price limit performance: evidence from the tokyo stock ... · price limit performance: evidence...

THE JOURNAL OF FINANCE . VOL. LII, NO. 2 . JUNE 1997

Price Limit Performance: Evidence from theTokyo Stock Exchange

KENNETH A. KIM and S. GHON RHEE*

ABSTRACT

Price limit advocates claim that price limits decrease stock price volatility, counteroverreaction, and do not interfere with trading activity. Conversely, price limit criticsclaim that price limits cause higher volatility levels on subsequent days (volatilityspillover hypothesis), prevent prices from efficiently reaching their equilibrium level(delayed price discovery hjfpothesis), and interfere with trading due to limitationsimposed hy price limits (trading interference hypothesis). Empirical research doesnot provide conclusive support for either positions. We examine the Tokyo StockExchange price limit system to test these hypotheses. Our evidence supports all threehypotheses suggesting that price limits may he ineffective.

DAILY PRICE LIMITS SUPPOSEDLY have two attributes to control volatility: first,they establish price constraints; second, they provide time for rational reas-sessment during times of panic trading. Price limits literally limit, or prevent,stock prices from rising above or falling below predetermined price levels. It isposited that such limits would have prevented the price freefall during the1987 crash. Price limits are also supposed to give frenzied traders time to cooloff. Many researchers and market participants blame panic behavior for theexcessive volatility that led to the October 1987 crash (Blume, MacKinlay, andTerker (1989) and Greenwald and Stein (1991)). For these reasons, many of theAsian stock exchanges have already adopted daily price limits (Rhee andChang (1993)). In fact, the Tokyo Stock Exchange (TSE) justifies its price limitsystem by stating that "it prevent(s) day-to-day wild swings in stock prices,"and that it also provides a "time-out" period (Tokyo Stock Exchange Fact Book(1994)).

Despite the appealing rationale to price limits, research confirming thesebeneficial aspects is lacking. Ma, Rao, and Sears (1989a) find evidence of pricereversals after limits are reached, indicating overreaction and subsequentcorrection. They also find that volatility subsides after limits were hit. Inreferring to the study of Ma et al. (1989a), however, Lehmann (1989) and

* Kim is from the University of Rhode Island. Rhee is from the Asian Development Bank onleave from the University of Rhode Island. We thank Yakov Amihud, Kee-Hong Bae, Philip Brown,Rosita Chang, Pin-Huang Chou, William Ferland, Jun-Koo Kang, Andrew Karoljd, Moon K. Kim,Gene Lai, Piman Limpaphayom, Robert Wood, Masahiro Yoshikawa, and seminar participants atthe Sixth Annual Pacific-Basin Finance (PACAP) Conference (Manila), University of Rhode IslandFinance Workshop, and Syracuse University Finance Workshop for their comments. We areespecially grateful to Rene Stulz (the editor) and an anonymous referee who provided insightfulsuggestions and comments.

885

886 The Journal of Finance

Miller (1989) hoth question the knowledge gained from examining volatilityafter limit days since postlimit prices will undouhtedly experience less vola-tility.

Price limit critics, on the other hand, contend that there are at least threeproblems with price limits: volatility spillover, delayed price discovery, andtrading interference. Fama (1989) reasons that if the price discovery process isinterfered with, underlying volatility may increase as a consequence. Thisnotion is supported by Kyle (1988) and Kuhn, Kurserk, and Locke (1991).Kuhn et al. (1991), for example, find that limits were ineffective in reducingvolatility during the 1989 U.S. mini-crash. Lehmann (1989) also suggests thatsupply and demand imbalances for trading actually induce prices to reachtheir limits, which implies a transfer of transactions to subsequent days.Therefore, rather than reducing volatility, price limits may cause volatility tospread out over a longer period of time because limits prevent large one-dayprice changes and prevent immediate corrections in order imbalance.^ Thisspillover to subsequent trading days is consistent with the volatility spilloverhypothesis.^

The delayed price discovery is another costly problem induced by pricelimits. As price limits represent upper and lower bounds on stock prices,trading usually stops (when limit-hits occur) until the limits are revisedcreating an interference with the price discovery process, as previously sug-gested by Fama (1989), Lehmann (1989), and Lee, Ready, and Seguin (1994).By putting constraints on price movements, stocks may be prevented fromreaching their equilibrium prices for that day. If limits block prices, thenstocks have to wait until a subsequent trading period, usually the next day, tocontinue toward their true price. This notion is consistent with the delayedprice discovery hypothesis.

Lauterbach and Ben-Zion (1993) cite the interference of liquidity (trading) asthe "obvious cost" to circuit breakers. This problem is also noted by Fama(1989) and Telser (1989). If price limits prevent trading, then stocks becomeless liquid, which may cause intensified trading activity on following days. Analternative interpretation is offered by Lehmann (1989). He contends thatorder imbalances, and the consequent lack of trading, induce prices to reachtheir limits. The implication is that on subsequent days, impatient investorswill buy or sell at unfavorable prices or patient investors will wait for prices toreach their equilibrium levels so order imbalances can be corrected. In bothcases, this implies that trading volume will be higher on the days followinglimit-days. These activities are consistent with the trading interference hy-pothesis.

^ Roll (1989) succinctly states, "Most investors would see little difference between a market thatwent down 20 percent in one day than a market that hit a 5 percent down limit four days in a row.Indeed, the former might very well be preferable."

^ In studying NYSE-imposed trading halts, Lee, Ready, and Seguin (1994) find increasedtrading volume and volatility on days following trading halts.

Price Limit Performance: Evidence from Tokyo Stock Exchange 887

We empirically test three hypotheses: the volatility spillover hypothesis, thedelayed price discovery hypothesis, and the trading interference hypothesis.For our study, we employ a new design to examine price limit performance.Lehmann (1989) and Miller (1989) both criticize the argument of Ma et al.(1989a) that volatility declines on days following limit days provide favorableevidence for price limits. They feel that such a finding is inevitable and trivialbecause volatility is biased (inclined) to decrease on days after high volatility.Furthermore, Lehmann (1989) states that it is difficult to interpret pricebehavior around limit moves without considering the supply and demand forliquidity. In direct response to their contentions, we compare the behavior ofstocks that reach a price limit to stocks that almost reach their daily limit. Byexamining the postlimit day behavior between both stock categories, we areable to conduct an analysis that is superior to studies that merely comparepostlimit days to limit days of stocks that hit limits. Since the former group ofstocks experience restraints in their price movement while the latter group ofstocks do not, any significant difference in postlimit day behavior can beassociated with the price limit.

This study is the first to provide empirical evidence against price limiteffectiveness. We study the TSE price limit system because a daily price limitsystem does not exist on the New York Stock Exchange (NYSE). Furthermore,the TSE is the second largest stock exchange in the world in terms of marketcapitalization and its price limit system has remained unchanged since 1973.The rest of this article is organized as follows: in Section I, we discuss ourmethods for appraising TSE price limits; in Section II, we present and discussour findings; and finally, in Section III we conclude.

I. The Approach

We use daily stock price data from 1989 to 1992 of the First Section of theTokyo Stock Exchange compiled by the Sandra Ann Morsilli Pacific-BasinCapital Markets (PACAP) Research Center of the University of Rhode Island.In this database, the daily opening, closing, high, and low prices are reported.We adjust our price data to reflect capital distributions that include stocksplits, reduction of capital, rights offerings, and stock dividends. Informationon capital distributions is also obtained from the PACAP databases.

Table I shows the daily price limits utilized by the TSE. Tick sizes andmaximum price variation for successive transactions are also reported. Asreflected in the table, the size of the daily price limit depends on the individualstock price. The price limit range for individual securities is based on theprevious day's closing price and is reestablished each day.

To find occurrences of prices reaching their limits, we identify days wherethe high price matches its previous day's closing price plus its price limit. Inother words, we assume upward limits are reached for a specific stock whenH, > C(_i + LIMIT^, where H< represents Day 's high price, Cj_i representsthe previous day's closing price, and LIMIT^ is the maximum allowable upwardprice movement for each Day t. Similarly, we assume downward limits are


Table I

Tick Size, Maximum Price Variation, and Daily Price LimitThe Tokyo Stock Exchange (TSE) utilizes three price stabilization mechanisms: tick size, maxi-mum price variation, and daily price limit. Tick size is the minimum allowable unit that stock pricemay deviate; maximum price variation is the maximum allowable trade-to-trade price change; anddaily price limit is the maximum allowable price change per day. The stock price determines thesethree values: the last sale price is used to determine tick size and maximum price variation, whilethe previous day's closing price is used to determine the daily price limits.

Price Range in Yen

0 < p < 100100 s p < 200200 < p < 500500 < p < 1,0001,000 s p < 1,5001,500 < p < 2,0002,000 £ p < 3,0003,000 < p < 5,0005,000 < p < 10,00010,000 < p < 30,00030,000 < p < 50,00050,000 < p < 100,000

Tick Size

1111

1010101010

100100100

Maximum PriceVariation

555

1020304050

100200300500

Daily Price Limit

305080

100200300400500

1,0002,0003,0005,000

(Source: TSE Fact Book, 1994)

reached when L < C^_i - LIMIT^, where L represents Day t's low price, andLIMITj represents the maximum allowable downward price movement.^

On days when price limits are reached, we classify stocks that did not reachthe price limit into two subgroups: stocks that came within at least 0.90(LI-MIT^ of reaching the daily limit; and stocks that came within at least 0.80(LI-MIT,), hut less than 0.90(LIMIT,) of reaching the daily limit. In the rest of thearticle, our stock categories for those stocks that did not hit price limits arereferred to as stockso.90 and stockso.so; where the subscripts denote the mag-

^ In using this approach, we discover occurrences where high (low) prices are greater (lesser)than their allowed price fluctuation, where prices move beyond their limits. This is caused by (i)stocks priced between ¥1000 and ¥10,000 using a tick size of ¥10, which often results in high or lowprices being a few yen over or under their allowed price level and (ii) using a base price todetermine the next day's price limits rather than the closing price when order imbalances occur.A special quote, tokubetsu kehai, is used as the base price in these circumstances (We thank MasaoTakamori and Eitaro Nakagawa of the TSE for this information.). In the TSE, successive trans-actions must be executed within the maximum price variation range. If successive orders on thesame side of the market arrive that exceed this maximum price variation, then a special quote isissued (current stock price plus the maximum price variation). Lehmann and Modest (1994a)provide an excellent description of the special quote process. Also, we have communicated withTSE officials to ensure clean samples, however, because price limits are enforced by the saitori,there may be occasions where limits were neglected inadvertently. Nevertheless, there is a veryslim chance of this happening and more importantly, if stocks^jt do contain nonhits, then theempirical flndings would be biased against us.


Table II

Summary StatisticsStocks are categorized into three groups based on the magnitude of their price movement on Day0 (the event day). Stocksît denotes stocks that reach their daily price limit. StockSo.90 denotestocks that experience a price change of at least 0.90(LIMIT() from the previous day's close, hut donot reach a price limit; where LIMIT, denotes the maximum allowable daily price movementon Day t. Stocksogo denote stocks that experience a price change hetween 0.80(LIMIT,) and0.90(LIMIT,). The sample size of each of these three categories during the study period 1989 to1992 are presented below, for both upward price movements and downward price movements.

Upward Price Downward PriceMovements Movements

t in = 1,915) StockShu in = 528)1989 n = 346 1989 n = 151990 n = 936 1990 re = 3691991 re = 286 1991 n = 561992 re = 347 1992 n = 88

Stockso.90 n = 342n = 1,125 Stockso.so « = 575

nitude of a stock's price movement on Day 0, the limit-hit-day.* Stocksît referto those stocks that reach their daily price limit.

Stocks that reach their limit are prevented from correcting their orderimbalance, while stocks that almost hit their limit are not. For example,assuming that the supply for immediacy in these two samples is identical, anydifferences on postlimit days may be associated with differences in the demandcomposition for immediacy. Under these conditions, limit up (down) days aredays where there is a larger imbalance of motivated buyers over sellers (sellersover buyers). If we assume that the supply of immediacy is not identicalbetween the two categories, then it is plausible to suppose that liquiditysuppliers become active less quickly with stocks in the stocksît sample. Li-quidity suppliers may fear the information content of the larger imbalance ofmotivated buyers over sellers (sellers over buyers) on limit up (down) days, andless likely to supply immediacy. Therefore, stocksît are more likely to experi-ence order imbalances for liquidity.^ Finally, we utilize the stockso so sample toshow that differences between stocksît and stockso.90 are not due to thedifference in price movement on Day 0 by showing that differences do not existbetween stockso.90 and stockso.go-

Table II reports the yearly breakdown of price-limit-hit occurrences andshows the number of occurrences for each of the three stock categories for bothupper and lower price movements. For our final samples, we identify 1,915

""We also examined a stockso.70 group and a stockso.6o group. The empirical findings arequalitatively similar to the stocksg 90 and stockso.go results, so we do not report these results for thesake of space and lack of additional insight. Complete empirical results are available from theauthors.

^ We thank an anonymous referee for his discussion on the demand and supply of immediacyand its potential effect on limit performance.


occurrences wbere upper daily price limits are reached and 528 occurrenceswbere lower price limits are bit. Interestingly, tbis implies tbat limits preventmore stock price increases tban decreases.

II. Empirical Findings

A. The Volatility Spillover Hypothesis

To test tbe volatility spillover bypotbesis, we utilize a 21-day event window:Day -10 to +10. For stockShit, Day 0 represents tbe limit-bit-day, forstockso.90, Day 0 represents tbe day tbe stocks experienced tbeir 0.90(LIMIT^)price movement and tbis similarly applies to stockso.so- Day ~1 represents tbeday before Day 0, and Day 1 is tbe day after Day 0, and so fortb.

Daily price volatility is measured by V^j = (r^j)^, wbere Y^j representsclose-to-close returns using Day ^ - 1 closing price and Day t closing price foreacb stock j . ^ We calculate tbis measure for eacb stock in all tbree stockcategories and find averages for eacb Day t. If tbe stockShj group experiencesgreater volatility during postlimit days tban tbe otber subgroups, tben tbisfinding supports tbe volatility spillover bypotbesis. We examine tbe effects ofupper price-limit-bits in tbe next section.'^

A.I. Empirical Results: Upper Limits

Table III contains tbe V data of price increases for stockShit, stockso.go, andstockSo.80 witb multiple limit day observations excluded from tbe sample.^Excluding observations wben stocks bit tbeir limit for tbe second or tbirdconsecutive day eliminates tbe bigb prelimit-day volatility bias tbat occurswben we categorize tbese consecutive bits as independent events. Conse-quently, tbis reduces tbe sample size for tbe stockshit group from 1,915 to1,653.

Of course, all stock categories experience tbeir bigbest level of volatility onDay 0. Tbis is tbe day wben stockShit reacb tbeir upper daily price limits and

^ Since our database contains daily high and low stock prices, we could have employed Parkin-son's (1980) extreme value method to measure volatility. However, Lehmann (1989) correctlypoints out that variance measures that use extreme values, such as Parkinson's, are subject tomeasurement error and that, "measurement errors are more probable on high volume days likelimit price days." In response to Lehmann's acumen, we therefore use a simple measure ofvolatility that does not incorporate extreme values.

' We do not report our volatility results for the lower limit-hit cases since the lower limit-hitfindings are qualitatively the same as the upper limit-hit findings. The lower limit-hit results canbe obtained from the authors upon request.

* We first considered using a sample that included each limit hit as a separate event eventhough it may have been a second or third consecutive limit day. Since these days would also beconsidered Day 0, this would bias the pre-event volatility upwards, while its affect on posteventvolatility is ambiguous. Using the complete sample, we find that stocks^it experience largervolatility preceding the limit day. However, regardless of whether these multiple hits are includedor excluded, the postlimit results remain virtually the same for both samples. Therefore, we onlyreport results without using consecutive limit day stocks as separate events.


Table III

Volatility Spillover: Upper Limit ReachesFor all three stock categories: stockshit, stockso.90, and stockso.so. we calculate volatility for eachday for the 21-day period surrounding the event Day 0. The stock categories are based on themagnitude of their price movement on Day 0. StockShit denotes stocks that reach their daily pricelimit. Stockso.90 denote stocks that experience a price change of at least 0.90(LIMIT,) from theprevious day's close, but do not reach a price limit; where LIMIT, denotes the maximum allowabledaily price movement on Day t. Stockso.so denote stocks that experience a price change between0.80(LIMIT,) and 0.90(LIMIT,). Day 0 denotes the day stocks^it reach their upper-limit-hits. Day- 1 represents the day before Day 0. We use daily returns-squared as our volatility measure, whichis calculated as follows:

where r^j denotes the daily return for each stocky on Day t. Here, V^j is multiplied by 10 . s>and > indicate that the left-hand figure is greater than the right-hand figure at the 0.01 and 0.05levels of significance, respectively, using the Wilcoxon signed-rank test.

Day StockShit Stocksogo StockSo.go

1.508 1.3381.506 1.4421.620 1.3631.624 1.5951.862 1.6332.214 1.798

» 2.202 2.1522.467 2.198

> 2.793 2.5764.076 3.656

» 12.690 s> 9.990» 2.333 . 2.197» 2.553 2.130» 1.745 1.665» 1.856 1.736

1.784 1.486» 1.745 1.466

1.645 1.1881.661 1.3041.667 1.3541.354 1.068

when stockso9o and stockso.go experience their extreme price increases. Foreach day, we compare volatiUty levels hetween stock categories hy using thenonparametric Wilcoxon signed-rank test. The symhols ";$>" and ">" signifythat the left hand volatility measure is greater than the right hand measure atthe 0.01 and 0.05 levels of significance, respectively. From Tahle III, we notedifferences in Day 0 volatility among stock suhgroups, hut this ohservationmerely reflects the different degrees of price movement that occur on Day 0,and no significance should he associated with this result hecause it exists hydesign.

10- 9- 8- 7- 6- 5- 4- 3- 2- 1

0123456789

10

1.5641.6761.5761.5981.7302.0222.9292.4523.3463.476

18.2344.1943.3332.3112.3551.7531.7831.5761.6581.7421.419


On Day 1, we observe a large drop in volatility for stockShit (from 18.234 onDay 0 to 4.194 on Day 1). Researchers may be tempted to conclude that pricelimits have effectively reduced volatility citing volatility decreases after upperprice limits were reached. In fact, Ma et al. (1989a) cite this phenomenon asproof that price limits reduce volatility. However, this interpretation is overlysimplified because volatility will naturally decline after extremely large vola-tility days. When we examine Day 1 volatility for the other two stock groups,we again see the same large drop in volatility despite the absence of limitreaches on Day 0. This finding supports Lehmann's (1989) and Miller's (1989)insight. Consequently, we interpret our results differently from Ma et al.(1989a); specifically, we note that the volatility of stockShit during the post-limit-day period does not drop as much as the volatility of the other stockcategories. On Day 1, the volatility of stocksît is almost twice as large as thevolatility of stockso.go- In fact, stocksît continue to experience greater volatilitythan stockso.go for up to four days after the limit-day. Additionally, we observethat the ordering of the estimated day zero volatilities across subgroups ispreserved without exception in Days 1 to 4. Similarly, the ordering in Days - 1to - 4 is preserved with only two exceptions. Apparently, all three stockcategories experience high volatility, ARCH-like episodes, but stocksît is theonly group with a materially different time path after Day 0, consistent withthe volatility spillover hypothesis.^

We feel that stocksît experience greater volatility on Days 1 to 4 becausestocks that reach their daily price limit may be prevented from correcting theirorder imbalance. This persisting volatility does not exist for stocksogo ^^dstockso.80 ^nd there are no postlimit-day differences between stockso go andstockso.80- In fact, for stocksît, we see tbat volatility on Day 1 is greater thanvolatility on Day - 1 (further reflecting evidence of volatility spillovers),whereas for the other stock groups volatility is lower on Day 1 than on Day - 1(This is verified with the Wilcoxon signed-rank test where all differences aresignificant at the 0.01 level.)

We interpret our findings as evidence tbat price limits cause stockShit tohave volatility spillovers. Stocks that reach their limit are prevented fromexperiencing larger price changes on Day 0. Price movement, in essence,becomes pent-up on limit days, which leads to volatility spillovers in subse-quent days. This interpretation implies that limits do not decrease volatility,but only spread volatility out over a longer period of time.i° This findingsuggests that price limits are not useful in mitigating volatility. In a related

" We are grateful to an anonymous referee for pointing out this important observation.^° We also considered reporting the day-to-day change in volatility for all stock subgroups. If

price limits were not causing volatility spillovers, then the change in volatility on Day 1, from Day0, for stockShit is the most biased among all stocks groups since they, by construction, experiencethe greatest volatility on Day 0. However, our results find that the magnitude of change forstockSo.90 is statistically higher than the magnitude of change for stocksît on Day 1, indicatingvolatility spillovers. For the remaining postlimit-days, the day-to-day change in volatility is thesame across all stock subgroups because, in general, volatility is known to be serially dependent.For the sake of space, we do not report these results.


study. Lee et al. (1994) observe greater volatility in the post-trading-haltperiod at the NYSE, which indicates that trading halts impede the priceadjustment process. Their results are consistent with our findings. Tradinghalts are like price limits except that they are determined subjectively byexchange officials.

B. The Delayed Price Discovery Hypothesis

To examine price limits' effects on efficient price discovery, we look at thefollowing two returns series for each of the three stock categories: KOQCQ) andr(CoOi). The first measure represents open-to-close returns on the limit daymeasured by ln(Co/Oo) and the second represents close-to-open returns mea-sured by ln(Oi/Co). In denotes the natural logarithm operator; O and C denoteopening and closing prices, respectively; and subscripts denote the day. Stockreturns can be positive, negative, or zero and are denoted as (+),(-), and (0),respectively. Consequently, nine returns series are possible: [+, +], [+, - ] ,[+, 0], [0, +], [0, - ] , [0, 0], [-, +], [-, - ] , and [-, 0], where the first returnsymbol represents r(OoCo) and the second return symbol represents r(CoOi).

We examine this particular return series to observe the immediate stockprice movement subsequent to price-limit-hits on Day 0. By comparing thereturn series results among all stock groups, we may be able to identify stockreturn behavior unique to the stocksît sample. The delayed price discoveryhypothesis posits that we will see positive (negative) overnight returns forstocks that reach their upper (lower) limit. Of course, stocks always experienceprice continuations and reversals, so the price continuation behavior ofstockShit would have to be greater than normal to conclude that limits aredelaying the efficient price discovery process. Therefore, we use the pricereturn behavior of stocks that do not reach a price limit to represent normalbehavior. These stocks also experience large price changes similar to stocksît,but without limit hits. If stocksît experience greater price continuation thanthe otber subgroups, then the implication is tbat price limits prevent stockprices from reaching tbeir equilibrium prices during event Day 0, therebydelaying tbe efficient price discovery process. This price continuation bebaviorimplies that price limits prevent rational or informed trading (Roll (1989)),otherwise we would observe price reversals in the context of overreactivebebavior (Ma et al. (1989a, 1989b)). We do not exclude consecutive limit daysfrom our sample since tbis would only underestimate tbe frequency of pricecontinuation.

For upper limit hits, we classify [+, +] and [0, +] as price continuations. Weinclude the latter as a price continuation since it represents stocks that openat the upper limit, remain unchanged on Day 0, and tben experience priceincreases overnight. Also, for upper limit bits, we classify [+, - ] , [0, - ] , [-, +],[-, 0], and [-, - ] as price reversals. The last three return series are consideredreversals because tbe first negative sign indicates reversals before tradingcloses on the limit day. Return series [+,0] and [0, 0] represent no change inprices. For lower limit hits, we classify the return sequences [-, - ] and [0, - ]

894 The Journal ofFinanee

as price continuations and the return sequences [-, +], [0, +], [+, - ] , [+, 0],and [+, +] as price reversals. Return series [-,0] and [0,0] represent nochange in prices.

Table IV, Panel A, presents tbe frequency of price continuations, pricereversals, and no changes. For stocks that hit their upper limit, price contin-uations occur 65 percent of the time and price reversals occur 25 percent of tbetime. In contrast, for stocks tbat almost hit the upper limit (stockso.go), pricecontinuations occur 50 percent of tbe time and price reversals occur 36 percentof the time. Stocksg so experience nearly identical return patterns as stocksg go-For lower limits, stockshit experienced price continuations 49 percent of thetime compared to 32 percent for stocksogo- Also, stockshjt experience reversals44 percent of the time compared to 61 percent for stocksg go-

Overall, price continuations occur more often for stocksj,it tban for stocksg go,even though both stock categories experience nearly identical price cbanges onDay 0.11 This implies tbat price limits delay the price discovery process, tbussupporting the delayed price discovery hypothesis. In addition, limits do notseem to prevent overreactive behavior since price reversal behavior is notpredominant for stocksît- Although reversals do occur after limit days, theyoccur more frequently in tbe absence of limits. From these results, we concludethat price limits seem to be preventing prices from continuing toward theirequilibrium prices on Day 0, without curbing overreactive behavior.

Before concluding our discussion on the delayed price discovery results, wemust determine wbetber the delay in price discovery found in the stockShusample could be due to maximum price variation rules rather than price limitrules.i2 George and Hwang (1995) and Lebmann and Modest (1994a,b) observethat maximum price variation rules slow tbe price discovery process and tbatconsecutive transactions must be made within prespecified maximum priceranges that lead to order breakup in the TSE. To test for this possibility, weidentify stocks whose closing prices match their high (low) prices on Day 0. Forthe stockShit sample, this identifies those stocks tbat closed at their price limit.Table IV, Panel B, reports the results. For both upper and lower price move-ments, stocks that close at their limit experience more continuations and fewerreversals. This evidence indicates tbat price limits prevent efficient pricediscovery for the stocksît sample. This is not to say, however, that maximumprice variation rules do not contribute to inefficient price discovery, but the

^ To test for statistically significant differences, we use a standard nonparametric binomialtest. The following z-statistic is used to answer the question "Do the stocksît sample experiencemore price continuations than the stockso.go sample?": z = (CONhit—PrCONogoNhit)/(PrCONo.9o(l - PrCONo.9o)Nhit)°'*. CONhit denotes the number of price continuations thatstockShit experience; PrCONo.go represents the proportion of price continuations that occur for thestockSo.90 sample and is calculated as CONQ 90/N0.90, where CONQ 90 denotes the number of pricecontinuations that stocksogo experience and NQ90 represents the stockso90 sample size; andfinally, Nît represents the stocksît sample size. The z-statistic is distributed normally sincesample sizes are all sufficiently large (See Olkin, Gleser, and Derman (1980, pp. 244-253)).

^ We are grateful to the referee who motivated this portion of our article.


Table IV

Delayed Price Discovery: Price Continuations and ReversalsTo identify price continuations and reversals, we look at the following two returns series: r(O,C,)and r(C,O,+i). The first measure represents open-to-close returns measured by ln(CyO,) and thelatter represents close-to-open returns measured by ln(O,+i/C,), where 0 and C denote openingand closing prices respectively and t represents the day. Specifically, we examine r(OoCo) andr(CoOi) for all stocks subgroups, where the first measure looks at the open-to-close returns for Day0 and the latter measure looks at the immediate following overnight returns. Stock return caneither be positive, negative, or zero, and is denoted as ( + ),(-), and (0), respectively. Consequently,nine returns series are possible: [ + , +], [ + , 0], [+, - ] , [0, +], [0, 0], [0, - ] , [-, +], [-, 0], and[-, - ] , where the first return represents KOQCQ) and the second return represents r(CoOi). Forupper limit hits, we classify [+, -I-] and [0, +] as price continuations, we classify [-I-, - ] , [0, - ] ,[-, +], [-, 0], and [-, - ] as price reversals, and we classify [ + , 0] and [0, 0] as no change. Forlower limit hits, we classify [-, - ] and [0, - ] as price continuations, we classify [-, +], [0, +],[ + , - ] , [ + , 0], and [+, +] as price reversals, and we classify [-, 0] and [0, 0] as no change. Wepresent the total proportions of continuations, reversals, and no change for each stock subgroup.Stocks are categorized into five categories based on the magnitude of their price movement on Day0 (the event day). StockShit denotes stocks that reached their daily price limit. StockSo.90 denotestocks that experience a price change of at least 0.90(LIMIT,) from the previous day's close, but donot reach a price limit; where LIMIT, denotes the maximum allowable daily price movementon Day t. StockSoso denote stocks that experience a price change between 0.80(LIMIT,) and0.90(LIMIT,). Day 0 denotes the day stocks^it experience their limit-hits. For the sake of space, weuse the abbreviation "S" for each stock group. For each stock group, the proportions may not addto 1.00 due to rounding. The last column reports the difference between S it and So.go- Z-valuesbased on a binomial test statistic is given in parenthesis. We do not report z-values for otherpairwise comparisons. Panel A reports the results for the entire sample. Panel B reports theresults only for stocks that closed on Day 0 at its high (low) price for stocks that experiencedextreme upward (downward) price movement. Panel B sample sizes for Upward Price Movementstocks are as follows: S it: n = 1518; S0.90: n = 293; Sogo: n = 425. Panel B sample sizes forDownward Price Movement stocks are as follows: S^^•^^. n = 3ill; S0.90: n = 124; So.go: n = 195.

Price Behavior

Upward Price MovementsContinuationReversalNo change

Downward Price MovementsContinuationReversalNo change

Panel B: Price Behavior

Upward Price MovementsContinuationReversalNo change

Downward Price MovementsContinuationReversalNo change

Shit

Panel A:

0.650.250.09

0.490.440.07

for Stocks that

0.700.210.09

0.590.350.06

So.90

Entire Sample

0.500.360.14

0.320.610.08

; Closed at Their

0.500.330.17

0.450.460.09

°0.80

0.530.340.12

0.360.570.08

High

0.470.360.17

0.390.500.11

Shit - So.90 (z-value)

0.15(13.13)-0.11 (-10.03)-0.05 (-5.42)

0.17 (8.37)-0.17 (-8.01)-0.01 (-0.84)

or Low Price on Day 0

0.20 (15.38)-0.12 (-9.99)-0.08 (-6.30)

0.14 (5.36)-0.11 (-4.37)-0.03 (-1.70)

896 The Journal ofFinanee

evidence does provide consistent support for the delayed price discovery hy-pothesis.

C. The Trading Interference Hypothesis

To test the trading interference hypothesis, we only present results for the10-day period from Day -4 to Day +5 because days outside tbis shorter eventperiod yield no additional insight. To support the trading interference hypoth-esis, we expect to fmd trading volume increases for the stocks it group on theday after a limit-hit-day indicating continued intense trading. With increasedtrading on subsequent days, the implication is tbat price limits preventrational trading on the event day, suggesting a harmful interference to liquid-ity. For otber stock subgroups, we expect to see decreased or stabilized tradingactivity on subsequent days because price limits do not interfere with tbeirtrading on Day 0.

To examine the trading activity behavior around limit-days, we use thefollowing turnover ratio as our measure for trading activity: TA^ = TVOL /SOUT j, wbere TVOL j represents trading volume for each stock j on Day tand SOUT j represents tbe total number of shares outstanding for stock j onDay t. We calculate this ratio for each stock in all three stock categories andthen fmd averages for eacb Day t. Because the liquidity interference hypoth-esis is interested in the day-to-day cbange in trading activity, we calculate apercentage change from the previous day as follows: lnCTA yTA^ . ) * 100. Intbis analysis, we present results using samples that exclude consecutive limit-days to be consistent with our volatility analysis. ^ Upper limit hits areexamined in the next section, i*

C.I. Empirical Results: Upper Limits

Table V presents the day-to-day trading activity cbanges for each of ourthree stock categories that show an overall pattern of trading increases as Day0 approaches. Not surprisingly, our results reveal increases in trading activityon Day 0 that are mucb larger than the changes on previous days. However,the most striking result is that stocks^it experience an increase in tradingactivity on Day 1, tbe day after the limit day. For stockso.go and stockso.so,trading decreases significantly on Day 1. This result is especially strikingbecause stockso.go and stockShit both experience nearly identical upward pricemovements on Day 0.

Tbe overall decline in trading for stocks with no limit hits indicates tbattraders, for tbe most part, obtain their desired positions on Day 0 in tbeabsence of price limits. In contrast, because price limits interfere with tradingfor stockShit on Day 0, traders wait for the subsequent day to obtain their

^^ While we do not report them, we also conducted our study using complete samples and findvery similar results, thus reflecting the robustness of our trading interference findings.

* Again, we do not report the results for the lower limit cases since the results are qualitativelythe same as the upper limit-hit findings.


Table VTrading Interference: Upper Limit Reaches

For all three stock categories: stockShu, stockso.90, and stockso go, we calculate t rading activity foreach day for the 11-day period surrounding the event Day 0. The stock categories are based on themagnitude of their price movement on Day 0. StockShit denotes stocks tha t reach their daily pricelimit. StockSo 90 denote stocks tha t experience a price change of at least 0.90(LIMIT,) from theprevious day's close, hut do not reach a price limit; where LIMIT, denotes the maximum allowabledaily price movement on Day t. Stockso.go denote stocks tha t experience a price change between0.80(LIMIT,) and 0.90(LIMIT,). Day 0 denotes the day stocks^it experience their upper-limit-hits.Day - 1 represents the day before Day 0. Trading activity (TA) is measured by a turnover ratiowhere for each company j on Day t, we divide daily t rading volume by daily total sharesoutstanding. For each day, we report the percentage change in trading activity from the previousday: ln(TAj,/TAj,_i) * 100, where In represents the na tura l log operator. We calculate thispercentage change for each stock j and report the daily means. :» and > indicate tha t theleft-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 StockShit StockSo9o Stockso.go

7.05% 8.09%9.86% 9.78%8.04% 7.68%

25.33% 15.13%< 82.48% > 74.01%:» -23 .94% -21 .82%< -45 .20% <K -33 .77%

-15 .60% -11 .76%< - 4 . 4 3 % - 9 . 4 1 %

- 9 . 0 5 % - 5 . 6 0 %

desired position. As posited by Lehmann (1989), on the days after prices reachtheir limits, impatient investors will buy or sell at unfavorable prices orpatient investors will wait for prices to be allowed to reach their equilibriumlevels so that order imbalances can be corrected. As a result, we observe highertrading activity on the days following limit-days, indicating order imbalancesfor liquidity. Our results indicate that, for the stockshit sample, investors areforced to wait until the next trading day to continue to transact.

C.2. The Relation between Volatility and Trading Volume

French and Roll (1986), Harris (1986), Karpoff (1987), Schwert (1989), andStoll and Whaley (1990), among others, document a positive relation betweenvolatility and trading volume. So far, we have shown that price limits interferewith trading activity. In this section, we investigate the effect that tradinginterference may have on the volatility to further support the trading inter-ference hypothesis. To examine this issue, we employ the following cross-sectional regression:

Yj = a + b{TA)j + c(Hit-Dummy)y + dj, (1)

- 4- 3- 2- 1

012345

12.70%10.52%9.50%

20.60%72.54%21.07%

-54.34%-14.97%-11.56%-10.11%


where V, is our previously discussed volatility measure for eacb stockj, TA, istbe previously introduced turnover ratio for eacb stock j , and Hit-Dummyrepresents a dummy variable tbat equals 1 for stocks tbat reacb an upper orlower price limit (stockShit) and 0 otherwise. The above regression is run foreacb day of our 21-day event period. We conduct two separate analyses forupper and lower price movements, wbere eacb sample includes two groups ofstocks tbat experience nearly identical upward (downward) price movement onDay 0: stockShit and stockso.go- We use samples that exclude consecutivelimit-bit-days to be consistent witb our previous analyses.

Naturally, we expect the trading activity variable to be significantly positiveon all prelimit days during our 21-day event period, consistent with previousliterature. On the event Day 0, we doubt tbat tbe typical positive relationbetween volatility and trading activity can prevail because of tbe tradingconstraints imposed by price limits. Tbis, tberefore, would imply that on Day0, the Hit-Dummy variable will become significantly positive. We also expectthe Hit-Dummy variable to remain significant on Days 1 to 4 because pricelimits, as we found earlier, cause volatility spillovers that last for four days.

Table VT reports tbe regression results for our upper limit analyses. ^ Asexpected. Table VI presents a positive significant relation between tradingvolume and volatility during tbe prelimit-day period. Days -10 to - 1 , and thepositive relation disappears on the event Day 0 due to tbe trading interferencetbat price limits cause. Tbis finding is further supported by tbe significantlypositive Hit-Dummy variahle on Day 0. More importantly, on Day 1, tbepositive Hit-Dummy variable indicates tbat tbe Day 0 price-limit-bits continueto explain the bigh volatility, wbile tbe trading activity variable does not.Furtbermore, consistent with our volatility spillover results and consistentwith our expectations, tbe dummy variable continues to remain significantuntil Day 4.

Tbese findings bave two very important implications: one, tbe trading in-terference caused by price limits disturbs the normal positive relation betweenvolatility and trading volume; and two, price limits, not bigb trading volume,directly cause tbe volatility spillovers on Day 1. On Days 2 to 4, price limitscontinue to explain the volatility spillovers.

III. Conclusion

We find evidence to support the position of price limit critics who questiontbe effectiveness of price limits in the stock markets. Using three categories ofstocks based on tbe magnitude of a one day price movement, we examine tbeTSE price limit system to compare volatility levels, price continuation andreversal activity, and trading activity patterns. For stocks tbat experiencelimit-hits, we document tbe following results: volatility does not return tonormal levels as quickly as tbe stocks that did not reacb price limits (volatilityspillover hypothesis); price continuations occur more frequently than for stocks

^^ The lower limit results (not reported) are qualitatively the same as the upper limit findings.


Table VI

Trading Interference: Regression Results for Upper Limit ReachesThe following cross-sectional ordinary least squares regressions are run to examine the relationbetween trading activity (TA) as measured by trading volume/shares outstanding and volatility(V):

V, = a + b{TA)j + c (Hit-Dummy )j + dj,

where Hit-Dummy equals 1 for stocks that reached an upper price limit (stocks^t) and 0 otherwise,y, is measured by the daily returns-squared for each stocky and TA is measured by a turnoverratio where for each company7, we divide daily trading volume by daily total shares outstanding.For each day, the percentage change in trading activity from the previous day is calculated asfollows: ln(TAj /TA^ ,_i) * 100, where In represents the natural log operator. The above regressionis run for each day for our 21-day event period. Our sample includes two groups of stocks thatexperience nearly identical upward price movement on Day 0: StockShit and StockSo.go- StockShitdenotes stocks that reach their daily price limit. Stockso.90 denote stocks that experience a pricechange of at least 0.90(LIMIT), from the previous day's close, but do not reach a price limit; whereLIMIT, denotes the maximum allowable daily price movement on Day t. Day 0 denotes the dayStockShit experience their upper-limit-hits. Consistent with previous volatility data, we multiply y,by 103.

Day

-10- 9- 8- 7- 6- 5- 4- 3- 2- 1

0123456789

10

Intercept

1.102**1.242**1.230**1.265**1.489**1.722**1.819**2.088**2.643**3.694**

12.610**2.296**2.238**1.350**1.378**1.385**1.440**1.229**1.380**1.342**1.041**

Trading Activity

0.129**0.083**0.110**0.093**0.077**0.098**0.075**0.068**0.058**0.058**0.0020.0070.032**0.055**0.066**0.058**0.053**0.066**0.058**0.058**0.064**

Hit-Dummy

0.0140.141

-0.087-0.003-0.063-0.116

0.797**0.0190.397

-0.5525.588**1.816**0.762**0.443*0.426*

-0.085-0.003-0.067-0.068

0.0720.031

Adj. R2

0.0840.0340.0620.0570.0220.0880.0390.0290.0130.0240.0660.0170.0150.0420.0560.0610.0380.0670.0380.0280.054

F-Value

106.25**41.20**77.49**71.43**27.73**

113.90**47.89**35.53**16.33**29.88**83.57**21.09**18.76**52.78**70.76**76.46**47.26**84.60**46.41**34.02**66.75**

** and * denote statistical significance at the 0.01 and 0.05 levels, respectively.

tbat did not reach limits (delayed price discovery bypothesis); and tradingactivity increases on the day after the limit day, while all otber stock sub-groups experience drastic trading activity declines (trading interference hy-pothesis). We attribute tbese findings to price limits.

Based on our results, we question tbe effectiveness of price limits in coun-tering overreaction and in reducing volatility. Furthermore, price limits seem


to cause delays in equilibrium price discovery and desired trading activity. Weconcede, however, that our small sample sizes are a weakness in our study.TSE price limits are set wide enough so that limit reaches are rare events.Nonetheless, based on our sample and analysis, the evidence against pricelimits appears to be significant.

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