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).

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.

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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

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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.

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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.

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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.

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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.

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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

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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: p

night Lt     0 Rtnight   ( j Rtday  j   j Rt  j )  VOLt   t j 1

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.

 Opent Rtnight : Close-to-open return on day t, Rtnight  ln   Closet

  . This is normalized by first 

substracting the firm-specific mean and then dividing by the firm specific standard deviation.

 Closet 1  day   . This is normalized by first Rtday  j : Open-to-close return on day t, Rt 1  ln   Opent 1  substracting the firm-specific mean and then dividing by the firm specific standard deviation.

VOLt : Volatility, measured as the mean of squared returns over the past 20 days. As noted above, the variable of primary interest is Rtnight . 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

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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

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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

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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

 HIGHt  LOWt  daily high and low prices. HLSpreadt    . As shown in Table 7,  0.5( HIGHt  LOWt )  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

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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.

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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.

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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%

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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

4,301

5,201

221 152

190 213

23 14

28 46

46 46

15 20

60 42

108 92

48 31

25 36

44 29

14 19

Number Observations All Firms Returns ≥ +5%: Number Returns ≤ -5%: Number APSW Number Times Returns ≥ +5% Number Times Returns ≤ -5% COMI Number Times Returns ≥ +5% Number Times Returns ≤ -5% EPICO Number Times Returns ≥ +5% Number Times Returns ≤ -5% NSGB Number Times Returns ≥ +5% Number Times Returns ≤ -5% SUCE Number Times Returns ≥ +5% Number Times Returns ≤ -5%

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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 All Firms Returns:

Overnight Intraday Volatility : High-Low SSR APSW Returns: Overnight Intraday Volatility : High-Low SSR COMI Returns: Overnight Intraday Volatility : High-Low SSR EPICO Returns: Overnight Intraday Volatility : High-Low SSR NSGB Returns: Overnight Intraday Volatility : High-Low SSR SUCE Returns: Overnight Intraday Volatility : High-Low Sum Squared Returns

Limits

Mean 0.0019 0.0064 0.0188 0.0071

Std. Dev. 0.0262 0.0383 0.0435 0.0157

Mean 0.0089 -0.0065 0.0247 0.0177

Std. Dev. 0.0217 0.0277 0.0360 0.0209

0.0009 -0.0017 0.0034 0.0211

0.0238 0.0259 0.0248 0.0224

0.0078 -0.0054 0.0252 0.0245

0.0182 0.0422 0.0477 0.0322

-0.0006 -0.0002 0.0229 0.0199

0.0277 0.0239 0.0209 0.0223

0.0094 -0.0009 0.0248 0.0220

0.0258 0.0149 0.0165 0.0289

0.0166 -0.0012 0.0191 0.0756

0.0587 0.0483 0.0406 0.0372

0.0098 0.0187 0.0301 0.0180

0.0271 0.0318 0.0212 0.0126

0.0011 0.0007 0.0118 0.0102

0.0186 0.0217 0.0159 0.0192

0.0121 -0.0016 0.0188 0.0100

0.0193 0.0207 0.0181 0.0089

-0.0006 -0.0002 0.0197 0.0171

0.0155 0.0190 0.0166 0.0188

-0.0009 0.0037 0.0244 0.0012

0.0172 0.0211 0.0174 0.0097

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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 p

night percent or more: Lt     0 Rtnight  0 DRtnight   ( j Rtday  j   j Rt  j )  VOLt   . j 1

night t

R

captures close-to-open returns on day t; the dummy for this variable after the

imposition of price limits is DRtnight . Rtday 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.

night t

R

D Rtnight

Rtday 1 Rtnight 1 Rtday 2 Rtnight 2 Volt (SSR) Constant LR statistic (Marg. Signif.) McFadden R2

Upper Limit 0.562 (0.035) 2.749 (0.575) 0.353 (0.030)

Lower Limit -0.749 (0.048) -0.287 (0.047) -0.459 (0.031)

0.356 (0.025) 0.070a (0.030)

-0.087 (0.026) -0.126 (0.027)

0.032 (0.026) 1.487 (0.040) -2.397 (0.043) 599.3 0.0000 0.291

0.092 (0.026) 1.692 (0.448) -2.550 (0.048) 952.9 0.0000 0.337

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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: p

night Lt     0 Rtnight   ( j Rtday  j   j Rt  j )  VOLt   t . j 1

night t

captures close-to-open returns on day t. Rtday captures open-to-close returns on day R 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

Rtnight D Rtnight Volt (SSR) LR statistic (Marg. Signif.) McFadden R2

Upper Limit 0.164 (0.096) 1.450 (0.648) 1.479 (0.332) 326.8 0.000 0.558

Lower Limit -3.416 (0.373) -0.348 (0.060) 2.667 (1.507) 497.5 0.000 0.594

COMI Upper Lower Limit Limit -0.137 0.224 (0.092) (0.085) 3.272 -0.714 (2.274) (0.134) 0.438 1.465 (0.264) (0.587) 69.9 180.6 0.000 0.000 0.173 0.332

Lower Limit -1.845 (0.233) -0.333 (0.154) 1.918 (0.691) 247.7 0.000 0.667

SUCE Upper Lower Limit Limit 0.620 -0.476 (0.154) (0.086) 1.181 -0.639 (0.598) (0.115) 3.786 0.351 (2.048) (0.394) 184.0 218.8 0.000 0.000 0.603 0.480

NSGB

Rtnight D Rtnight Volt (SSR) LR statistic (Marg. Signif.) McFadden R2

Upper Limit 0.583 (0.121) 0.606 (6.108) 0.847 (0.154) 107.3 0.000 0.396

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EPICO Upper Lower Limit Limit 0.663 -1.528 (0.108) (0.125) 2.067 -0.630 (0.244) (0.118) 0.482 0.244 (0.287) (0.139) 181.1 289.9 0.000 0.000 0.384 0.495

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 p

night five percent or more: Lt     0 Rtnight   ( j Rtday  j   j Rt  j )  VOLt   t . j 1

night t

captures close-to-open returns on day t. Rtday captures open-to-close returns on day R 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.

Rtnight Rtday 1 Rtnight 1 Rtday 2

Rtnight 2 Volt (SSR) Constant LR statistic (Marg. Signif.) McFadden R2

Upper Limit Pre-Limit Limit a 0.803 2.968a (0.052) (0.911) a 0.598 0.495a (0.059) (0.053)

Lower Limit Pre-Limit Limit a -0.806 -1.558a (0.047) (0.099) a -0.357 -0.948a (0.044) (0.069)

0.150a (0.045) 0.268a (0.058)

0.799a (0.063) -0.189 (0.300)

-0.100a (0.033) -0.176a (0.041)

-0.155b (0.070) 0.606 (6.108)

0.068 (0.090) 0.388a (0.055) -2.567a (0.063) 443.8 0.000 0.359

-0.125 (0.069) 0.317a (0.071) -3.239a (0.178) 390.3 0.000 0.408

-0.068 (0.064) 0.500a (0.039) -2.456a (0.055) 453.9 0.000 0.330

0.080 (0.153) 0.436a (0.057) -3.699a (0.189) 711.8 0.000 0.561

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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: Lt     0 R

night t

p

night   ( j Rtday  j   j Rt  j )  HiLot   t . j 1

night t

captures close-to-open returns on day t. Rtday captures open-to-close returns on day R 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 covers January 4, 1998 through December 31, 2001.

Rinight ,t

Riday ,t 1 Rinight ,t 1 Riday ,t  2 Rinight ,t  2 Volt (High-Low) Constant LR statistic (Marg. Signif.) McFadden R2

Upper Limit Pre-Limit Limit a 0.865 3.008a (0.050) (0.887) 0.534a 0.580a (0.054) (0.054)

Lower Limit Pre-Limit Limit a -0.890 -1.698a (0.048) (0.093) -0.356a -0.990a (0.043) (0.073)

0.185b (0.077) 0.200a (0.054)

0.901a (0.063) -0.077 (0.079)

-0.098a (0.029) -0.188a (0.040)

-0.187a (0.043) 0.040 (0.048)

0.087c (0.051) 1.400b (0.694) -2.565a (0.063) 400.5 0.000 0.322

-0.159a (0.047) 1.214b (0.564) -3.000a (0.100) 372.8 0.000 0.410

-0.088 (0.361) 1.077 (0.701) -1.077 (0.070) 458.1 0.000 0.367

0.059 (0.109) 0.687c (0.361) -3.697a (0.199) 712.0 0.000 0.578

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