100 40 5.71-4.00
 100 - 150 60 6.00-4.00
 150 - 200 80 5.33-4.00
 200 - 300 100 5.00-3.33
 300 - 400 130 4.33-3.25
 400 - 500 160 4.00-3.20
 500 - 700 200 4.00-2.86
 700 - 1000 250 3.57-2.50
 1000 - 1500 300 3.00-2.00
 1500 - 400 2.67-

Note: (a) The Rand is the South African currency unit: Rand 1 = US$ 0.65
in December 1999.
Table 2

Data Description

Source: JSE Equity Trading (JET) Systema
 Daily returns file and daily
 closing price file

Sample period: 1990.1-1999.12 inclusive.
 The entire period is divided into
 5 equal subperiods.
 Subperiod 1 (1990-1991)
 Subperiod 2 (1932-1993)
 Subperiod 3 (1994-1995)
 Subperiod 4 (1996-1997)
 Subperiod 5 (1998-1999)

Selection criteria: All listed equity securities

Basic data unit: Return adjusted for all capital
 changes and including dividends

Note: (a) The JET System was created by the Johannesburg Stock Exchange
Committee, a Regulatory body that comprises fifteen stock brokers
elected annually and the Registrar of Financial Institutions as a
government- appointed member.
Table 3

Descriptive Statistics on Portfolio Daily Return Series

 Original Return Series Residual Return
 Series
Statistics LPLP HPLP LPLP

No. of Obs. 2921 2921 2921
Mean (%) 0.096 0.147 0.039
Variance (%) 0.781 0.946 0.555
Skewness 0.320 0.907 0.531
Kurtosis 2.304 5.008 4.262
Min. (%) -3.289 -4.426 -3.289
Max. (%) 4.648 7.734 2.298
Kolmogorov Stat. 0.067 (**) 0.087 (**) 0.136 (**)

 Residual
 Return
 Series
Statistics HPLP

No. of Obs. 2921
Mean (%) 0.025
Variance (%) 0.546
Skewness 0.568
Kurtosis 4.707
Min. (%) 3.529
Max. (%) 2.294
Kolmogorov Stat. 1.423 (**)

Note: a(**) = significant at the 1% level
Table 4

Comparison of Volatilities between LPLP and HPLP

(based on original returns data)

Sample Holding Number Standard Deviation (%)
Period Period of
 (Days) Obs. LPLP HPLP

Full period 1 2921 0.781 0.946
(1990-1999) 2 1460 1.244 1.478
 3 973 1.606 1.885
 5 486 2.443 2.872

Subperiod 1 1 582 0.921 0.839
(1990-1991) 2 291 1.432 1.380
 3 194 1.891 1.867
 5 97 2.834 2.979

Subperiod 2 1 591 0.677 0.742
(1992-1993) 2 295 1.046 1.097
 3 197 1.373 1.479
 5 98 1.912 1.996

Subperiod 3 1 587 0.551 0.665
(1994-1995) 2 293 0.920 0.975
 3 195 1.167 1.244
 5 97 1.877 1.798

Subperiod 4 1 584 0.891 1.249
(1996-1997) 2 292 1.461 1.981
 3 194 1.875 1.875
 5 97 2.843 3.782

Subperiod 5 1 582 0.792 1.086
(1998-1999) 2 291 1.247 1.429
 3 194 1.695 2.212
 5 97 2.400 2.400

Sample Modified
Period Levene
 Statistic

Full period 37.04 (**)
(1990-1999) 16.93 (**)
 7.24 (**)
 3.30 (**)

Subperiod 1 6.66 (**)
(1990-1991) 0.74
 0.39
 0.06

Subperiod 2 0.59
(1992-1993) 0.00
 0.30
 0.13

Subperiod 3 8.76 (**)
(1994-1995) 0.90
 0.08
 0.77

Subperiod 4 39.25 (**)
(1996-1997) 16.80 (**)
 5.45 (**)
 4.15 (**)

Subperiod 5 33.89 (**)
(1998-1999) 19.18 (**)
 8.05 (**)
 7.30 (**)

Notes:

a(**) = significant at the 1% level.

b(*) = significant at the 5% level.
Table 5

Average Price Limit Rate for LPLP and HPLP

Same Average Price Limit Rate (%)
Period LPLP HPLP

Full period 5.443 7.776
Subperiod 1 6.504 9.360
Subperiod 2 6.390 9.164
Subperiod 3 5.843 8.920
Subperiod 4 4.620 6.628
Subperiod 5 3.861 4.811
Table 6

Total Trading Days of Stocks affected by Price Limits

Sample Average Number Total Trading Days Average Trading Days
Period of Listed Firms of Stocks Affected of Stocks Affected
 by Price by Price Limits

Subperiod 1 307 5,358 17.45
Subperiod 2 307 2,427 7.91
Subperiod 3 322 3,582 11.12
Subperiod 4 340 16,717 49.17
Subperiod 5 487 39,810 81.75
Table 7

Comparison of Volatilities between LPLP and HPLP

(based on original returns data)

Sample Holding Number Standard Deviation (%) Modified
Period Period of Levene
 (Days) Obs. LPLP HPLP Statistic

Full period 1 2921 0.555 0.546 1.02
(1990-1999) 2 1460 0.857 0.836 0.77
 3 973 1.085 1.048 1.49
 5 486 1.628 1.568 1.56

Subperiod 1 1 582 0.687 0.622 3.70
(1990-1991) 2 291 1.101 0.988 2.41
 3 194 1.359 1.212 1.78
 5 97 1.966 1.743 0.88

Subperiod 2 1 591 0.523 0.489 0.95
(1992-1993) 2 295 0.777 0.698 1.32
 3 197 0.976 0.872 0.64
 5 98 1.380 1.287 0.44

Subperiod 3 1 587 0.359 0.349 0.76
(1994-1995) 2 293 0.545 0.515 1.73
 3 195 0.679 0.656 0.81
 5 97 0.961 0.771 6.64

Subperiod 4 1 584 0.617 0.660 0.74
(1996-1997) 2 292 0.942 1.031 1.68
 3 194 1.261 1.362 0.61
 5 97 1.902 2.085 0.32

Subperiod 5 1 582 0.524 0.548 0.17
(1998-1999) 2 291 0.789 0.817 0.28
 3 194 1.068 1.086 0.14
 5 97 1.533 1.576 0.90

Notes:

(a)(**) = significant at the 1% level.

(b)(*) = significant at the 5% level.

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ENDNOTE

* Please address all comments to Christopher Ngassam, Ph.D., Associate Professor of Finance, Department of Entrepreneurial Studies. School of Business, Norfolk State University. Norfolk, Virginia, 23504-8060, USA: phone (757) 823-9534; e-mail: cngassam@nsu.edu. I would like to thank Professor Basu Sharma, the editor of this journal and two anonymous referees for helpful comments on an earlier draft. I also wish to thank participants of the 2002 Financial Management Association International Annual Meetings (Session on Emerging Stock Market Volatility and Diversification) in San Antonio, Texas for valuable suggestions that were later incorporated in the final revision of the paper. All remaining errors are of course mine.