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Investigating the Performance of Price Limits in a Small Emerging Stock
                                  Exchange Market....
limit hit of -5% for four days in a row. In fact, Roll advances, investors might actually
prefer a huge one day drop. Vola...
hit limits are constrained to fluctuate within the price bands imposed while the other
category of stocks experience uncon...
Table I

                                    Tick Size on the SEM

Tick size is the minimum allowable unit that stock pric...
Table II
                                      Summary Statistics

Stocks are categorized into three groups based on the m...
of each stock in all three categories is calculated for each day of the 15-day window;
Table III reports the mean for each...
their daily limit may be prevented from correcting their order imbalance. In the few
cases where volatility is higher in t...
that price limits attenuate volatility. The finding is consistent with that of Kim and Rhee
(1997) on the Tokyo Stock Exch...
hypothesis, which casts doubt over the effectiveness of price limits in stock markets. We
find that stocks that hit their ...
References

Blume, Marshall E., A. Craig MacKinlay, and Bruce Terker, 1989, Order imbalances and
stock price movements on ...
Stock Exchange of Mauritius, Rules and Regulations, http://www.semdex.com/rules.htm

Stock Exchange of Mauritius, Trading ...
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  1. 1. Investigating the Performance of Price Limits in a Small Emerging Stock Exchange Market. VINAY PRASANDJEET NUNDLALL International Business School Brandeis University Waltham MA 02452-9110 USA ABSTRACT This paper investigates the effectiveness of price limits in containing volatility using data from a small emerging stock exchange market. Critics of price limit systems argue that volatility is higher on days following price limit hits (the volatility spillover hypothesis) and that trading is hampered because of price blocks. Price limit advocates argue that price limits decrease volatility. Examining the Stock Exchange of Mauritius during the period when it imposed a ±6% price limit system, we find supporting evidence for the spillover hypothesis, implying that price limits are ineffective at reducing volatility. I. Introduction Price limits started drawing increased attention after the 1987 crash. Some authors, such as Blume, MacKinlay and Terker (1989) suggest that panic behaviour caused excessive volatility which ultimately led to the collapse of financial markets. Various committees and commissions investigating causes of the crash recommended the implementation of circuit breakers (e.g. Brady Commission, Miller Report). Price limits, it was argued, can control volatility by establishing price constraints which then prevent prices from moving beyond pre-determined levels. They also provide a break allowing rational reassessment during times of panic trading, effectively cooling off panicked trades. Price limits now exist in many stock exchanges spread around the world. An early study on the rationale of price limits is Ma, Rao and Sears (1989a) which finds evidence of price reversals after prices hit a limit. The study concludes that price limits serve to correct prices when the market overreacts. The authors also find that volatility is mitigated after limit hits, but however this argument is dismissed by Lehmann (1989) and Miller (1989). The latter argue that prices after a limit hit are in all likelihood less volatile. However, there are reasons to believe that price limits impose costly distortions in the market. Lehmann (1989) further contends that trade imbalances induce prices to reach their limits, thus transferring transactions to subsequent days. Limits restrict volatility on the day of the event and prevent corrections in order imbalance but then cause volatility to spread out over a longer time span. This is called the volatility spillover hypothesis. Roll (1989) also refers to the same phenomenon when stating that investors would see very little difference between a one-day market drop of 20% and a
  2. 2. limit hit of -5% for four days in a row. In fact, Roll advances, investors might actually prefer a huge one day drop. Volatility spillover is empirically proven to exist in the Tokyo Stock Exchange by Kim and Rhee (1997) in a study that this paper closely follows in spirit and in methodology. A problem that markets sometimes have to face is delayed price discovery. If the price discovery process is interfered with, Fama (1989) suggests that volatility increases as a result. Lehmann (1989) and Lee, Ready and Seguin (1994) find empirical support of this hypothesis. In essence, once limits are hit trading stops until the limits are revised, thus causing an interference. (Note that this version of events would occur more distinctly when we have a trading halt that is triggered by limit hits). However, as limits block prices, stocks have to wait for the next trading day to continue toward their equilibrium prices. Kuhn, Kuserk and Locke (1991) find evidence delayed price discovery in their study of the 1989 US mini-crash. Kim and Rhee (1997) also confirm the hypothesis using data from the Tokyo Stock Exchange. They find that stocks that close at their limits are more likely to continue trading than reversing when trades are resumed. Furthermore, price limits that prevent trading (or equilibrium level of trading) cause stocks to become less liquid. As a result, trade activity might intensify over days following a limit hit. This is the trading interference hypothesis, noted by Fama (1989), Telser (1989) and Lauterbach and Ben-Zion (1993). Lehmann (1989) has a slightly different view of the mechanism at work; order imbalances and mitigated trading cause limit hits. Following Kyle (1988), two types of traders are typically identified in the market: long term, value-based patient traders and short term, impatient traders (also known as noise traders). Noise traders look for immediate execution of transactions because of their trading strategies, liquidity needs and fads. We call this demand for immediacy and it confronts noise traders with high transactions costs in the short run but does not prevent them from trading. On the other hand, patient traders help stabilize markets by buying when net sales from impatient traders substantially moves prices (or selling when net buying from impatient traders substantially moves prices). Lehmann’s argument then is that order imbalances and the resulting thinning down of trade push prices to their limits. On subsequent days, therefore, we see a flurry of activity as impatient investors trade at unfavorable prices to correct order imbalances. However, it is also interesting to note Subramanyam’s (1994) postulate that as prices move in the neighbourhood of their limits, there is an ex-ante increase in volatility because investors expect a limit hit and thus advance their trades. As a result, we may see an increase in trading activity in days preceding the limit hit. In this paper, two hypotheses, volatility spillover and trading interference, are empirically tested following the Kim and Rhee (1997) design and methodology. This design springs from the criticism by Lehmann (1989) and Miller (1989) in response to the argument of Ma et al (1989a) that volatility declines on days after limit hits. The fact is that volatility is bound to decline after being high. Lehmann also suggests that price movements around limit hits should be examined along with trading activity and order imbalances. The Kim and Rhee design examines the post limit behaviour of two categories of stocks, those that hit limits and those that almost hit limits. The rationale is that since stocks that 2
  3. 3. hit limits are constrained to fluctuate within the price bands imposed while the other category of stocks experience unconstrained price fluctuations, any difference in post limit behaviour must be associated to price limits. To our knowledge, studies of this kind have not been carried out on a small, emerging stock market characterized by frequent long episodes of inactivity and illiquidity. The Stock Exchange of Mauritius is ideal to study as it had a restrictive daily price limit of ±6% from its inception in 1989 through June 2001. It is expected that the flurry of activity on days surrounding limit hits would be more significant given the long episodes of inactivity in the market. The rest of the paper is organized as follows: Section II gives a brief overview of the characteristics of the SEM and discusses the design of the study, Section III presents and discusses findings on the volatility spillover hypothesis, Section IV presents and discusses findings on the trading interference hypothesis and Section V concludes. II. Data and Design We use daily stock price data on 868 trading days’ worth of observations on all companies traded on the Stock Exchange of Mauritius during the period from 5 January 1998 to 20 June 2001. Unfortunately, daily opening, closing, high and low prices are not published or publicly available for that period, so we end up with only daily closing prices and daily trading volumes. Prices are adjusted for stock splits and stock dividends. During that time period, there were 41 companies listed on the exchange, and all of them were indiscriminately subject to a ±6% price limit. The price limit is determined using the last day’s closing price. Another control on price movements is the tick size, which is the minimum allowable unit by which stock prices can change by. Table I below shows the different price levels and the corresponding tick sizes. In the SEM, a price limit hit does not automatically trigger a trading halt. There are two types of trading halts: market halt and security halt. A trading halt may be imposed by the Stock Exchange for a time period during a market day or may be extended beyond one market day. Among reasons listed, market halts occur in cases of technical failure of the electronic system (the Automated Trading System or ATS), or when the market index, the SEMDEX, drops by more than 5% at the opening session. Security halts occur when out-of-the-ordinary events occur, such as receipt of price sensitive information about a traded security by the Exchange and unusual movements in price and volume traded in a security. So when a stock price hits the limit, trade may continue at the limit price until session closes, unless the Exchange feels there is something suspicious about it, at which time they will decide to impose a halt. 3
  4. 4. Table I Tick Size on the SEM Tick size is the minimum allowable unit that stock price may deviate. The last sale price is used to determine tick size. Price Range in Mauritian Rupees Tick Size 0<p<1 1 1 ≤ p < 10 5 10 ≤ p < 50 10 50 ≤ p < 100 50 100 ≤ p < 500 100 500 ≤ p < 1,000 500 p ≥ 1,000 1,000 Source: ATS Schedule In order to identify the occurrence of an event, we find the days where prices match their previous trading day’s closing price plus the price limit for an upward hit, or previous day’s closing price minus the limit for a downward hit. That is, there is an upward hit for a specific stock when Pt ≥ Pt-1 + 0.06 Pt-1, where Pt is Day t’s closing price, Pt-1 is closing price on Day t – 1 and 0.06 is the daily price limit. Similarly, we have a downward limit reached when Pt ≥ Pt-1 - 0.06 Pt-1. We also identify two other categories of stocks that did not reach their limits; stocks that came within at least 90% of reaching the daily limit, (a price movement of more than |5.4%|) and stocks that came within at least 80% of reaching their daily limits, but less than 90% of their limit (a price movement between |4.8% | and |5.4%| ). For the sake of brevity, we will call stocks that hit their limits stocks hit and the two other categories of stocks that did not hit their limits stocks90 and stocks80, where the subscript denotes the magnitude of the stock price movement on Day 0, the event-day. We assume that stocks that hit their limits are constrained from correcting their order imbalance; e.g., on limit up days there are more motivated buyers than sellers, as the latter want to wait for a more favourable price, and on limit down days, there are more motivated sellers than buyers, the latter waiting for further drops in price. Stocks that almost hit their limits are not constrained in this manner. Stockshit are more likely to suffer from order imbalances for liquidity than stocks0.90 and stocks0.80. There should be no marked difference between stocks0.90 and stocks0.80. Using a 15-day event window, we set out to find the difference between days after the limit hits for the different groups of stocks. The population of hits is quite small as we have only 107 upper hits and 85 lower hits for 868 trading days. We believe this may be caused by two things; the small number of listed companies (only 41), and a buy and hold strategy common in new emerging stock markets. Table 2 below reports summary statistics on limit hit occurrences for the three categories for lower and upper reaches. We note that there are about 26% more upper hits than downward hits. 4
  5. 5. Table II Summary Statistics Stocks are categorized into three groups based on the magnitude of their price movement on the event day (Day 0). Stockshit denotes stocks that reached their daily price limit, stocks0.90 denotes stocks that had a price change of at least 0.90*LIMITt from the previous day’s close, but did not actually reach the limit. LIMITt denotes the maximum daily price movement allowed on day t. Stocks0.80 denotes stocks that experienced a price change between 0.80*LIMIT t and 0.90*LIMITt. The sample size of each of the three categories during the period January 1998 through to June 2001 are presented below for both upward price movements and downward price movements. Upward Price Downward Price Movements Movements Stockshit n = 85 Stockshit n = 107 Stocks0.90 n = 113 Stocks0.90 n = 78 Stocks0.80 n = 42 Stocks0.80 n = 44 III. VOLATILITY SPILLOVER HYPOTHESIS: EMPIRICAL FINDINGS (i) Test Design For the study of a small emerging stock market, we utilize a 15-day window. The 15- day window starts from Day -7 and ends at Day +7. Day 0 represents the limit-hit-day for stockshit and the day stocks0.90 and stocks0.80 reached 90% of the limit and 80% of the limit respectively. Day -1 represents the day before the event and Day 1 is the day after the event and so forth. Ma et al (1989a) and Kim and Rhee (1997) instead use a 21-day window. The extra days did not seem to matter for this market. We presume that market players are myopic in new, small markets and that they have not reached the level of sophistication expected in bigger exchanges. Thus a smaller time horizon surrounding an event may make more sense. We measure daily volatility Vt , j by taking returns squared; Vt , j = (rt , j ) , where rt , j is 2 Pt − Pt −1 the daily percentage returns using closing day prices: rt , j = × 100 . Note that Pt −1 we are not using natural log differences because price limits on the market are calculated using the simple formula above. Maximum (minimum) returns were frequently greater (less) than the +6% (-6%) limit because of the tick size. Hence, it is not uncommon to find volatility being greater than the 36% we would have expected to see. The volatility 5
  6. 6. of each stock in all three categories is calculated for each day of the 15-day window; Table III reports the mean for each day. If the post-limit volatility is greater for stockshit than for the other categories, then we would find support for the volatility spillover hypothesis. We analyze upper and lower limit hits separately. Following Kim and Rhee (1997), we have excluded from our sample consecutive hits because treating each hit individually would cause a high pre-limit-day volatility bias. Clustered limit hits within a 4 day horizon were also excluded. Finally, whenever trading halts were imposed, those observations too, were dropped from the final sample. As a result, the final sample for empirical investigation was reduced to 66 lower limit hits and 65 upper limit hits. (ii) Results We find empirical evidence for the volatility spillover hypothesis for both upper limit hits and lower limit hits in the SEM. On Day 1, volatility for stockshit is consistently more than two times higher than that for stocks90 and stocks80. Volatility for stockshit remains higher on Day 2 and Day 3, except for one case among lower limit hits, where volatility for stocks80 is higher, but not statistically significant. Table III presents results for upper limit hits on each of the 15 days for the three categories of stocks; stockshit, stocks0.90, and stocks0.80. Mean volatility is highest for all three subgroups of stock on Day 0, because that is when all stocks reach their most extreme price. For each day of the event window, we compare volatility levels using the Wilcoxon signed-rank test. This is a non-parametric test that compares the median value of two vectors, here the vectors of volatility for each stock in each category, for each day. However, in the tables, it is the mean volatility that we report for the sake of presentation. The symbols “>>” and “>” signify that the left hand volatility is greater than the right hand volatility at the 0.01 and 0.05 levels of significance respectively. As expected, we see a significant difference in Day 0 volatility among the three subgroups. However, this difference exists by design. On Day 1, volatility for stockshit is more than halved, dropping from 38.46 to 15.67, but falls slower on Day 3, to 11.13. This is evidence of persistence in volatility which is frequently encountered in emerging markets. Ma et al (1989a) interpret this drop in volatility as evidence that price limits attenuate volatility. However, Lehmann (1989) and Miller (1989) contend that if volatility is extremely high, it naturally has to decline sometime – it is akin to saying “sunshine after the rain”. On comparing stockshit with the two other categories, we see that despite the drop in volatility for stocks90 and stocks80, volatility for the stockshit group is still significantly greater. Volatility for stocks that have hit an upper limit is higher for 6 out of 7 days following the hit. We thus find empirical evidence for the volatility spillover hypothesis over three days for upper limit hits in the SEM. Volatility for stockshit on Day -1 is smaller than volatility on Day 1, while for stocks 90 and stocks80 volatility on Day -1 is greater than volatility on Day 1. This may have two interpretations. First, it reinforces the spillover hypothesis. Second, stocks that reach 6
  7. 7. their daily limit may be prevented from correcting their order imbalance. In the few cases where volatility is higher in the pre-limit-hit period for stocks hit, it may be the case that traders anticipate the hit and start advancing their trade. Table III Volatility Spillover: Upper Limit Hits For all three stock categories stockshit, stocks0.90, and stocks0.80, volatility is calculated for each day for the 15-day period surrounding the event day (Day 0). The stock categories are based on the magnitude of their price movement on the event day. Stockshit denotes stocks that reached their daily price limit, stocks0.90 denotes stocks that had a price change of at least 0.90*LIMITt from the previous day’s close, but did not actually reach the limit. LIMITt denotes the maximum daily price movement allowed on day t. Stocks0.80 denotes stocks that experienced a price change between 0.80*LIMITt and 0.90*LIMITt. Day 0, the event day, denotes the day when Stockshit reach their upper limit hits. Day -1 is the day before Day 0, Day 1 the day after Day 0 and so forth. Volatility measure is daily returns-squared, calculated as follows: Vt , j = (rt , j ) 2 where rt,j denotes the percentage daily return for each stock j on Day t. >> and > indicate that the left hand figure is greater than the right hand figure at the 0.01 and 0.05 levels of significance, respectively, using the Wilcoxon signed-rank test. Day Stocks0.80 Stockshit Stocks0.90 -7 0.70 << 3.16 >> 1.47 -6 2.32 15.91 >> 2.02 -5 1.12 << 2.98 2.98 -4 3.28 << 7.26 > 4.18 -3 5.40 < 4.79 5.35 -2 5.29 << 7.59 8.94 -1 10.39 << 11.40 13.39 0 25.66 << 38.46 >> 33.62 1 1.53 << 15.67 >> 3.32 2 1.88 << 11.13 >> 4.00 3 2.83 << 6.07 >> 2.82 4 3.49 << 5.20 3.31 5 5.83 3.84 > 2.16 6 3.87 << 6.59 > 1.18 7 5.05 15.50 > 1.61 Table IV gives the analogous results for lower limit hits. Again we see the same pattern: volatility of stockshit after the hit is higher than volatility of stocks in the other categories after the hit, and remains so for three days after. The evidence suggests that stocks that reach their limit are constrained to a price change equivalent to their limit, but that price changes continue, or spillover, on subsequent days. Price limits only seem to spread volatility over a longer period of time. This result provides evidence against the notion 7
  8. 8. that price limits attenuate volatility. The finding is consistent with that of Kim and Rhee (1997) on the Tokyo Stock Exchange. Table IV Volatility Spillover: Lower Limit Hits For all three stock categories stockshit, stocks0.90, and stocks0.80, volatility is calculated for each day for the 15-day period surrounding the event day (Day 0). The stock categories are based on the magnitude of their price movement on the event day. Stockshit denotes stocks that reached their daily price limit, stocks0.90 denotes stocks that had a price change of at least 0.90*LIMITt from the previous day’s close, but did not actually reach the limit. LIMIT t denotes the maximum downward daily price movement allowed on day t. Stocks0.80 denotes stocks that experienced a price change between 0.80*LIMITt and 0.90*LIMITt. Day 0, the event day, denotes the day when stockshit reach their lower limit hits. Day -1 is the day before Day 0, Day 1 the day after Day 0 and so forth. Volatility measure is daily returns-squared, calculated as follows: Vt , j = (rt , j ) 2 where rt,j denotes the percentage daily return for each stock j on Day t. >> and > indicate that the left hand figure is greater than the right hand figure at the 0.01 and 0.05 levels of significance, respectively, using the Wilcoxon signed-rank test. Day Stocks0.80 Stockshit Stocks0.90 -7 0.47 << 1.11 << 2.09 -6 0.42 << 2.88 5.57 -5 1.04 << 2.66 < 6.29 -4 3.25 << 3.98 4.87 -3 3.30 << 5.18 5.21 -2 0.79 << 3.83 4.52 -1 2.87 << 6.39 > 3.83 0 26.23 << 42.28 >> 32.41 1 1.95 << 8.88 >> 3.06 2 2.93 2.48 > 1.14 3 1.63 << 2.11 > 1.24 4 0.66 << 3.40 2.27 5 2.46 >> 1.15 2.06 6 0.91 << 1.28 1.30 7 0.74 >> 1.06 > 1.92 V. Conclusion Applying a design pioneered by Kim and Rhee (1997), we investigate the price limit system of the SEM to compare volatility levels using daily data on three categories of stocks based on the size of one day price movements (stocks that hit their limit and stocks that nearly hit their limit). We find supporting evidence for the volatility spillover 8
  9. 9. hypothesis, which casts doubt over the effectiveness of price limits in stock markets. We find that stocks that hit their limits continue to exhibit high volatility for up to three days, and sometimes beyond, when compared to stocks that nearly hit their limits. As such, it debunks the notion that price limits help to mitigate volatility. Narrow price limits, such as the ± 6% band that existed in the SEM before June 2001, only spread volatility over a three day period. For stocks that hit the upper limits, volatility is two to three times higher than for stocks that only reach 90% or 80% of their upper limits over three days following the limit hits. For stocks that hit the lower limits, the comparative volatility level is about two time higher, and also persists over three days after the limit hit. On June 21, 2001, in a sensible move, the SEM increased the price limit band to ± 15%, thus possibly making limit hits less frequent. One area for further research would be to make a comparative study in order to see whether price fluctuations within larger bands has any effect on reducing volatility spillover. The SEM is not the only exchange to change its daily price limit. In 1997, the Stock Exchange of Thailand increased their limit threefold from ±10% to ±30%, while the Tokyo Stock Exchange reduced their limits from ±7% to ±3.5% in 1998. The effect of price limits on volatility still remains a subject of debate, and inconclusive. Another area of research would be to find the characteristics of firms that hit their limits in a small market like the SEM. Finally, studies on tests for market efficiency need to be carried out on the SEM to investigate whether investors anticipate limit hits. 9
  10. 10. References Blume, Marshall E., A. Craig MacKinlay, and Bruce Terker, 1989, Order imbalances and stock price movements on October 19 and 20, 1987, Journal of Finance 44, 827-848. Fama, Eugene F., 1989, Perspectives on October 1987, or What did we learn from the crash?, in Robert W. Kamphuis, Jr., Roger C. Kormendi, and J.W. Henry Watson, Eds.: Black Monday and the Future of the Financial Markets (Irwin, Homewood, Ill.) French, Kenneth, and Richard Roll, 1986, Stock return variances: The arrival of information and the reaction of traders, Journal of Financial Economics 7, 5-26. Kim, Kenneth A., and S. Ghon Rhee, 1997, Price limit performance: Evidence for the Tokyo Stock Exchange, Journal of Finance 52, 885-901. Kuhn, Betsy A,. Gregory J. Kuserk, and Peter Locke, 1991, Do circuit breakers moderate volatility? Evidence from October 1989, The Review of Futures Markets 10, 136-175. Kyle Albert S., 1988, Trading halts and price limits, The Review of Futures Markets 7, 426-434. Lauterbach, Beni, and Uri Ben-Zion, 1993, Stock market crashes and the performance of circuit breakers: Empirical evidence, Journal of Finance 48, 1909-1925. Lee, Charles M.C., Mark J. Ready, and Paul J. Seguin, 1994, Volume, volatility, and the New York Stock Exchange trading halts, Journal of Finance 49, 183-214. Lehmann, Bruce N., 1989, Commentary: Volatility, price resolution, and the effectiveness of price limits, Journal of Financial Services Research 3, 205-209. Ma, Christopher K., Ramesh P. Rao, and R. Stephen Sears, 1989a, Volatility, price resolution, and the effectiveness of price limits, Journal of Financial Services Research 3, 165-189. Miller, Merton H., 1989, Commentary: Volatility, price resolution, and the effectiveness of price limits, Journal of Financial Services Research 3, 201-203. Roll, Richard, 1989, Price Volatility, International market links, and their implications for regulatory policies, Journal of Financial Services Research 3, 211-246. Schwert, William G., 1989, Why does stock market volatility change over time? Journal of Finance 44, 1115-1153. Stock Exchange of Mauritius, website http://www.semdex.com/ Stock Exchange of Mauritius Factbook, http://www.semdex.com/Final-25_02.pdf 10
  11. 11. Stock Exchange of Mauritius, Rules and Regulations, http://www.semdex.com/rules.htm Stock Exchange of Mauritius, Trading Rules, http://www.semdex.com/trading_rules.htm Stoll, Hans, and Robert Whaley, 1980, stock market structure and volatility, Review of Financial Studies 3, 37-71. Telser, Lester G., 1989, October 1987 and the structure of financial markets, in Robert W. Kamphuis, Jr., Roger C. Kormendi, and J.W. Henry Watson, Eds.: Black Monday and the Future of the Financial Markets (Irwin, Homewood, Ill.) 11

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