Directory UMM :Data Elmu:jurnal:J-a:Journal Of Banking And Finance:Vol24.Issue4.2000:

Regulation of the Warsaw Stock Exchange: The

portfolio allocation problem

Wojciech W. Charemza

a,*

, Ewa Majerowska

b,1

a

Department of Economics, University of Leicester, University Road, Leicester LE1 7RH, UK b

Department of Economics, University of Gdansk, 80-824 Sopot, Poland

Abstract

The paper analyses the risk reduction e€ect of limits which are imposed on stock exchange price movements. As a result of the maximisation of tradersÕutility functions subject to expected price constraints, a model similar to the capital asset pricing model (CAPM) is developed, where the observed returns are corrected for the appearance of constraints. An analysis of returns from six securities traded on the Warsaw Stock Exchange has been carried out. The models have been estimated by the two-limit Tobit model and compared with the results for the corrected returns. The results show that the trade barriers increase the portfolio risk. Ó_{2000 Elsevier Science B.V. All rights} re-served.

JEL classi®cation:G12

Keywords:CAPM; Price constraints; Regulation; Emerging markets

1. Introduction

The problem of the optimal portfolio allocation, especially that of ®nding a relationship between the rate of return of a risky asset and the level of risk of this asset is well known in literature. The seminal model is the capital asset www.elsevier.com/locate/econbase

*_{Corresponding author. Tel.: +44-2116-252-2899; fax: +44-2116-252-9081.}

E-mail addresses:wch@le.ac.uk (W.W. Charemza), em@panda.bg-univ.gda.pl (E. Majerowska). 1_{Tel./fax: +48-58-5502549.}

0378-4266/00/$ - see front matterÓ_{2000 Elsevier Science B.V. All rights reserved.}

pricing model (CAPM) developed by Sharpe (1964) and Lintner (1965) based on the contributions of Markowitz (1952, 1958). Further applications and developments of theCAPMmodel are too numerous to be listed here (for some important further developments see Black (1972), Cuthberston (1996), Merton (1973), Thomas and Wickens (1992), and Slade and Thille (1994)). In all these, and in similar models, it is assumed that there are no restrictions and limitations concerning price movements. Such models, where the price is as-sumed to settle at a freely negotiated level, determined by supply and demand, are herein called unconstrained. Although this is the case for many contem-porary markets, nevertheless, in some stock markets, the price of an asset is regulated in such a way that it cannot move by more than a ®xed percentage above or below that of the previous session price. Such regulations have been applied in numerous emerging stock markets (e.g., in China, Lithuania, Poland, Turkey) and also in some mature ones (France). Evidently if the price is not allowed to settle at its equilibrium level because of the presence of institutional constraints, demand may not match supply (or vice versa) and disequilibrium occurs.

This paper proposes a simple model of the optimal portfolio allocation in the case where some prices in the market are regulated (disequilibrium) prices developed from the Sharpe±Lintner version of CAPM. The regulation takes the form of an imposition of price barriers. An estimated model can be used for assessing the impact of such price regulations on the relative risk of the market portfolio. A simple empirical analysis of a stock market in which disequilibrium prices appear, namely, that of the Warsaw Stock Exchange, is carried out.

2. Principal assumptions of the model

It is assumed that the market in which the portfolio allocation decisions are made might be inecient, but the only form of ineciency which might possibly exist is that caused by price regulation (appearance of price straints). Charemza et al. (1997) have shown that appearance of such con-straints, even if they are binding, does not necessarily imply ineciency. Following Elton and Gruber (1991), it is assumed that if the price restrictions are not binding (or more strictly, they are not expected to be binding), the general assumptions of the ecient market hypothesis hold and, in particular, that:

1. there are no taxes;

2. there are no transaction costs and other imperfections;

3. investors can borrow and lend at the risk-free rate an unlimited amount at the same time;

5. there is a ®xed number of assets on the market and they are available for all investors;

6. there is freedom of entry and exit for both buyers and sellers.

The above assumptions imply normality of distribution of the rates of re-turn. Assuming that the portfolio is fully described by the mean and variance of returns, the distribution is described as symmetric (lack of skewness) and has a kurtosis value equal to 3. Regarding the investors, the following assumptions are made:

1. Investors behave rationally, they are risk-averse and maximise expected util-ity of wealth.

2. They are interested only in two features of security: expected returns and risk, the latter expressed by the variance of returns.

3. All investors have identical perceptions of each security and homogeneous expectations.

4. Each investor de®nes a period of time as an investing horizon and these pe-riods are not identical.

5. They have full access to information about the market.

6. Investors are price takers; this means that they assume that their own buying and selling activity will not a€ect asset prices.

7. All investors can lend and borrow without any limitations at a risk-free rate

rat the same time.

8. The separation principle holds, so that the investors take homogeneous de-cisions regarding the composition of the risk portfolio at the ecient fron-tier, and then decide, individually, according to the degree of the particular investor_Õs risk aversion, on the composition of the risk portfolio and the riskless asset.

Evidently, no empirical markets, let alone an emerging market, is fully consistent with the above assumptions. It is generally agreed that, in the absence of price limits, emerging market anomalies causing a lack of eciency (or more precisely, predictability of returns) are not more severe than those of mature markets (see, e.g., Claessens et al., 1995; Richards, 1996). In partic-ular, Buckberg (1995) and Harvey (1995a) found emerging markets behaviour to be consistent with the CAPM model. It is also argued that market ine-ciencies tend to evolve (diminish) over time and it is possible to capture the convergence towards market eciencies (see Harvey, 1995b; Emerson et al., 1997).2

If the price limits are not reached, the organisation of trade at the Warsaw Stock Exchange is that of a batch system order-driven market. Orders are submitted prior to trading and then a price is determined which maximises the

session turnover. As shown by Madhavan (1992) such a system is relatively transparent, with a minimal degree of market asymmetry and, in particular, in equilibrium the market can be regarded as semi-strong ecient. This con®rms the rationale of using CAPM as the equilibrium foundation for analysis of the Warsaw Stock Exchange.

3. Derivation of the model: an outline

Let us introduce the following basic notation:

The Sharpe±Lintner CAPM model could be used to describe equilibrium in terms of either returns or prices. Let the expected value of the portfolio at the end of period for theith investor bel_iand the variancer2

i. The utility function of theith investor isVi…li;r2i†, with the usual assumptions:

If the investor is not constrained on any of the prices (or more precisely, if the quantities traded are not constrained due to the fact that the price for any asset reaches its upper or lower limit) the problem of his/her decision-making is the maximisation of the investor_Õs utility function with respect towijin proportion

to the wealth held in assetjby theith investor:

max

Let the expected value of the portfolioibe described as (see Brennan, 1992)

liˆ

theith portfolio. The variance of the portfolio ofith investor is de®ned as

m the number of investors, iˆ1;2;. . .;m,

n the number of assets,jˆ1;2;. . .;n,

~

pj expected price of assetjat the end of period, de®ned as the

expected value of the price of the jth asset conditional on information available at the beginning of the period pj0 initial price of assetj,

covpj;k† covariance between prices of assetsjandkat the end of

r2

The sum of wealth proportions in a portfolio for each investor is equal to one so that

winˆ1ÿ

Xnÿ1

jˆ1

wij:

In order to ®nd the optimal value of the portfolio, it is necessary to calculate the derivative of the utility function with respect to each asset. Let us calculate it with respect to the ®rst asset:

o_Vi

The ®rst order condition is

Vi1 p~1

So far the result is consistent with the Sharpe±Lintner model. Let us now assume that the price of thenth asset is constrained as

~

nis an expected price of assetnin the equilibrium situation anddis the

maximal admissible (by the regulator) price movement. In particular, if the price constraints are not binding, the price dynamics are described by a mar-tingale processp

nˆp

0

n (see Charemza et al., 1997).

Assume now that the price _Ôhits a boundary_Õ (lower or upper limit) with probabilityx. Then:

Let rik ˆwikpk0 be the amount invested in asset k, for kˆ1;2;. . .;n, ljˆ …p~jÿp0j†=p

0

j is the expected rate of return of asset j, and rjk is the

covariance of the rates of returns between assets j and k. It can be shown that:

Brennan, 1992) for the constrained price we obtain

l1ÿr‡ …rÿd†

For the aggregate market we have

l_ÿrI‡ …r

whereXis a variance and covariance matrix and Iis a vector of units. Solving Eq. (6) by substituting hMˆ …lMÿr†=r2M, wherelM and r2M are,

respectively, the expected rates of returns and the variance of the market portfolio, we get (details of computations are included in the discussion paper version, see Charemza and Majerowska (1998), and are available on request)

r1ˆr‡b1…rMÿr† ÿ …rÿd†

For an individual assetj, if the price of nth is constrained, we have

rjˆrf ‡bj…rMÿrf† ÿ …rf ÿd†

which leads to a solution

The expected value of thejth return is then

As a result we have a model of the rate of return of an individual asset as a function of the rate of return of a risk-free asset (rf), the level of systematic risk

and the initial prices of assetsjth andnth, where the price of thenth asset is limited, and standard CAPM where thisnth price is not limited.

4. Empirical assessment: Warsaw Stock Exchange

Eq. (11) gives rise to a formulation of a simple CAPM-like empirical model for a stock market with regulated prices. Ignoring, for high-frequency data (session-to-session returns) the e€ect of a riskless asset and allowing for con-stant transactional costs, the model can be formulated as

r_tˆa‡brm

t ‡et; …12†

whererm

t denotes the session-to-session returns from the market portfolio in

time (session)tandrtis the return from an individual security corrected by the

censored prices. Suppose that there areN‡1 securities included in the market portfolio, and that they are ordered in such a way that the security investigated in (12) is the last, (N+ 1)th one. Hence, a generalisation of (10) givesr

t being

de®ned as

r_tˆrtÿcft;

where the correction factorcft is

cftˆd

and wherertis the observed, possibly censored, return of theN‡1 security in

time t, d is the relative constraint on price movements (fraction of the last period price which creates the upper or lower limit for returns, see (3)), pi

t; iˆ1;2;. . .;N‡1, is the price of theith security in timet,x‡it andxÿit are

the probabilities of hitting the upper and lower barrier by theith price,wi_{is a}

weight denoting market share of ith security, and z‡it and zÿit are the selector

As the empirical observation implies (see also Fig. 1), the frequencies of hits change over time. In particular, after 1995, the frequency of hits becomes visibly smaller compared to the earlier years. Hence, sensible estimates forx‡

it

andxÿ

it seem to be the empirical frequencies of the lower and upper hits within

the sample computed in a recursive manner, that is taking into account only information available up to timet.3For the ®rst 100 observations the values of

x‡

it andxÿit are held constant and equal the empirical frequencies of hits for this

period. After the 100th observation the frequencies have been updated recur-sively. Finally, the value of parameterdis given by market regulations andwi

are the weights of the stock market index.

Model (12) has been estimated for the six longest-established securities traded at the Warsaw Stock Exchange. The Warsaw Stock Exchange was established on 16 April 1991, with initially two sessions a week in 1991 and 1992, three sessions a week from the beginning of 1993 until the end of 1994 and ®ve (daily) sessions since then. Detailed descriptive and econometric analyses of Warsaw Stock Exchange can be found in Gordon and Rittenberg (1995), Boøt and Miøobeßdzki (1994a,b) and Shields (1997a,b). For our pur-poses it is important to note that, on a trading session, transactions are made at a single price, established by the regulator at a level which maxi-mises demand and supply. This single price is established in a ta_^tonnement

process, where o€ers to sell and buy are lodged with the _Ôauctioneer_Õ before the price is established. If, however, the single price evaluated in this way is greater or lower than the last session price by more than 10%, it is arti®cially

Fig. 1. Original returns fromTonsil.

reduced and kept at a level which is exactly 10% above (below) the last session price. Normally, trading takes place at such regulated price leaving a part of demand or supply in excess.4 Hence, for the Warsaw Stock Ex-change the parameterd introduced to Eq. (3) above is equal to 10%. The six companies selected for estimation are: Exbud (EXB, construction services),

Kable (KAB, cable factory), Krosno (KRO, glass factory), Prochnik (PRO, confection produces), Swarzedz (SWA, furniture factory) and Tonsil (TON, electronics company). These six companies are the longest established on the market and, at the beginning of the existence of the Warsaw Stock Ex-change, represented the majority of the trade. Over time the number of companies listed on the stock exchange has grown rapidly. Nevertheless, these six well-established ÔmatureÕ companies are still regarded as being representative for the entire market. Other major companies have usually been introduced to the market at a much later date and their inclusion would shorten the data sample signi®cantly. We start from almost the beginning of the series, discarding only the ®rst nine observations; our sample contains 966 data points from the 10th session (25 June 1991) until the end of 1996. We do not use direct quantitative information concerning the identi®cation of the disequilibrium trading sessions. Instead, we have assumed that if re-turns were closer than 0.05% to its upper or lower boundary (that is, if the published price was equal or higher than 1.095 times the previous session price, or 0.905 or lower than the previous session price), the upper (lower) boundary was hit. This 0.05% tolerance limit allows us to account for rounding errors of published prices. The source of the data was from de-tailed information published in Gazeta Bankowa (daily) and Rzeczpospolita

(weekly).5 In a few instances missing observations were interpolated. For sessions in which trading was suspended and the stock market statistics denoted zero returns, we randomise the returns by inserting a random number equal to 10% of the standard deviation of returns. Simple auto-correlation analysis of the returns (of which details are not given here but are available on request) do not reveal any substantial autocorrelation in the series, with the largest autocorrelation coecients of about 0.24. The lack of substantial autocorrelation supports the rationale for the adopted method of interpolation of zero returns. In some cases, where prices were allowed to go beyond that limit due to its occasional suspension, we censored the data as if the upper or lower limit was hit.

4

Occasionally, if demand is greater than supply (or the opposite) by more than ®vefold, the transactions might be suspended altogether. Also, there are special regulations which allow some of the securities to be traded at a freely negotiated prices (duringextra timetrading). For simplicity, these are ignored herein.

Tables 1±3 brie¯y summarise the descriptive characteristics of the series. In Table 1 the frequencies of limit hits (censoring) are given. In Table 2 the de-scriptive measures for the series of all returns are presented, together with the Doornik and Hansen (1994) modi®cation of the Bowman and Shenton (1975) test of normality. Under the null hypothesis of normality the statistic has a

v2…2_† distribution. Statistics signi®cant at the 0.05 level of signi®cance are denoted by *. Table 3 gives analogous characteristics computed for the_Ô equi-librium_Õreturns only, that is for the case where the lower or upper barriers were not hit.

The statistics con®rm the relative homogeneity of the sample. For all the series the characteristics are of a similar magnitude, and the distributions of the returns are close to being symmetric. For equilibrium returns the null

hy-Table 1

Frequencies of limit hits (censoring)

EXB PRO KAB KRO SWA TON

Lower 0.069 0.106 0.091 0.084 0.086 0.112

Upper 0.079 0.085 0.085 0.069 0.077 0.090

Total 0.148 0.190 0.176 0.153 0.162 0.202

Table 2

Descriptive statistics and normality tests for all returns

EXB PRO KAB KRO SWA TON

No. of obs. 966 966 966 966 966 966

Mean 0.0028 0.0022 0.0028 0.0015 0.0013 0.0016

SD 0.0464 0.0504 0.0513 0.0482 0.0484 0.0535

Skewness )0.0650 )0.0927 )0.0761 )0.0742 )0.0651 )0.0930

Ex. kurtosis )0.0688 )0.3451 )0.4612 )0.2619 )0.2488 )0.6585

Normality 0.8097 6.959 _{11.016 3.780 3.177 24.711}

Table 3

Descriptive statistics and normality tests for equilibrium returns

EXB PRO KAB KRO SWA TON

No. of obs. 823 782 796 818 809 771

Mean 0.0023 0.0050 0.0041 0.0034 0.0026 0.0045

SD 0.0332 0.0343 0.0378 0.0352 0.0345 0.0386

Skewness )0.0578 0.1799 0.0458 0.0688 0.0364 )0.0024

Ex. kurtosis 0.4556 0.4621 0.2849 0.2359 0.3490 0.0117

pothesis of normality can only be marginally rejected for two of the series (for all returns the censored tails clearly makes the distributions non-normal). The source of some non-normality seems to be excess kurtosis, presumably caused by a concentration of randomised returns around zero for the days where trading was suspended and zero returns recorded. Generally, it might be concluded that the distributions of equilibrium returns are consistent with the assertion of ecient trading taking place during the sessions where price limits were not hit.

Corrected returns can vaguely be interpreted as returns which would have happened if the price limits were not binding. Figs. 1±3 show, re-spectively, the series of uncorrected returns, corrected returns and the correction factor computed for one of the companies analysed, Tonsil. Figs. 4 and 5 show distributions of the original and corrected returns. The ®gures indicate that most of the corrections happen in the early years of the op-eration of the Warsaw Stock Exchange, where hits of the barriers were frequent. The distribution of the corrected returns exhibits a much smaller unconditional variance and greater concentration than that of the original returns.

Two alternative ways of identi®cation of the market returns variable rm t were used. Firstly, the published ocial Warsaw Stock Exchange share index,

WIG, computed for all the shares traded on the market was used as the r_tm

Fig. 3. Correction factor.

variable. Alternatively, it was assumed that the entire market consisted of only six securities and an arti®cial Laspeyres type index for these six com-panies only was constructed (WIG6). For each of the six securities the r_tm variable has been constructed by adjusting the WIG6index by the exclusion of price and quantity weight information on the modelled security. In other words, rm

t represents the returns from the ®ve remaining shares. The com-parison of the originalWIG andWIG6is given in Fig. 6. It shows that until 1994 the development of both indices was almost identical. With the increase in number of securities traded at the Warsaw Stock Exchange the dynamics of both indices started to di€er and the prices of new securities, other than those included inWIG6, were rising faster than the prices of the six securities analysed herein.

The model (12) has been estimated by the full-information maximum like-lihood method in the case where the correction factor was used and, for comparison, by the two-limit Tobit model (see e.g. Rosett and Nelson, 1975; Maddala, 1983, pp. 161±162) in case where the returns were left uncorrected (that is, assuming cf ˆ0). These methods give, under the normality assump-tion, the asymptotically unbiased and asymptotically ecient estimators. Strictly speaking, in both cases the same general likelihood function has been used, assuming thatetIIDN…0;r2e†(see Davidson and MacKinnon, 1993, p.

539):

Lˆ X

rl_<r

t<ru

ln 1

re

/ r

t ÿaÿbr

m t re

‡X

r

tˆrl

ln U r

l_ÿaÿbrm

t re

‡X

r

tˆru

ln 1

ÿU r

u_ÿaÿbrm

t re

;

where /_†; U_† denote, respectively, the density and cumulative density functions of the standard normal distribution, ru _{and r}l _{are the upper and}

lower limits of for the returns. The di€erence is that for the corrected returns the limits imposed are very wide, so that the probability of reaching them is practically equal to zero, while for the uncorrected returns the limits are equal to that imposed on the Warsaw Stock Exchange (‹10%). For the corrected returns, this is a rather computationally expensive way of ®nding the maxi-mum likelihood estimates. Nevertheless, the fact that identical methods applied in both cases increases comparability of the results.6Tables 4±9 show the exemplary estimation results (full set of results is available from the

au-6_{All computations were conducted with the use of the}

GAUSSpackage and theCMLlibrary. The program for estimation of the two-limit Tobit model and detailed results are available on request.

thors on request). The tables give the estimated parameters and their standard errors together with the basic characteristics: log-likelihood function, stan-dard deviation of residuals, Durbin±Watson statistic, Box±Pierce Q statistic for testing the joint hypothesis of residual autocorrelation up to 12th order (denoted asQ(12)), and the augmented Dickey±Fuller statistic with 12 aug-mentations (ADF(12)) for testing the hypothesis of a unit root in the resid-uals. It is important to note that, for the maximum likelihood residuals, the autocorrelation and unit root (cointegration) statistics have to be treated with caution and regard as only a crude indication of the residuals properties. They indicate stationarity of residuals for all estimates, but exhibit some moderate autocorrelation (normally of order greater than one) for most of the series.

5. Conclusions and suggestions for further research

The estimation results show the intercepts a being close to zero and Ôinsigni®cantÕ (that is, with relatively large standard errors). This is gener-Table 4

Exbud: Estimation based onWIG6

Method Constant

0.0016 0.8489 Log-likelihood 0.0521

(0.0014) (0.0572) Resid. SD 0.0399

DW 1.7900

Q(12) 25.1120

ADF(12) )8.6716

Max. likelihood and corrected returns

0.0014 0.6887 Log-likelihood )13.4933

(0.0011) (0.0448) Resid. SD 0.0399

DW 1.7900

Q(12) 21.6856

ADF(12) )8.9167

OLS and uncorrected returns

0.0016 0.7672 Log-likelihood NA

(0.0013) (0.0412) Resid. SD 0.0398

DW 1.7900

Q(12) 24.7205

ADF(12) )8.7425

OLS and corrected returns

0.0021 0.6426 Log-likelihood NA

(0.0013) (0.0409) Resid. SD 0.0395

DW 1.7900

Q(12) 21.7364

ally in line with the non-zero beta CAPM theory and con®rms the decision to omit the low-variation riskless asset from the model. It also indicates that the securities were not, on average, systematically underpriced or overpriced. The two-limit Tobit estimates of the bs are visibly higher than the corresponding ordinary least squares (OLS) estimates. This is not surprising as, due to the nature of censoring, the unconditional (unscaled)

OLS estimates or regression parameters are normally below these of the Tobit, since the latter estimates have their probability mass censored. It is interesting to note that the estimates of relative risk are consistently, and markedly, higher for the corrected rather than for the uncorrected returns. It seems that the result of a lower risk associated with the uncorrected returns can have at least two, mutually consistent, explanations. As the de®nition of beta implies, (b_iˆriM=r2M), it is equal to the ratio of the

covariance of the ith asset examined with the market portfolio to the variance of this portfolio. For the restricted market, the covariance is likely to be relatively high, due to the possible quantity spillover e€ect from the restricted to unrestricted markets (see Charemza et al., 1997). It is worth noting that the market price of risk, often denoted as thelambda coecient (see Cuthbertson, 1996, pp. 38±41), may still be lower for the restricted Table 5

Exbud: Estimation based onWIG

Method Constant

0.0001 0.9776 Log-likelihood 4.2294

(0.0002) (0.0552) Resid. SD 0.0367

DW 1.9300

Q(12) 11.9209

ADF(12) )9.1005

Max. likelihood and corrected returns

0.0006 0.7347 Log-likelihood )13.3631

(0.0010) (0.0448) Resid. SD 0.0365

DW 1.9200

Q(12) 12.7896

ADF(12) )9.2312

OLS and uncorrected returns

0.0003 0.8559 Log-likelihood NA

(0.0012) (0.0351) Resid. SD 0.0365

DW 1.9400

Q(12) 13.1503

ADF(12) )9.2061

OLS and corrected returns

0.0007 0.7974 Log-likelihood NA

(0.0012) (0.0350) Resid. SD 0.0365

DW 1.9200

Q(12) 15.5036

than for the unrestricted market, despite the fact that the beta coecients are generally higher, since expected returns are normally lower in the case of the restricted market. Since it is often hypothesised that in emerging markets investors behaviour is determined by the relative risk rather than market price of risk, the interpretation given above places into question the rationale for regulated trading and suggests the abolition of price barriers.

Secondly, this result can be interpreted in the light of the micro-market structure models with an exogenous random supply (see Brown and Jen-nings, 1989; OÕHara, 1995, pp. 157±160). The disappearance of the quantity restriction signal increases the variance of the return but, at the same time, increases the informational eciency of the price signal. With no restrictions in portfolio allocation, the traders are able to diversify portfolio in such a way that would minimise the correlation between the asset returns shifting the portfolio opportunity set so that risks corresponding to particular ex-pected returns become smaller. This again acts towards the decrease in the correlation of assets returns with portfolio returns, resulting in smaller beta

values. Table 6

Kable: Estimation based onWIG6

Method Constant

0.0017 1.2987 Log-likelihood 3.8900

(0.0014) (0.0546) Resid. SD 0.0398

DW 1.9400

Q(12) 8.8438

ADF(12) )8.8699

Max. likelihood and corrected returns

0.0037 0.1513 Log-likelihood )13.4148

(0.0012) (0.0575) Resid. SD 0.1022

DW 1.5200

Q(12) 150.9664

ADF(12) )9.3610

OLS and uncorrected returns

0.0010 1.1384 Log-likelihood NA

(0.0013) (0.0444) Resid. SD 0.0396

DW 1.9100

Q(12) 7.6310

ADF(12) )8.6982

OLS and corrected returns

0.0019 )0.8493 Log-likelihood NA

(0.0032) (0.1100) Resid. SD 0.0981

DW 1.59

Q(12) 103.6018

Generally, stocks on the Warsaw market can be classi®ed as medium to high risk. For those stocks where thebs are greater than one (which indicates a risky asset), namely forProchnik, Kable, Swarzedz and Tonsil, the bs for the cor-rected returns are much smaller, in the ranges for the low-risk assets. This seems to con®rm the conclusion that much of the risk comes to the market through the existence of the price regulation. There do not seem to be sub-stantial di€erences between the two-limit Tobit and maximum likelihood results obtained for theWIG6andWIGprice indices. It is worth noting that theOLS results indicate that theWIG6portfolio is generally more risky than theWIG portfolio.

It is important to note that by estimatingbeta coecients only a one-pass test of allocative market eciency has been completed. The second pass would be to estimate the security market line by regressing the expected returns on estimated bs. This would also allow for further testing the Sharpe±Lintner CAPM against the Black (1972)zero-beta CAPM (see Campbell et al., 1997, pp. 196±203). In our study, however, we use data for six securities only, which would make results of any cross-section regression analysis questionable. In order to perform the second-pass testing, it would be necessary to increase the number of securities investigated.

Table 7

Kable: Estimation based onWIG

Method Constant

)0.0009 1.1959 Log-likelihood 3.8759

(0.0014) (0.0089) Resid. SD 0.0413

DW 1.7900

Q(12) 39.2968

ADF(12) )9.1208

Max. likelihood and corrected returns

0.0034 0.2175 Log-likelihood )13.3961

(0.0012) (0.0535) Resid. SD 0.1030

DW 1.5000

Q(12) 152.2807

ADF(12) )9.3493

OLS and uncorrected returns

0.0001 0.9441 Log-likelihood NA

(0.0013) (0.0389) Resid. SD 0.0404

DW 1.7800

Q(12) 31.5686

ADF(12) )8.8406

OLS and corrected returns

0.0026 )0.7176 Log-likelihood NA

(0.0032) (0.0944) Resid. SD 0.0982

DW 1.5900

Q(12) 111.0097

Generally, it does not seem that the regulation of the Warsaw Stock Exchange through the imposition of price limits is e€ective. It is expensive, increases market ineciency and, as the history of the Warsaw Stock Exchange reveals, does not shelter the market from the boom±bust events. At the same time, it does not seem to reduce relative risk in allocative portfolios. Portfolios would be more ecient if the correlation between them was allowed to decrease, and this requires the abolishment of price barriers.

Acknowledgements

Charemza gratefully acknowledges ®nancial support of A.C.E. Project

Structural change and spillovers in the East European reform process. Maj-erowskaÕs research was undertaken with the support from the European Union PHARE ACE Programme 1996, which is also gratefully acknowl-edged. We are indebted to Alan Baker, Derek Deadman, Kalvinder Table 8

Tonsil: Estimation based onWIG6

Method Constant

(stand. error)

bparam. (stand. error)

Characteristics

Two-limit Tobit and uncorrected returns

)0.0011 1.1992 Log-likelihood 3.6053

(0.0016) (0.0593) Resid. SD 0.0425

DW 1.8800

Q(12) 17.8873

ADF(12) )10.0200

Max. likelihood and corrected returns

0.0016 0.0712 Log-likelihood )49.3331

(0.0012) (0.1020) Resid. SD 0.1091

DW 1.5600

Q(12) 105.0891

ADF(12) )9.4989

OLS and uncorrected returns

)0.0004 0.0172 Log-likelihood NA

(0.0014) (0.0417) Resid. SD 0.0421

DW 1.8500

Q(12) 17.5701

ADF(12) )9.5713

OLS and corrected returns

0.0010 )1.0312 Log-likelihood NA

(0.0033) (0.1021) Resid. SD 0.1030

DW 1.6500

Q(12) 72.2625

Shields, to participants of the conference Financial Regulation, Financial Intermediation and Economic Growth, Groningen, December 1997, and particularly to two anonymous referees for their helpful comments on earlier drafts of the paper. We are solely responsible for any remaining de®ciencies.

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Table 9

Tonsil: Estimation based onWIG

Method Constant

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