The Magnetic Attraction of Price Limits C. L. Osler* E. Tooma* Abstract This paper provides evidence that price limits exert a magnet effect on prices. As a result, price limits may increase conditional volatility rather than reduce it as intended. We investigate price dynamics on the Egyptian Stock Exchange because, under the tight limits imposed in 1997, trading is halted there relatively frequently. We employ a logit model of the probability of reaching a limit with pooled time-series data from individual firms. Results show that the conditional probability of reaching a limit rose substantially after the limits were imposed. September 2003 * Brandeis University. Mailstop 32, Waltham, MA 02454. The authors thank Blake LeBaron, Paroma Sanyal, and Naari Subramanyam for helpful discussions, but take responsibility for remaining errors.
Transcript
The Magnetic Attraction of Price Limits
C. L. Osler*
E. Tooma*
Abstract
This paper provides evidence that price limits exert a magnet effect on prices. As a result,
price limits may increase conditional volatility rather than reduce it as intended. We
investigate price dynamics on the Egyptian Stock Exchange because, under the tight
limits imposed in 1997, trading is halted there relatively frequently. We employ a logit
model of the probability of reaching a limit with pooled time-series data from individual
firms. Results show that the conditional probability of reaching a limit rose substantially
after the limits were imposed.
September 2003
* Brandeis University. Mailstop 32, Waltham, MA 02454. The authors thank Blake LeBaron, Paroma
Sanyal, and Naari Subramanyam for helpful discussions, but take responsibility for remaining errors.
The Magnetic Attraction of Price Limits
Price limits have become commonplace in stock markets around the world. As of
2001, at least 14 different countries had such restrictions, which halt trading on a
particular firm if it’s share price moves more than a certain amount. The limits in
question ranged from five percent to thirty percent (Table 1).
Despite the widespread adoption of price limits, there is little agreement on their
likely effects. On the one hand, regulators hope that price limits—and circuit breakers
more generally—may curb market volatility. Indeed, Greenwald and Stein (1991)
indicate that circuit breakers may stabilize markets “by reducing transactional risks,
thereby encouraging value buyers to bring their demands to market” (p. 444). On the
other hand, other observers (Ferguson 1988, Miller 1991, Subramanyam 1994) have
pointed out that circuit breakers may actually increase price variability. The possibility
that a limit may be triggered, making further trading impossible, could induce traders to
concentrate their trading earlier in the day. As a result, the existence of limits could have
a destabilizing “magnet” effect that pulls prices toward the limit, generating volatility
rather than suppressing it.
The relevant empirical literature does not resolve this tension. Studies of futures
markets find that price limits either stabilize markets (Kuserk at al. 1989, Arak and Cook
1997) or at least do not create a magnet effect (Berkman and Steenbeek 1998). The one
extant study of price limits on a stock market finds evidence consistent with the magnet
effect (Cho et al. 2002).
2
The effects of price limits are rarely studied in stock markets because the limits
are usually sufficiently wide that they are rarely reached. Indeed, Subramanyam (1994)
noted in his original exposition of the effect, “there may be a shortage of data points to
test this …, because the levels of the DJIA have not often approached the trigger points
since the circuit breakers were put in place.”
This article examines the effects of price limits in a market with a tight five
percent limit: the Egyptian Stock Exchange. For the firms studied here, limits were hit
on 8 percent of trading days during the period January 4, 1998 through December 31,
2001, when limits were in place. Our data include opening and closing prices for the five
firms for which data exist. These data permit us to compare the limit time period with an
earlier no-limit time period, January 3, 1994 through January 31, 1997. Fortunately, these
firms account for over ten percent of total trading, and the results are qualitatively
consistent whether firms are examined as a group or individually. More specifically, we
use logit regressions to examine the conditional probability of reaching a five percent
daily return given the overnight return, before and after the imposition of limits.
Our results provide strong evidence that price limits exerted a magnet effect on
the Egyptian Stock Market. The effect of a 100 basis point rise in overnight returns on the
conditional probability of hitting the upper limit tripled. For lower limits the change was
less dramatic, but still statistically and economically significant. This asymmetry between
upper and lower limits may reflect the absolute prohibition of short sales on the Egyptian
market.
3
The paper has three sections and a conclusion. Section I discusses the relevant
theoretical and empirical literature. Section II describes the data and methodology.
Section III presents the results. Section IV concludes.
I. LITERATURE
The possibility that circuit breakers such as price limits might destabilize prices
through a magnet effect became widely appreciated soon after the Brady Commission
Report on the 1987 stock market crash suggested their use. Ferguson (1988, p. 15) argued
that price limits act as magnets when prices become close to the limits, since “[a]nyone
who thinks they might want to sell, or, worse, need to sell, will be very skittish in a
market that can be closed. These investors will sell at the first sign of conditions that have
been associated with previous closing. … The most predictable result of a policy of
closing a market is to make the market more unstable and chaotic than before.” Miller
(1991) takes the same view.
The possibility that price limits could exert a magnet effect was elaborated
theoretically in Subramanyam (1994). His model, based on Kyle (1985), includes
informed traders, discretionary and non-discretionary liquidity traders, and market
makers. These agents trade in a three period model, in which trading takes place in
periods one and two and the true value of the security is revealed in period three. The key
agents for the magnet effect are the discretionary traders, who face a fixed cost if they
face a trading halt in period two and are unable to trade. In a market without price limits,
the discretionary trader would split his trades across periods, in order to “reduce the price
impact of his trade by trading in a dispersed fashion across periods” (p. 244). When limits
4
are in place, the discretionary trader may choose to concentrate his trades in the first
period. The likelihood of such concentration rises with the cost of failing to trade and
with the proximity of the asset’s true value to the limits.1 2
The possibility that prices might be stabilized by circuit breakers is elaborated by
Greenwald and Stein (1991). They highlight that, after a large volume shock,
transactional risk rises dramatically, in consequence of which value traders will trade less
aggressively. This, in turn, increases the risk faced by market makers, intensifying the
responsiveness of prices to volume. Together, these forces can cause markets to function
less efficiently after large volume shocks. They suggest that trading halts, during which
order books would be opened for general inspection or trades would be pooled, to be
executed later at a common equilibrium price.
In practice, the price limits actually imposed in reality do not correspond exactly
to either of the circuit breaker mechanisms suggested by Greenwald and Stein. In stock
markets, trading is simply halted until the end of the trading day; there is no opening of
order books or pooling of trades. In futures traded on the CBOT, trading beyond the price
limit is simply forbidden for the rest of the trading day. In any case, the theoretical
arguments are sufficiently mixed that the effects of real world price limits can only be
ascertained empirically.
To our knowledge, existing evidence on the effects of price limits on stock
markets is so far limited to one paper: Cho et al. (2002), which studies the Taiwan Stock
Exchange (TSE). Using a GARCH econometric specification that incorporates
1 The rationality of daily price limits has also been discussed by Brennan (1986) and by Ackert and Hunter
(1989), although neither addressed the effects of limits on price movements. 2 Kim and Rhee (1997) and Tooma (2003) both provide evidence in support of this argument from the
Tokyo Stock Exchange and the Egyptian Stock Exchange respectively.
5
momentum effects to intraday data, the authors document a statistically and economically
significant tendency for stock prices to accelerate toward the upper bound, though very
little evidence of acceleration toward the lower bound as the price approaches the bounds.
Evidence from the Taiwan Stock Exchange may not be relevant to all stock exchanges,
however, since trading on that market may continue once prices have reached the limit. In
other markets, like the Egyptian Stock Exchange, a given firm’s shares may not be traded
again until the next morning once the shares reach their price limit.
Evidence from futures markets generally fails to find a magnet effect from price
limits. Arak and Cook (1997) examine the T-Bonds futures market from 1980 to 1987,
traded on the CBOT, focusing on price behavior near limits. They find that prices tend to
reverse course in the first five minutes after the morning open, and that the behavior is
related to the market’s proximity to a price limit. This is consistent with the hypothesis
that limits tend to calm the market. However, the potential policy relevance of this result
is limited since it only considers the first five minutes of trading. Additional evidence of a
calming effect in the T-bond futures market is provided in Kuserk et al. (1989).
Berkman and Steenbeek (1998) study the Nikkei 225 futures contract, which is
traded on the OSE, a market with strict price limits, and also on the Singapore
International Monetary Exchange (SIMEX), which has no price limits. If price limits
exerted a magnet effect, the Nikkei futures on the OSE could have a relatively low (high)
price compared to Nikkei futures on SIMEX when the price approaches the lower and
(upper) limit.3 Their empirical results provide no evidence of such an effect. These results
3 The tests in Berkman and Steenbeek (1998) are well constructed; a limitation of their study, however, is
that the results could be due to strong arbitrage links between the OSE and SIMEX and is not necessarily
inconsistent with the existence of a gravitation effect.
6
seem inconclusive, however, since traders may not be concerned about the OSE limits
given the possibility of unwinding their positions in the relatively lenient Singapore
SIMEX even after OSE price limits are hit.
Though the futures market evidence fails to demonstrate a magnet effect from
price limits, its relevance to stock markets may be limited. In futures markets, there is
usually another contract with a slightly longer maturity available that can serve as a very
close substitute to the contract in question. It is well-known that prices on futures
contracts with close maturity dates are highly correlated: traders who cannot close out a
position in one contract may be able to hedge their position fairly well by trading
contracts with the next maturity date. In stock markets, by contrast, close substitutes are
not readily available. For this reason, it may not be sound to generalize from futures
market results to stock markets.4
In short, the limited evidence available suggests that price limits seem to have
exerted a magnet effect on stocks on the Taiwan Stock Exchange but not in futures
markets. Given the widespread use of price limits on stock markets, and the fact that
price limits are implemented differently in some markets than they are on the Taiwan
Stock Exchange, the need for further evidence on the effect of stock price limits per se is
clear.
II. DATA AND METHODOLOGY
This paper examines the effect of price limits on the Egyptian Stock Exchange.
This market, considered one of the oldest in the world since it dates to the era of British
4 The differences between these studies could in also be related to differences in the way price limits are
carried out in practice since, as noted earlier, all trading is halted in stock markets while in some futures
markets only trading beyond the price limit is halted.
7
colonial rule, is advantageous for our purposes because price limits are set at five percent,
as tight as those on any other stock exchange. Tight limits should tend to heighten the
frequency of days on which the limits are hit, increasing the power of our statistical tests.
There are 1,151 companies listed on the Egyptian Stock Exchange, with a total
market capitalization of L.E. 121 billion (or roughly $20 billion) as of October 2002. Of
these firms, the 100 most heavily traded accounted for 96 percent of trading by value, 85
percent of trading by volume, and 34 percent of total market capitalization in October
2001. Unlike the NYSE, the Egyptian Stock Exchange is an order-driven market that
does not utilize designated market makers. Investors issue orders that are posted on a
large screen in the Exchange, and the market uses a periodic batch process mode to match
these orders and determine equilibrium prices. Trading hours are from 11:30 a.m. to 3:30
p.m. Sunday through Thursday. There is a three-hour pre-opening session in which bids
and offers are matched to determine the opening price. If a stock hits the price limit
during trading hours, all trading on the stock ceases for the day.
The available data, kindly provided by the Egyptian Financial Group, cover five
major Egyptian Stock Exchange companies from January 3, 1994 to December 31, 2001.5
These were the only companies for which individual intraday returns were available both
before and after the limits were imposed on February 1st, 1997. The companies are Arab
Polavara Spinning and Weaving (APSW), Commercial International Bank (COMI),
Egyptian Pharmaceuticals (EPICO), National Societe General Bank (NSGB), and Suez
Cement (SUCE). Fortunately, these five firms are all fairly actively traded: together, they
5 We thank Ms. Heba El-Zoaiby for sharing the data, which are adjusted to account for dividend payouts,
capital distributions and stock splits.
8
account for 12 percent of total trading (by value) on the Egyptian Stock Exchange during
the decade 1992 to 2001.
Table 2 provides descriptive statistics returns, volatility, and the frequency with
which prices moved 5 percent or more for the pre-limit and limit periods. In the pre-limit
period, there are a total of 4,301 firm-day observations. Prices rose five percent or more
on 5.1 percent or 221 of those occasions; prices fell five percent or more on 3.5 percent
or 152 occasions. In the limit period, there are 5,201 firm-day observations. Prices hit the
upper limit on 3.7 percent or 190 occasions, and hit the lower limit on 4.1 percent or 213
occasions.
According to the magnet effect, “the probability of the … price crossing either
circuit breaker bound increases” under price limits (Subramanyam 1994, p. 245). We test
this by examining explicitly the probability of reaching the price limit. We ask: Given
overnight (close-to-open) returns of Rtnight
, what is the probability that the full daily price
move reaches five percent after trading opens? The overnight return establishes the
proximity of price to the limit at the open. Presumably, the probability of reaching the
limit increases with this proximity. Our inquiry focuses on how this probability changes
when limits are imposed. A magnet effect would increase this probability. A calming
effect would reduce it.
We estimate two logit models, one for the probability that prices rise by the limit
amount in a given close-to-close period, one for the probability that prices fall by the
limit amount in a given close-to-close period. Besides the overnight return, the
independent variables in our benchmark model include two days’ worth of lagged
9
overnight and intraday returns, volatility, and dummies for whether prices hit an upper
(lower) limit on t-1 or t-2. The benchmark estimating equation is thus:
tt
p
j
night
jtj
day
jtj
night
tt VOLRRRL
)(1
0
Variable definitions, presented below, apply to regressions for price rises; corresponding
definitions apply to regressions for price declines. (Note: subscripts indicating individual
firms are suppressed.)
Lt: Dummy variable capturing whether the stock’s close-to-close return reaches or
exceeds five percent on day t.
night
tR : Close-to-open return on day t,
t
tnight
tClose
OpenR ln . This is normalized by first
substracting the firm-specific mean and then dividing by the firm specific
standard deviation.
day
jtR : Open-to-close return on day t,
1
1
1 lnt
tday
tOpen
CloseR . This is normalized by first
substracting the firm-specific mean and then dividing by the firm specific
standard deviation.
tVOL : Volatility, measured as the mean of squared returns over the past 20 days.
As noted above, the variable of primary interest is night
tR . We take as evidence of
the magnet effect a significant increase in this variable’s coefficient between the pre-limit
and limit periods. Further lags of returns permit us to capture return autocorrelation
which tends to be higher in emerging markets than in developed markets (Bekaert and
Harvey (1997)). To determine that two additional lags of daily and overnight return were
10
sufficient, the model was re-estimated repeatedly, beginning with four lags and
eliminating insignificant terms. Volatility is included because, given the strong
autocorrelation of volatility in financial markets, high volatility on t-1 increases the
likelihood that prices move by the limit amount on day t.
One advantage of our formulation is that we can distinguish magnet effects from
momentum effects by comparing the behavior of prices before and after the imposition of
price limits. The response of prices to overnight and other lagged returns before the
imposition of limits should capture momentum effects; any change in that response upon
the imposition of price limits should capture magnet effects.
III. RESULTS
The results strongly support the presence of a magnet effect on the Egyptian
Stock Exchange after price limits were imposed in 1997. As discussed earlier, the
coefficient on day-t overnight returns is critical for determining the presence or absence
of a magnet effect. We infer the presence of a magnet effect if that coefficient rises
between the pre-limit and limit sample periods, and indeed the coefficients on overnight
returns rise substantially, for both the upper- and lower-limit regressions (Table 4). For
upper limits, the effect rises by more than five times its original value, from 0.56 to 3.31;
for lower limits, the effect decreases less dramatically, from -0.75 to –1.04. The greater
intensity of the effect of price limits on price behavior near upper limits may reflect the
fact that short sales are strictly prohibited on the Egyptian Stock Exchange. This
potentially limits some agents from trading as they would prefer on the knowledge that
prices are falling. Our results partially parallel those of Cho et al. (2002), who also find a
11
stronger effect of price ceilings than price floors. However, results in Cho et al. suggest
that price floors have little or no effect, while our results suggest that price floors have an
effect symmetric to that of price ceilings, but more moderate.
More broadly, the regression results seem sensible. The likelihood ratio statistics
are very high and are significant at the 99% level. The explanatory power is substantial,
since the McFadden R2s are 29 percent (37 percent) for the upper (lower) limit
regressions. As expected, the coefficient on volatility is consistently positive and
significant, and coefficients on the additional lagged returns suggest substantial return
autocorrelation.
To further substantiate the rise in the likelihood of reaching a limit for a given
overnight return, we ran similar tests for each individual firm. The results are generally
consistent with those reported above for all five firms (Table 5), and are surprisingly
precise given the relatively small amounts of data per firm. McFadden R2s range from 17
percent to 67 percent, and average 47 percent. Of the ten regressions (five firms, upper
and lower limits), the change in the coefficient on concurrent overnight returns has the
right sign in each case, is statistically significant at the five percent level in eight cases,
and is statistically significant at the ten percent level in one more case.
It is possible the changed coefficient on concurrent overnight returns is not
capturing the effect of price limits but instead represents the effect of some other,
neglected change across sub-samples. To investigate this possibility we report non-nested
regressions in which all the coefficients are allowed to change between periods (Table 6).
The changes in the coefficient on overnight returns remain quite strong for both upper
and lower limits. The coefficient for the upper limits rises by a factor of four, from 0.81
12
to 2.92, while the coefficient for the lower limits rises by a factor of almost three, from -
0.85 to –1.51. Note that, though the coefficient rises more for the upper limits, as before,
the asymmetry between upper and lower limits is less extreme.
Previous research suggests that price volatility may be more accurately measured
using the gap between daily high and low prices (Rogers and Satchell 1991, Tooma
2003). With this in mind, we re-estimate the unrestricted split-sample regressions with
volatility measured as a twenty-day moving average of the proportionate spread between
daily high and low prices.
)(5.0 tt
tt
tLOWHIGH
LOWHIGHHLSpread . As shown in Table 7,
the results are quite similar to those associated with the previous volatility measure.
These results consistently indicate that, after price limits were imposed early in
1997, there was a statistically significant increase in the conditional likelihood of prices
on the Egyptian Stock Exchange moving by five percent. Of course, we must also inquire
whether the increased likelihood is economically significant, for which purpose we turn
again to non-nested regressions of Table 5. For upper limits, we find that before the limits
were imposed an increase in overnight returns of one percent increased the likelihood of
returns reaching five percent that day by 19.5 percent. After the imposition of limits this
figure is three times higher, at 62.0 percent. For lower limits, the corresponding figures
were 19.4 percent and 33.0 percent. To us, these changes from the pre-limit to limit
periods seem economically significant.
IV. CONCLUSION
This paper examines whether the imposition of daily price limits changes the
price formation process in stock markets. In particular, we investigate whether price
13
limits bring increased conditional price volatility. As our laboratory we use the Egyptian
Stock Exchange, where tight five percent price limits imposed in early 1997 have brought
relatively frequent trading halts. Logit regressions on intraday data for five individual
firms provide strong evidence that the conditional likelihood the prices move by five
percent was substantially higher under the limits, conditional with Subramanyam’s
(1994) “magnet effect.” The increase in this conditional likelihood is economically and
statistically significant for both upper and lower limits. The increase is more substantial
for the upper limits, which may reflect the Egyptian Stock Exchange’s outright ban on
short sales.
These results suggest that price limits are not an unmitigated blessing, since they
effectively increase conditional volatility. To fully evaluate the consequences of price
limits, however, it would also be important to examine their effects on unconditional
volatility and, more generally, on the rationality of trading and overall market efficiency.
We leave these inquiries for future research.
14
REFERENCES
Ackert, L., and William Hunter, 1989, Tests of a Simple Optimizing Model of Daily
Price Limits on Future Contracts. Center for Study of Futures Markets, Working
Paper No. 193.
Arak, M., and R.E. Cook, 1997, Do Daily Price Limits Act as Magnets? The Case of
Treasury Bond Futures, Journal of Financial Services Research, 12:1, 5-20.
Bekaert, Geert, and Campbell R. Harvey, 1997, Emerging Equity Market Volatility,
Journal of Financial Economics 43: 29-78.
Berkman, H., and Onno W. Steenbeek, 1998, The Influence of Daily Price Limits on
Trading in Nikkei Futures, Journal of Futures Markets, 18:3, 265-279.
Brennan, M. E., 1986, A Theory of Price Limits in Futures Markets, Journal of Financial
Economics 16, 213-233.
Cho, D.D., Russell, J., Tiao, G.C., and Ruey Tsay, 2002, The Magnet Effect of Price
Limits: Evidence from High Frequency Data, University of Chicago, Working
Paper.
Ferguson, R., 1988, What to Do or Not to Do, About the Markets, Journal of Portfolio
Management, 14:4, 14-19.
Harris, L., 1998, Circuit Breakers and Program Trading Limits: What have we learned?,
in: R.E. Litan and A.M. Santomero, eds., Brookings-Wharton Papers on
Financial Services, (Brookings Institutions Press, Washington DC) 17-63.
Kim, K. A., S. G. Rhee, 1997, Price Limit Performance: Evidence from Tokyo Stock
Exchange, Journal of Finance 52, 885-901.
Kim, K.A., 2000, Price Limits and Stock Market Volatility, Economic Letters 71 (2001),
131-136.
Kuserk, Gregory J., Eugene Moriarty, Betsey Kuhn, and J. Douglas Gordon, “An
Analysis of the Effect of Price Limits on Price Movements in Selected
Commodity Futures Markets,” CFTC Division of Economic Analysis Research
Report, 1989.
Miller, M.H., 1991, Financial Innovations and Market Volatility. Oxford: Basil
Blackwell, Inc.
Rogers, L.C., and S.E. Satchell, 1991, Estimating Variance from High, Low, and Closing
Prices, Annals of Applied Probability 1: 504-512.
Subrahmanyam, A., 1994, Circuit Breakers and Market Volatility: A Theoretical
Perspective, Journal of Finance 49, 527-543.
Tooma, E.A., 2003, Evaluating the Performance of Symmetric Price Limits: Evidence
from the Egyptian Stock Exchange, Brandeis University, Working Paper.
15
Table 1. Stock Market With Price Limits, 2003
Market Price Limit
Austria 15%
Belgium 5-10%
Egypt 5%
Finland 15%
France 15%
Luxembourg 5%
Portugal 15%
China 10%
Japan 10-60%
Korea 15%
Malaysia - 30%
Taiwan 7%
Thailand 30%
Turkey 10%
16
Table 2. Frequency of (Absolute) Returns At or Above Five Percent This table shows the number of days on which returns reached or exceeded five percent
for five major firms on the Egyptian Stock Exchange, based on daily data. The Pre-Limits
period covers January 3, 1994 through February 1, 1997. The Limit period covers
January 4, 1998 through December 31, 2001.
Pre-Limits Limit
Number Observations 4,301 5,201
All Firms
Returns ≥ +5%: Number 221 190
Returns ≤ -5%: Number 152 213
APSW
Number Times Returns ≥ +5% 23 28
Number Times Returns ≤ -5% 14 46
COMI
Number Times Returns ≥ +5% 46 15
Number Times Returns ≤ -5% 46 20
EPICO
Number Times Returns ≥ +5% 60 108
Number Times Returns ≤ -5% 42 92
NSGB
Number Times Returns ≥ +5% 48 25
Number Times Returns ≤ -5% 31 36
SUCE
Number Times Returns ≥ +5% 44 14
Number Times Returns ≤ -5% 29 19
17
Table 3: This table presents mean returns and return volatility for five major firms on the
Egyptian Stock Exchange, based on daily data. Overnight returns are log price changes
between the close on day t and the open on day t+1. Intraday returns are log price
changes between the open on day t and the close on day t. High-Low volatility is a
twenty-day trailing average of the absolute difference between high and low prices as a
percent of their average. SSR volatility is a twenty-day trailing average of the sum of
squared returns (with overnight and intraday returns entered separately). The Pre-Limits
period covers January 3, 1994 through February 1, 1997. The Limit period covers
January 4, 1998 through December 31, 2001.
Pre-Limits Limits
All Firms Mean Std. Dev. Mean Std. Dev.
Returns: Overnight 0.0019 0.0262 0.0089 0.0217
Intraday 0.0064 0.0383 -0.0065 0.0277
Volatility : High-Low 0.0188 0.0435 0.0247 0.0360
SSR 0.0071 0.0157 0.0177 0.0209
APSW
Returns: Overnight 0.0009 0.0238 0.0078 0.0182
Intraday -0.0017 0.0259 -0.0054 0.0422
Volatility : High-Low 0.0034 0.0248 0.0252 0.0477
SSR 0.0211 0.0224 0.0245 0.0322
COMI
Returns: Overnight -0.0006 0.0277 0.0094 0.0258
Intraday -0.0002 0.0239 -0.0009 0.0149
Volatility : High-Low 0.0229 0.0209 0.0248 0.0165
SSR 0.0199 0.0223 0.0220 0.0289
EPICO
Returns: Overnight 0.0166 0.0587 0.0098 0.0271
Intraday -0.0012 0.0483 0.0187 0.0318
Volatility : High-Low 0.0191 0.0406 0.0301 0.0212
SSR 0.0756 0.0372 0.0180 0.0126
NSGB
Returns: Overnight 0.0011 0.0186 0.0121 0.0193
Intraday 0.0007 0.0217 -0.0016 0.0207
Volatility : High-Low 0.0118 0.0159 0.0188 0.0181
SSR 0.0102 0.0192 0.0100 0.0089
SUCE
Returns: Overnight -0.0006 0.0155 -0.0009 0.0172
Intraday -0.0002 0.0190 0.0037 0.0211
Volatility : High-Low 0.0197 0.0166 0.0244 0.0174
Sum Squared Returns 0.0171 0.0188 0.0012 0.0097
18
Table 4. Logit Estimation of the Probability of Reaching the Limit
This table reports results from a panel logit model estimation of the probability that prices
for five firms on the Egyptian Stock Exchange moved upwards (downwards) by five
percent or more:
t
p
j
night
jtj
day
jtj
night
t
night
tt VOLRRDRRL )(1
00 .
night
tR captures close-to-open returns on day t; the dummy for this variable after the
imposition of price limits is night
tDR . day
tR captures open-to-close returns on day t. Volt
captures price volatility, measured as the square root of the mean of the sum of squared
half-day returns over the previous twenty days. The pre-limit period covers January 3,
1994 to February 1, 1997. The limit period covers January 4, 1998 through December 31,
2001. Standard errors are in parentheses; results in bold are statistically significant at the
1% level.
Upper Limit Lower Limit
night
tR 0.562
(0.035)
-0.749
(0.048)
D night
tR 2.749
(0.575)
-0.287
(0.047)
day
tR 1
0.353
(0.030)
-0.459
(0.031)
night
tR 1 0.356
(0.025)
-0.087
(0.026)
day
tR 2
0.070a
(0.030)
-0.126
(0.027)
night
tR 2 0.032
(0.026) 0.092
(0.026)
Volt (SSR) 1.487
(0.040)
1.692
(0.448)
Constant -2.397
(0.043)
-2.550
(0.048)
LR statistic
(Marg. Signif.)
599.3
0.0000
952.9
0.0000
McFadden R2 0.291 0.337
19
Table 4. Individual-Firm Logit Estimation of the Probability of Reaching the Limit
This table reports firm-specific logit estimates of the probability that prices for five firms
on the Egyptian Stock Exchange moved upwards (downwards) by five percent or more:
tt
p
j
night
jtj
day
jtj
night
tt VOLRRRL
)(1
0 .
night
tR captures close-to-open returns on day t. day
tR captures open-to-close returns on day
t. Volt captures price volatility, measured as the square root of the mean of the sum of
squared half-day returns over the previous twenty days. The pre-limit period covers
January 3, 1994 to February 1, 1997. A constant term plus lagged returns for two full
days (intraday and overnight) were included in the regression but are suppressed here to
save space. The limit period covers January 4, 1998 through December 31, 2001.
Standard errors are in parentheses; results in bold are statistically significant at the 1%
level.
APSW COMI EPICO
Upper
Limit
Lower
Limit
Upper
Limit
Lower
Limit
Upper
Limit
Lower
Limit
night
tR 0.164
(0.096) -3.416
(0.373)
0.224
(0.085)
-0.137
(0.092) 0.663
(0.108)
-1.528
(0.125)
D night
tR 1.450
(0.648)
-0.348
(0.060)
3.272
(2.274) -0.714
(0.134)
2.067
(0.244)
-0.630
(0.118)
Volt (SSR) 1.479
(0.332)
2.667
(1.507) 1.465
(0.587)
0.438
(0.264)
0.482
(0.287)
0.244
(0.139)
LR statistic
(Marg. Signif.)
326.8
0.000
497.5
0.000
69.9
0.000
180.6
0.000
181.1
0.000
289.9
0.000
McFadden R2 0.558 0.594 0.173 0.332 0.384 0.495
NSGB SUCE
Upper
Limit
Lower
Limit
Upper
Limit
Lower
Limit
night
tR 0.583
(0.121)
-1.845
(0.233)
0.620
(0.154)
-0.476
(0.086)
D night
tR 0.606
(6.108) -0.333
(0.154)
1.181
(0.598)
-0.639
(0.115)
Volt (SSR) 0.847
(0.154)
1.918
(0.691)
0.351
(0.394)
3.786
(2.048)
LR statistic
(Marg. Signif.)
107.3
0.000
247.7
0.000
184.0
0.000
218.8
0.000
McFadden R2 0.396 0.667 0.603 0.480
20
Table 6. Non-Nested Logit Estimation of the Probability of Reaching the Limit
This table compares pre-limit and limit period logit regressions of the probability that
prices for five firms on the Egyptian Stock Exchange moved upwards (downwards) by
five percent or more: tt
p
j
night
jtj
day
jtj
night
tt VOLRRRL
)(1
0 .
night
tR captures close-to-open returns on day t. day
tR captures open-to-close returns on day
t; Volt captures price volatility, measured as the square root of the mean of the sum of
squared half-day returns over the previous twenty days. Standard errors are in
parentheses; results in bold are statistically significant at the 1% (superscript a) and 5%
(b) levels. The pre-limit period covers January 3, 1994 to February 1, 1997; the limit
period covers January 4, 1998 through December 31, 2001.
Upper Limit Lower Limit
Pre-Limit Limit Pre-Limit Limit
night
tR 0.803a
(0.052)
2.968a
(0.911)
-0.806a
(0.047)
-1.558a
(0.099)
day
tR 1
0.598a
(0.059)
0.495a
(0.053)
-0.357a
(0.044)
-0.948a
(0.069)
night
tR 1 0.150a
(0.045)
0.799a
(0.063)
-0.100a
(0.033)
-0.155b
(0.070)
day
tR 2
0.268a
(0.058)
-0.189
(0.300)
-0.176a
(0.041)
0.606
(6.108)
night
tR 2 0.068
(0.090)
-0.125
(0.069) -0.068
(0.064)
0.080
(0.153)
Volt (SSR) 0.388a
(0.055)
0.317a
(0.071)
0.500a
(0.039)
0.436a
(0.057)
Constant -2.567a
(0.063)
-3.239a
(0.178)
-2.456a
(0.055)
-3.699a
(0.189)
LR statistic
(Marg. Signif.)
443.8
0.000
390.3
0.000
453.9
0.000
711.8
0.000
McFadden R2 0.359 0.408 0.330 0.561
21
Table 7. Logit Estimation of the Probability of Reaching the Limit Using
Alternative Volatility Measure
This table compares pre-limit and limit period logit regressions of the probability that
prices 6 for five firms on the Egyptian Stock Exchange moved upwards (downwards) by
five percent or more: tt
p
j
night
jtj
day
jtj
night
tt HiLoRRRL
)(1
0 .
night
tR captures close-to-open returns on day t. day
tR captures open-to-close returns on day
t. HiLot captures price volatility, measured as a twenty-day trailing average of the daily
proportionate distance between high and low prices. Standard errors are in parentheses;
results in bold are statistically significant at the 1% (superscript a), 5% (b), and 10% (c)
levels. The pre-limit period covers January 3, 1994 to February 1, 1997. The limit period
