Transcript of "Investigating Perfomance of Price Limits.doc"
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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
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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
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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.
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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.
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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
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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
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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
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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
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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.
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