individual stock returns

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Individual stock market riskand price valuation: the case

of Titan S.A.Paraschos Maniatis

Department of Business Administration,Athens University of Economics and Business, Athens, Greece and

Kuwait-Maastricht Business School, Salmiya, Kuwait

Abstract

Purpose The purpose of this study is twofold: to test the hypothesis that the closing prices ofTitan S.A. stock can be approximated by a random walk; and to valuate the risk associated to thisstock. The first question is equivalent to the efficient market hypothesis (EMH) and, therefore, to the

predictability of stocks closing price. The second question follows the first in a natural way,since stocks predictability and risk are in an inverse relationship.

Design/methodology/approach Thepaper investigates the existence of unitroots in the stock andin all stock index, in the lines of Dicky-Fuller modeling. It then investigates the stocks risk focusing theinterest in the behavior of thetime seriesvolatility under the hypothesis thatthey can be described by anautoregressive scheme. Finally, it looks at the relationship between stock returns and market returns inthe lines of the market model.

Findings The study concludes that although the predictability of the stock returnsis impossible, therisk associated with the stock can to some extent be statistically rationalised.

Originality/value The papers value lies in looking into the probability that if the EMH is evenapproximately true, accepting above-average risks is the only way to obtain better-than-averagereturns.

KeywordsStock markets, Financial risk, Stock returns, GreecePaper typeCase study

1. Literature reviewThe efficient market hypothesis, risk and risk measuresThe efficient market hypothesis. What the efficient market hypothesis (EMH) isconcerned with is under what conditions an investor can earn excess returns in a stock.In every day terms, the EMH is the claim that all information available is alreadyreflected in the price of the stock.

This statement in the EMH context is equivalent to the statement that the stocksclosing price Pt is a random walk. And since the best forecast for the tomorrows price in a

random walk is todays price forecast Pt1 EPt1=Pt; Pt21;. . .

P1 all known Pt,it results that all past information is useless. The origin of the modern finance stochastic isBacheliers (1990) work who claimed in his thesis Theorie de la Speculation, that thelogged closing prices lnPtof a stock constitute a time series in which lnP t-lnPt21(whichBachelier defines as the shares returns) are stationary independent increments, normallydistributed with zero mean and finite variance. In the finance literature, the EMH andthe Bacheliers claims are lumped together and collectively labeled random walk theories(RWT), which come in three different versions:

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Vol. 37 No. 4, 2011

pp. 347-361

q Emerald Group Publishing Limited

0307-4358

DOI 10.1108/03074351111115304


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(1) The weak RWT. No technical analysis trading system based on price data alonecan ever outperform the market. The weak version of RWT is just Bacheliersclaim that one cannot create information about tomorrows prices from lookingat what happened in the past.

(2) The semi-strong RWT. No trading scheme based on any publicly availableinformation will be able to outperform the market. According to semi-strongRWT, not only is technical analysis useless, fundamentals are too. However, thesemi-strong version applies only to publicly available information of the sort onecan see in the financial releases of the companies or listening to governmentalpronouncements. All such publicly available information has already been takeninto account in setting the current price of the stock. But perhaps there is stillhope for a winning portfolio-selection strategy by employing insider sources ofinformation. For this case one has.

(3) The strong RWT. No trading scheme based upon any information sourceswhatsoever can outperform the market. Thus, the strong version claims that no

matter where one gets information, it will prove useless in the long-term inobtaining better than market average increment results.

These ideas come with assumptions, either explicit, like Bacheliers statisticalproperties, or implicit, like the EMHs inherent assumptions about the pricingmechanisms and rationality on the part of investors.

There is, however, something inherently paradoxical about the EMH. On the onehand,the EMH claims that is useless to gather information; it will do no better at all in thedevelopment of a trading strategy that will outperform the market. On the other hand,the EMH claims that all available information has already been incorporated into theprice of the stock. But how can thishappen if no one gathers information? In order for theEMH to be valid, there must be a sufficiently large number of traders who do not believe

it. So it can be true if the traders do not think it is true [. . .

]. Further, if the EMH is evenapproximately true, then it should be impossible to make consistentlybetter-than-average returns. Yet, the empirical evidence clearly indicates otherwise;stock exchange markets in all over the world exhibit such better results. How can thisfact be reconciled with consistently better results? The answer is probably that betterresults can only be obtained by accepting above-average risks.

Risk measured by volatility. If the random walk hypothesis is true, it would appearthat one cannot really study stock prices in any empirical sense. After all, the aim of mostempirical research is to use explanatory variables to explain the variation in a dependentvariable. In the present case, the behavior of stock prices cannot be explained empiricallyother than to say that their changes are inherently unpredictable. What is then theinterest in the investigation of stock price behavior? One answer is that one can try to

explain the volatility of stock prices. In particular, to investigate whether volatilitychanges over time in any particular way.

In stock markets, volatility is related to risk. That is, if a stock is highly volatile thenits price can increase quite substantially, but it can also decrease substantially.An investor interesting in purchasing such a volatile stock might make large gains ifthe price rises substantially, but could also make losses if it drops. This argumentsuggests that volatility is a measure of the riskiness of a stock. However, one has to becareful in equating volatility with risk.

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For all figures and calculations, we have used the STATISTICA program. The originaldata and the calculation details are shown in the appropriate STATISTICA files,appended to this text. However, for convenience reasons, we have embedded themain results in the text.

3. Statistical analysisThe statistical analysis includes investigation of unit roots existence in the time series,risk valuation applying volatility analysis of the time series and risk valuation on thebase of the market model.

3.1 Testing for unit roots in the stock and the marketFigure A1 shows in adjusted scaling the closing prices of the stock and market index.The two-time series exhibit a remote but clear similarity in cycles and a rather oppositetrend. The similarity in the cyclical movements implies that both time series follow moreor less the same market behavior. This conclusion is supported by the spectral analysisof the time series. Figures A2 and A3 show the results of spectral analysis of the timeseries, after trend elimination and mean extraction. The periodograms of the stock andmarket exhibit common cycles of duration approximately 60, 120 and 240 days.Therefore, regardless of the opposite trends the series seem to move in the same variationpattern. However, each series considered individually does not exhibit the form of astationary time series, since the time mean of the series changes with the time. The mostof the econometric studies of the stock (and financial in general) time series contain a unitroot i.e. they exhibit behavior of a random walk. The consequences of the existence ofunit root are fatal in relation to the possibility of forecast the future values of the stock.

In order to give evidence to this anticipation, we check the hypothesis of existence ofunit roots in the series considering them as a random walk. The analysis relates to theeffective markets hypothesis, since under this hypothesis the closing prices is a random

walk and the best prediction for the stock is its last realized value. Therefore, the testing ofthe hypothesis is reduced to testing whether the time series is a random walk or not.In the following, we test the hypothesis that the time series of the stock and all stock

indexes are random walks (with or without drift). For this purpose, we apply theDickey-Fuller unit root test. According to the formulation of the unit root tests,the models to be tested are:

DPt d bPt21 1t 1

and:

DMt d bMt21 1t 2

The term 1t in the models is a random variable (residuals) with zero mean and

constant variance.The regressions results are shown in Tables I and II.Testing the values of theb estimates in the above regressions according to the testing

schemeH0:b 0 against the alternativeH1:b , 0 at level of significance 5 percent, theunit root hypothesis cannot be discarded t 22.84690 . 23.14 in model (1) and inmodel (2) t 20.135337 . 23.14. Hence, the time series P and M can be regarded asrandom walks and there is no better forecast for their closing values than their lastrealized values. Nevertheless, one can still have some information on the risk exposure

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of the stock, investigating the stocks volatility, in particular investigating thepossibility that the volatility can be described by an autoregressive scheme.

3.2 Volatility of stock and market

Figure A4 shows the volatilities of the closing values of the stock and market. Theshape of the schedules gives some evidence that the courses of these two variables arerelated. Indeed, this anticipation is enforced by the regression of the stocks volatilityVP to markets volatility VM, as obtained by the model:

VPt a bVMt 1t 3

Table III shows the regression results.As shown in Table III, the relationship of the two variables is poor (adjustedR2 10

percent) but the regressions parameters are significantly different to zero (p-level 0for intercept andslope). Hence, the stocks volatility follows in a remote way the behavior

of the markets volatility. However, since the scope of the study is the investigation isthe stocks predictability, it is necessary to check the stocks (and the markets)predictability by investigating the behavior of each variable considered as a univariatevariable. For this purpose, we consider each variable as an autoregressive scheme.Figures A5-A7 show the autocorrelation and the partial autocorrelation functions forthe stocks volatility. The shape of the autocorrelation function advocates for theanticipation that the stocks volatility is a white noise. However, estimating theautoregressive scheme:

VPt a bVPt21 4

ParameterParameter

estimate

Standarderror of

parameter t (244) p-level Adj.R2Dickey-Fuller critical value for

left-hand t-test at 5 percent

d 3.537515 11.61601 0.304538 0.760978 0.00000 23.14 (for 246 observ.)

b 20.000815 0.00602 20.135337 0.892457

Table II.Regression results for

unit root test in the model

DMt d bMt21 1t

ParameterParameter

estimate

Standarderror ofparameter t (244) p-level Adj.R2

Dickey-Fuller critical value forleft-hand t-test at 5 percent

d 0.876131 0.311221 2.81514 0.005274 0.02818 23.14 (for 246 observ.)b 20.0533309 0.018725 22.84690 0.004791

Table I.Regression results for

unit root test in the modelDPt d bPt21 1t

Parameter Parameter estimate Standard error of parameter t(244) p-level Adj.R2

a 0.000153 0.000026 5.851587 0.000000 0.09944216b 0.497922 0.094008 5.296565 0.000000

Table III.Regression results

in the modelVPt a bVMt 1t


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Positive and significant values for the model parameters are obtained. The parametersestimation is shown in Table IV.

Based on thep-level values for the model parameters, we cannot reject the hypothesisthat the stocks volatility is an AR(1) scheme. Therefore, the stocks volatility is in some

degree, within a confidence interval, predictable. For comparison reasons, we give inTable V the estimation results for the autoregressive scheme:

VMt a bVMt21 1t: 5

In this model, the behavior of the markets volatility as a white noise cannot be rejected,since the betas estimate is not significant at a 5 percent significance level (the estimationresults are shown in Table V). It is likely that the specific cyclical character of thecompanys activity renders offers to the stocks volatility a degree of predictability,which is not enjoyed by the markets volatility.

3.3 The market model

In this paragraph, we investigate the risk valuation based on the market model.The market model is defined as:

RPt a bRMt 1t

a intercept.

b slope (the beta coefficient in financial vocabulary).

RPt Pt 2 Pt21=Pt21 the returns of the individual stock in time t.

RMt Mt 2 Mt21=Mt21 the returns of the market (all stocks index) in time t.

1t regressions residual error in time t.

In most of times b, the estimate ofb, is interpreted as the measure of risk associated tothe stock in the sense that if b , 1 the stock is less responding to the market variationsand more responding if b . 1. However, a better risk measure is the variance explainedby the regression: if (SRP)

2 is the total variance of the depended variable RS can beanalyzed as:

SRP2 b2SRM

2 Se2

ParameterParameter

estimateAsympt.

standard errorAsympt.

t (244) p-levelLower

95 percent conf.Upper

95 percent conf.

a 0.000225 0.000027 8.333619 0.000000 0.000171 0.000278

b 0.134196 0.063570 2.110991 0.035791 0.008980 0.259412

Table IV.Parameters estimates inthe autoregressive model

VPt a bVPt21 1t

ParameterParameter

estimateAsympt.

standard errorAsympt.

t (244) p-levelLower

95 percent conf.Upper

95 percent conf.

a 0.000145 0.000015 9.805888 0.000000 0.000116 0.000174b 20.029237 0.064161 20.455674 0.649030 20.155618 0.097144

Table V.Parameters estimates inthe autoregressive modelVMt a bVMt21 1t

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In this context, the variance b2(SRM)2, explained by the regression, is considered to be

the systematic risk of the stock, associated to the market variations, while the term(Se)2, the not explained part of variance by the regression, is considered as the specificrisk of the stock due to its individual character. We see that b is involved again in the

stock risk but it plays a different role as parameter in the risk measurement. The ratiob2SRM

2=SRP2, which is the squared regressions coefficient of determination,

measures the portion of the stocks systematic risk in the total stocks risk.In Table VI, we read ap-level value .0.05 for the regressions intercept and a zero

p-level value for the beta coefficient. From these values, we conclude that the intercept isnot statistically significant, while the statistical significance of the beta coefficientcannot be rejected at significance level 5 percent. Further, the value of betas estimate(0.676685), although less than one, indicates sufficient response of the stocks returns tothe market ones. In this aspect, the risk associated to the stock, according to the financialinterpretation of beta, is less than the market risk. However, much better interpretable isthe systematic stocks risk as measured byR2, which counts for 29.4 percent of the totalstocks risk, and the specific risk 100 2 29.4 70.6 percent. The two measures are not

contradictory, they do not measure exactly the same thing: beta measures the responseof the returns to the market returns;R2 measures the risk which can be attributed to themarket risk, while 1 2 R2 measures the risk the connected to the specific character of thestock. From this point of view, both beta coefficient andR2 measure risk, but differentkinds of risk.

4. ConclusionsSummarizing the findings of the analysis, we can proceed to the following conclusions:

. The time series of the Titan stock is exposing the characteristics of a randomwalk, which discards any hope of forecasting its future closing prices, even in aconfidence interval. Differing the time series one will obtain a white noise, which

is cannot offer any further information. The same conclusion is valid for the allstocks time series. The above results do confirm the long experience from thestock exchange market: the market is unpredictable. If this was not the case, thespeculators could systematically obtain (a few) positive profits. But this outcomehas never been confirmed by the stock exchange practice and experience.

. The positive value of the beta coefficient in the market model regression showsthat the movements of the Titan stock follow the movements of the all stocksindex. The practical meaning of this result is that the investor has to anticipatethe all stocks index in order to estimate the evolution of his own stocks.

. As indicated by the value of beta coefficient the cyclical character of Titansactivities does not substantially differentiate its returns from the market returns.

.

The Titans stock is exposed to a specific risk about 70 percent of the globalstocks risk.

Parameter Parameter estimate Standard error of parameter t (244) p-level R2

a 20.001110 0.000807 21.37584 0.170134 0.29410088b 0.676685 0.066651 10.15259 0.000000

Table VI.Regression results

in the modelRPt a bVMt 1t


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. Although, the closing prices of the stock do not offer any prediction help, thestocks volatility can to an extent be foreseen, since its volatility can plausiblybe described by an autoregressive scheme AR(1). Besides, regressing the stocksvolatility to markets volatility, one obtains statistically significant estimates of

intercept and slope, which can offer additional information for the stocksvolatility.

. Given the high degree of risk in the stock, one has to reckon with increasedspeculation profits in order to restore the balance higher risk/higher profits.

Reference

Bachelier, L. (1900), Theorie de la Speculation, Gautier-Villars, Paris.

Further reading

Aivazian, S. (1970), Etude Statistique des Dependences, Mir, Moscow.

Arkin, H. and Colton, R. (1964), Statistical Methods, Barnes & Noble, New York, NY.Aunon, J. and Chandrasekar, V. (1998), Introduction to Probability and Random Processes,

McGraw-Hill, New York, NY.

Black, F. (1993a), Beta and return, Financial Analysis Journal, Vol. 48, pp. 36-8.

Black, F. (1993b), Beta and return, Journal of Portfolio Management, Vol. 20, pp. 8-18.

Blake, D. (1990), Financial Market Analysis, McGraw-Hill, London.

Blume, M. (1975), Betas and the regression tendencies, Journal of Finance, Vol. 30, pp. 785-95.

Brailsford, T. (1995), An empirical test of the effect of the return interval on conditionalvolatility, Applied Economic Letters, Vol. 2, pp. 156-8.

Brailsford, T. and Davis, K. (1995), Valuation with imputation, JASSA, Vol. 1, pp. 14-18.

Brailsford, T. and Faff, R. (1993), Modelling Australian stock market volatility, Australian

Journal of Management, Vol. 18, pp. 109-32.Brailsford, T. and Josev, T. (1997), The impact of the return interval on the estimation of

systematic risk in Australia, Pacific-Basin Finance Journal, Vol. 5, pp. 357-76.

Brailsford, T., Faff, R. and Oliver, B. (1997), Research Design Issues in the Estimation of Beta,Vol. 1, McGraw-Hill Series in Advanced Finance, New York, NY.

Brealey, R.A. and Myers, S.C. (1991), Principles of Corporate Finance, McGraw-Hill,New York, NY.

Brooks, R., Faff, R. and Lee, J. (1992), The form of time variation of systematic risk:some Australian evidence,Applied Financial Economics, Vol. 2, pp. 191-8.

Chan, L. and Lakonishok, J. (1993), Are reports of betas death premature?,Journal of PortfolioManagement, Vol. 19, pp. 51-62.

Chatfield, C. (1996), The Analysis of Time Series , Chapman & Hall, London.Collins, D., Ledolter, J. and Rayburn, J. (1987), Some further evidence on the stochastic properties

of systematic risk,Journal of Business, Vol. 60, pp. 425-48.

Corhay, A. (1992), The intervaling-effect bias in beta; a note, Journal of Banking & Finance,Vol. 16, pp. 61-73.

Davies, D. (1992), The Art of Managing Finance, McGraw-Hill, London.

Dimson, E. (1979), Risk measurement when shares are subject to infrequent trading,Journal ofFinancial Economics, Vol. 7, pp. 197-226.

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Draper, P. and Paudyal, K. (1995), Empirical irregularities in the estimation of beta: the impactof alternative estimation assumptions and procedures, Journal of Business Finance and

Accounting, Vol. 22, pp. 157-77.

Efimov, A.V. (Ed.) (1988), Random Functions in Higher Mathematics Part 3, Mir, Moscow.

Fabozzi, F. and Francis, J. (1977), Stability tests for alphas and betas over bull and bear marketconditions, Journal of Finance, Vol. 32, pp. 1093-9.

Fabozzi, F. and Francis, J. (1979), Mutual fund systematic risk for bull and bear markets,Journal of Finance, Vol. 34, pp. 1243-50.

Faff, R. (1992), Capital market anomalies: a survey on the evidence, Accounting ResearchJournal, Vol. 5, pp. 3-22.

Faff, R., Lee, J. and Fry, T. (1992), Time stationarity of systematic risk: some Australianevidence, Journal of Business Finance and Accounting, Vol. 19, pp. 253-70.

Fama, E. (1976), Foundations of Finance, Basic Books, New York, NY.

Fama, E. and French, K. (1992), The cross-section of expected returns, Journal of Finance,Vol. 47, pp. 427-65.

Fama, E. and French, K. (1993), Common risk factors in the returns on stocks and bonds,Journal of Financial Economics, Vol. 33, pp. 3-56.

Fama, E. and French, K. (1996), Multifactor explanations of asset pricing anomalies, Journal ofFinance, Vol. 51, pp. 55-84.

Handa, P., Kothari, S. and Wasley, C. (1989), The relation between the return interval and betas:implications for the size effect, Journal of Financial Economics, Vol. 23, pp. 79-100.

Hawawini, G. (1983), Why beta shifts as the return interval changes, Financial AnalysisJournal, Vol. 39, pp. 73-7.

Huang, D.S. (1969), Regression and Econometric Methods, Wiley, New York, NY.

Lehn, J. and Wegmann, H. (1992), Einfuerung in die Statistik, Teubner, Stuttgart.

Lintner, J. (1986), The valuation of risk assets and the selection of risky investments in stock

portfolios and capital budgets,Review of Economics and Statistics, Vol. 47 No. 1, pp. 13-37.McInish, T. and Wood, R. (1986), Adjusting for beta bias: an assessment of alternative

techniques: a note, Journal of Finance, Vol. 41, February, pp. 277-86.

Murray, L. (1995), An examination of beta estimation using daily Irish data,Journal of BusinessFinance and Accounting, Vol. 22, pp. 893-906.

Ross, S.A. (1976), The arbitrage theory of capital asset pricing, Journal of Economic Theory,Vol. 13 No. 3, pp. 341-60.

Scholes, M. and Williams, J. (1977), Estimating betas from non-synchronous data, Journal ofFinancial Economics, Vol. 5, pp. 309-27.

Sharpe, W.F. (1963), A simplified model for portfolio analysis, Management Science, Vol. 9No. 2, pp. 277-93.

Theil, H. (1970),Principles of Econometrics, Wiley, New York, NY.Ventsel, H. (1973), Theorie des Probabilites, Mir, Moscow.

(The Appendix follows overleaf.)


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Appendix. STATISTICA files

Figure A1.Closing prices of stockand market index 1,400

1,600

1,800

2,000

2,200

2,400

14

15

16

17

18

19

0 16 32 48 64 80 96 112 128 144 160 176 192 208 224 240

P (Left)

M (Right)

Figure A2.Spectral analysis of stock

Period

Note:No. of cases: 246

Periodogramv

alues

0

10

20

30

40

50

0

10

20

30

40

50

0 20 40 60 80 100 120 140 160 180 200 220 240 260

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Figure A4.Stock and market

volatilities0.0002

0.0002

0.0006

0.0010

0.0014

0.0018

0.0022

0.0026

0.0030

0 16 32 48 64 80 96 112 128 144 160 176 192 208 224 240

VP

VM

Figure A3.Spectral analysis of market

Period

Note:No. of cases: 246

Periodogramv

alues

0

2e5

4e5

6e5

8e5

1e6

1,2e6

1,4e6

1,6e6

0

2e5

4e5

6e5

8e5

1e6

1,2e6

1,4e6

1,6e6

0 20 40 60 80 100 120 140 160 180 200 220 240 260


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Figure A5.Autocorrelation

function VP

33.71 0.0037

33.67 0.0023

31.71 0.0027

30.26 0.0026

23.50 0.0150

22.97 0.0109

22.73 0.0068

20.72 0.0080

9.93 0.1928

8.97 0.1752

8.79 0.11777.95 0.0933

5.98 0.1124

5.98 0.0503

4.48 0.0342

Q p

15 +0.013 0.0615

14 +0.086 0.0617

13 +0.074 0.0618

12 +0.161 0.0619

11 +0.045 0.0621

10 +0.031 0.0622

9 +0.088 0.0623

8 +0.205 0.0625

7 +0.061 0.0626

6 +0.027 0.0627

5 +0.058 0.06294 +0.088 0.0630

3 +0.004 0.0631

2 +0.077 0.0632

1 +0.134 0.0634

Lag Corr. S.E.

1.0Note:Standard errors are white-noise estimates

0.5 0.0 0.5 1.0

Figure A6.Partial autocorrelationfunction VP

15 -0.020 0.0638

14 +0.057 0.0638

13 +0.014 0.0638

12 +0.130 0.0638

11 +0.039 0.0638

10 0.010 0.0638

9 +0.029 0.0638

8 +0.190 0.0638

7 +0.055 0.0638

6 +0.003 0.0638

5 +0.037 0.0638

4 +0.087 0.0638

3 0.015 0.0638

2 +0.060 0.0638

1 +0.134 0.0638

Lag Corr. S.E.

1.0 0.5 0.0 0.5 1.0

Note:Standard errors assume AR order of k1

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Figure A7.Forecasts; model: (1,0,0)

seasonal lag: 12 input VP

0.001

0.000

0.001

0.002

0.003

0.004

0.001

0.000

0.001

0.002

0.003

0.004

20 0 20 40 60 80 100 120 140 160 180 200 220 240 260 280

Observed Forecast 90.0000%

Notes:Start of origin: 1; end of origin: 246

Figure A8.Autocorrelation

function VM

26.84 0.0301

24.90 0.0356

24.42 0.0275

23.70 0.0224

22.44 0.021222.43 0.0131

22.41 0.0077

21.17 0.0067

13.20 0.0675

11.43 0.0760

11.40 0.0440

3.54 0.4712

3.00 0.3917

0.44 0.8029

0.21 0.6450

Q p

15

Note:Standard errors are white-noise estimates

0.086 0.0615

14 +0.043 0.0617

13 +0.052 0.0618

12 +0.069 0.0619

11 +0.007 0.062110 +0.008 0.0622

9 +0.069 0.0623

8 +0.176 0.0625

7 0.083 0.0626

6 0.010 0.0627

5 +0.176 0.0629

4 +0.046 0.0630

3 +0.101 0.0631

2 +0.030 0.0632

1 0.029 0.0634

Lag Corr. S.E.

1.0 0.5 0.0 0.5 1.0


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Figure A10.Forecasts; Model: (1,0,0)seasonal lag: 12 input: VM

5e4

0

5e4

0.001

0.002

0.002

5e4

Notes:Start of origin: 1; end of origin: 246

0

5e4

0.001

0.002

0.002

20 0 20 40 60 80 100 120 140 160 180 200 220 240 260 280

Observed Forecast 90.0000%

Figure A9.Partial autocorrelationfunction VM

15

Note:Standard errors assume AR order of k1

0.070 0.0638

14 +0.013 0.0638

13 0.005 0.0638

12 +0.078 0.0638

11 0.013 0.0638

10 0.008 0.0638

9 +0.075 0.0638

8 +0.138 0.0638

7 0.107 0.0638

6 0.010 0.0638

5 +0.176 0.06384 +0.052 0.0638

3 +0.103 0.0638

2 +0.029 0.0638

1 0.029 0.0638

Lag Corr. S.E.

1.0 0.5 0.0 0.5 1.0

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Corresponding authorParaschos Maniatis can be contacted at: [email protected]

To purchase reprints of this article please e-mail: [email protected] visit our web site for further details: www.emeraldinsight.com/reprints

Figure A11.Stock and market returns0.06

0.04

0.02

0.00

0.02

0.04

0.06

0 16 32 48 64 80 96 112 128 144 160 176 192 208 224 240

RP

RM

Figure A12.Regression of RP to RM

RM

RP

0.06

0.04

0.02

0.00

0.02

0.04

0.06

0.04 0.03 0.02 0.01 0.00 0.01 0.02 0.03 0.04 0.05

Note:y = 0.001+ 0.677* x+ eps


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individual stock returns

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