Testing Limited Arbitrage: The Case of the Tunisian Stock Market

International Journal of Empirical Finance Vol. 2, No. 2, 2014, 65-74 Testing Limited Arbitrage: The Case of the Tunisian Stock Market Salem Brahim 1, Kamel Naoui 2, Akrem brahim 3 Abstract This paper aims at showing that arbitrage, theoretically used as a mechanism of establishing equilibrium in financial markets, is limited in reality. Because of numerous obstacles and risks to arbitrage, assets prices become more and more biased and exhibit numerous anomalies. Like Lam and Wei (2011), in our study we show that arbitrage is limited. To this end, we use a sample of 20 firms listed on the Tunis Stock Exchange (TSE) over a period stretching from July 2007 to June 2012. The results indicate that arbitrage is limited and does not play a fundamental role in stabilizing prices. 1. Introduction If all investors are rational, efficiency prevails as each investor is able to correctly evaluate assets and no one would deviate from the fundamental value. However, Shleifer and Summers (1990 : 19-20 ) argue that because of irrational investors behavior, price may deviate in the long term from its fundamental value making rational arbitrageurs unable to fully bring asset prices to their equilibrium value because of price risk. It follows from this line of thinking that financial rationality cannot only be limited to observing the fundamentals. Some investors, with limited rationality, i.e. they are unable to process all of public information available on the market, naively base their decisions only on market prices. Delong et al (1990b) qualify investors who buy when prices rise and sell after they drop by "positive feedback traders" and propose a model in which these investors do indeed affect prices and do cause excess volatility. Then, according to what efficient markets theory predicts, arbitrage transactions must be made to compensate for the "positive feedback traders" effect on market price. However, behavioral finance indicates that arbitrage is a risky business and therefore limited when we consider investors risk aversion. It follows that arbitrageurs cannot thoroughly eliminate pricing errors. The limits to arbitrage originate from rational agents fear of the destabilizing effect on prices caused by "feedback traders". Indeed, Delong et al (1990b) argue that in the presence of "positive feedback traders", arbitrageurs tend to predict their reactions and engage into massive purchases or sales to better repurchase or resell later. This means that arbitrageurs seek less to hedge part of the disequilibrium and to exploit more irrationality of some investors. Arbitrageurs who know irrational agents behavior, "feedback traders", and who dispose information on the fundamentals, may have an interest in raising market price above the equilibrium price and then sell in better conditions. In other words, arbitrageurs in the presence of "feedback traders" destabilize the market and this is because of price risk. Thus, based on destabilizing arbitrage theory, in line with the work of Santana and Wadhwani (1992), Bohl and Siklos (2004), we can highlight the limits to arbitrage relying on the presence of "positive feedback traders" in the market. In their presence, arbitrage operations become destabilizing and therefore asset prices deviate from their fundamental values and exhibit excess volatility. The more the weight of "positive feedback traders" is important in the market, the more the deviation of prices from their fundamental values can be potentially important. 1 Institut supérieur d informatique,tunis El Manar University 2 Department of accounting and finance, Business School of Tunis Manouba University 3 Phd in finance,tunis El Manar University 2014 Research Academy of Social Sciences http://www.rassweb.com 65

S. Brahim et al. Therefore evidence of the presence of "positive feedback traders" in the market informs us about their destabilizing impact on asset prices and their ability to boost volatilities. We may conclude that their presence in the market reflects limits to arbitrage due to price risk. Then, this paper is structured into two sections. The first section will focus on the limits to arbitrage. We will try to highlight the limits to arbitrage relying on the presence of "positive feedback traders." The second section will empirically apply different econometric techniques to highlight the possible presence of "positive feedback traders" using the Tunisian stock market as our case study. 2. Highlighting limits to arbitrage in the Tunisian stock market Behavioural finance theory is based on two assumptions, namely irrationality of some investors and limits to arbitrage. Shleifer and Summers (990, pp. 19-20) argue that "investors are not fully rational and arbitrage is risky and therefore limited". According to efficient markets theory, deviation of asset price from its fundamental value and excess volatility do not strongly impact markets efficiency insofar as their effects on prices are temporary. Arbitrageurs (rational) are fully aware of the fundamental value of assets; therefore they are able, without making errors, to permanently reset asset prices to their fundamental values. In reality, it is quite the opposite and arbitrage found itself limited as a result. Prices may deviate significantly from their fundamental values, entailing excess volatility without arbitrageurs being able to bring assets prices to their fundamental values. In this section, we examine the limits to arbitrage and their impact on the persistence of the deviation between assets prices and their fundamental values. We show that behaviour of arbitrageurs, supposed to be rational, cannot neutralize the behaviour of irrational investors. In the second section, under certain circumstances, behaviour of arbitrageurs in the presence of "feedback traders" may exacerbate rather than reduce deviation of asset prices from their fundamental values Shleifer (2000). Arbitrage: theoretical limits According to Sharpe and Alexander (1990), arbitrage is defined as "the simultaneous purchase and sale of the same asset in two different markets at different and profitable prices." This definition assumes that rational agents know the fundamental value of all assets which are subject of arbitrage. If rational agents find that the same asset can be traded at two different prices, they buy at a lower price and simultaneously resell at a higher price, and therefore they make a profit without taking any risk. The process continues until equilibrium between asset prices and their fundamental values is restored. Theoretical limits of arbitrage Black and Scholes (1973) and Modigliani and Miller (1953) systematically used arbitrage, particularly while evaluating derivative assets. Arbitrage provides the opportunity to achieve, with certainty, a profit with no investment nor risk. Financial markets often offer arbitrage opportunities to rational agents to take advantage of some imbalances in these markets. The hypothesis of no arbitrage rests on strong restrictive assumptions: Hypothesis of market completeness or perfection: This hypothesis assumes that markets are perfect and therefore there are no barriers to conducting transactions. There are no transaction costs and taxes that could compromise potential profits, in which case investors would have no interest to invest. Hypothesis of neutral risk probability: arbitrageurs attitude towards risk does not intervene in their decisions to use or not any strategy. Occurrence probabilities of similar attitudes have no impact on their trading strategies. Hypothesis of preferences rationality: Investors should have an increasing utility function and an expected utility maximizing behaviour. 66

International Journal of Empirical Finance Hypothesis of investor s finite horizon: The hypothesis of no arbitrage requires a finite horizon in which arbitrage benefits might be achieved. If there is an arbitrage opportunity, agents wait for that horizon to enjoy profits. If the assets which are subject of arbitrage have an infinite lifetime, arbitrage opportunities will create uncertainties as assets prices at interim dates cannot be clearly defined, and arbitrage may persist. Thus, this set of hypotheses is a theoretical limit to arbitrage in the sense that they are perfect and do not correspond to financial markets reality. Broihanne et al (2004) show that arbitrage is rarely perfectly riskless without even considering aspects related to market imperfections such as transaction costs or restrictions on short sales. In the following section, we will examine in more detail factors leading to limits to arbitrage with examples illustrating the mentioned limits. Factors leading to limits to arbitrage Delong, Shleifer and Waldman (1990a) have challenged Friedman thesis of investor behaviour based on the sole criterion of fundamental value and oppose the supposed rationality of some investors and their actions against intervention of irrational agents. These authors show that, in many cases, arbitrage is not without risk and is therefore limited by many factors. Risks inherent in arbitrage For arbitrage to be without risk, it is necessary that funds can be held during an indefinite period. In other words, they can be deferred without cost till achievement of equilibrium. However, in reality, Shleifer and Summers (1990), Baker et al (2002) and Wei and Zhang (2006) argue that arbitrage is not an operation with certain results and that sometimes it may need investments. Shleifer and Summers (1990) distinguish two types of risk that may affect arbitrage. The fundamental risk: This risk refers to the risk of asset dispersion before convergence to the fundamental value occurs. This risk is due to unexpectedly disclosing fundamental information leading to an appreciation of the fundamental value. Then, if price changes the way arbitrageurs had not planned, then these latter can be induced into liquidating their funds and record losses. The financing risk: This risk is associated with the fact that the convergence of the asset to its fundamental value is often slow to occur. Indeed, limited access to capital and access to credit, may explain why long-term arbitrage cannot be maintained indefinitely. An arbitrage that is slow to become profitable because the initial disequilibrium persists or worsens leads to withdrawals and liquidation of funds. Wei and Zhang (2006) identified a third source of risk to arbitrage: operational risk. Operational risk: This risk is caused by market imperfections such as transaction costs or heavy constraints on short sales. This risk may limit convergence between asset price and its fundamental value. Sometimes some arbitrage transactions are impossible to make because of regulatory and institutional reasons. Shleifer (2000) adds a fourth source of risk to arbitrage, namely "noises traders." risk. "noises traders' risk is caused by the presence of" noises traders "(irrational market agents who act on non-fundamental information and who deviate assets from their fundamental values (Shleifer and Vishny (1997)). This risk arises from arbitrageurs inability to anticipate future price movements in the presence of "noises traders". Accordingly, if variation of asset prices is not consistent with expectations of rational agents (arbitrageurs), they will be forced to liquidate their finds and abandon profits that may be recovered from arbitrage operations. 3. Methodology Data The selected sample consists of 20 companies listed on the Tunisian stock market over a study period stretching from July 2007 until June of 2012. To calculate the market index monthly return, our choice was 67

S. Brahim et al. focused on a more general index, namely the Tunindex. To extract the chosen approximate measure, namely IVOL, for the year 2012, we should regress the market model on the performance of the 20 companies in the sample and the market index return for the period July 2010 until June 2010, i.e. the last 36 months ending in June of that year. The same procedure is followed for the 2011 and 2010 years. Each sub-sample consists of 720 observations. To calculate standard deviation of a set of clustered data, we must choose in advance which model is better suited to our data. In other words, we shoould choose among the fixed effects model or the random effects model. The choice of one or the other is determined by the Hausman test. This test is to test the presence or not of a correlation between the specific effects and the independent variables of the fixed effects and random effects model. The Hausman test is based on the following hypotheses: H 0 : There is no systematic difference in the coefficient. H 1 : There is a difference between coefficients. Our study will try to highlight breaches to the unique price principle. Specifically, it questions the hypothesis of no arbitration which is persistently violated as the unique price principle, which states that an asset may have a unique price equal to its fundamental value, is not verified. Explicitly, our empirical study attempts to highlight the limits to arbitrage on the Tunisian stock market. A number of recent studies have shown that companies which invest more deserve low returns. This negative investment - return relationship is often referred to as assets growth anomaly. Studies of Titman et al, (2004 ) and Cooper et al. (2008 ) argue that this anomaly exists because investors are too slow to incorporate correct information in asset prices which leads to poor assessment. If an asset is undervalued, profit opportunities that attract rational investors and arbitrage activities should correct this misalignment. In an ideal environment where arbitrage opportunities are risk- and costless to operate, prices should accurately reflect all available information and in case of mispricing it should be corrected immediately. However, in a realistic market where arbitrage is risky and expensive, feasible arbitrage possibilities are limited. Investors need information to locate arbitrage opportunities, which may be less obvious when information is inaccurate. However, professionals such as institutional investors are more likely to locate these opportunities. Transaction costs can be another obstacle, since they reduce arbitrage profitability, which leads to the reduction of their attractiveness for arbitrageurs. When arbitrage is riskier, information is uncertain and transaction costs are higher and therefore arbitrage opportunities provided by mispricing of assets growth are less attractive to arbitrageurs. If information collected from assets growth is properly and gradually incorporated into stock prices, we should observe a stronger assets anomaly when arbitrage is riskier. This argument leads us to formulate the hypothesis which states that: "mispricing varies negatively with total assets growth and positively with arbitrage costs." Idiosyncratic volatility of returns (IVOL) IVOL is defined by Pontiff (2006) as the standard deviation of the residual value of a market model with time series: with: R i,t is the monthly individual return of the stock. R m,t : is the monthly return of the market index with 36 months of returns. According to Pontiff (2006), the calculation of this measure needs full history of 36 months ending in June of year t. Pontiff (2006) shows that arbitrageurs prefer fewer stocks with greater idiosyncratic volatility of returns. Using idiosyncratic volatility of stock returns as a proxy for arbitrage costs, Duan, Hu, and McLean (2010) and McLean (2010) show that when arbitrage costs are lower, the negative relationship between short interest or equity returns of the last 3-5 years and past stocks returns is lower. 68

International Journal of Empirical Finance Application of market model on the Tunisian stock market The Hausman test results are given in the following table: Table 3.1 : comparative Test of cross-section random effect cross-section random chi-sq statistic Chi-Sq.d.f Prob 2012 2,72992 1 0,0985 2011 0,683784 1 0,4083 2010 1,696237 1 0,1928 Table 3.2 : Test of cross-section random effect R fixed Random var (dif) Prob 2012 0,665154 0,703771 0,000546 0,0985 2011 0,769997 0,793638 0,000817 0,4083 2010 1,023604 1,055213 0,000589 0,1928 The results indicate that for all time intervals there is no significant difference between the coefficients obtained by the fixed effect model on the one hand and the random effect model on the other. In fact, the difference between the two effects ranged between 0.0005 and 0.0008. Therefore, the null hypothesis of the Hausman test (i.e. cross-section random is the appropriate model) is verified. The Hausman test allowed us to validate the random effect model. Therefore, we can proceed to the second step by regressing the market model through OLS. The regression results are given in the following table: Table 3.3Results of regression 2010 2011 2012 variable C R C R C R coefficient -0,006818 1,055213 0,000791 0,793638 0,00017 0,70377 std.error 0,0044582 0,097177 0,004476 0,084108 0,0049 0,09753 t-stat -1,487982 10,85863 0,176742 9,4359 0,03421 7,21593 prob 0,1373 0,0000 0,8598 0,0000 0,9727 0,0000 R 2 0,157928 0,12424 0,08802 0,156587 0,122845 0,08632 The above table indicates that for all levels, coefficients of the independent variable (market return) are significant. Moreover, we should point out that the R 2 coefficient varies between 8.8% and 15.8%, indicating that the model s explanatory power is relatively low. This can be explained by the fact that market return cannot explain variation in stock returns. We proceed now to the third step to determine whether the series of residual values and their standard deviations are admitted by this stacked data regression. 69

S. Brahim et al. Table 3.4: Descriptive statistics of IVOL series distribution 20 16 Series: IVOL Sample 2009M07 2012M06 Observations 60 12 Table (3.4) shows that for IVOL series, skewness and kurtosis statistics are respectively different from 0 and 3. Moreover, the Jarque-Berra statistic scores a zero probability below the 5% level, therefore we reject the hypothesis of the series normal distribution. This series presents first a skewness (S) coefficient of (3.074179) which is greater than 0, then it is skewed to the right. Second, the series has a kurtosis (K) coefficient of (15.05725) which is greater than 3, and therefore the IVOL series distribution is leptokurtic. The table shows that this series has a mean of (0.086695) with a maximum value of (0.501502) and a minimum value of (0.010546). The effects of the limits to arbitrage on assets growth anomaly The regression proposed by Lam and Wei (2011) tests the null hypothesis which states that mispricing and limits to arbitrage may explain assets growth anomaly. Thus, regression of the basic model proposed by Lam and Wei (2011) is given by the following equation: with: R i,t : is gross monthly returns between July of year t and June of year t-1. TAG i,t-1 : Total assets growth between year t-1 and year t. IVOL i,t-1 : proxy for arbitrage costs. Measuring assets growth 8 4 0 0.0 0.1 0.2 0.3 0.4 0.5 Mean 0.086695 Median 0.073722 Maximum 0.501502 Minimum 0.010546 Std. Dev. 0.078117 Skewness 3.075121 Kurtosis 15.23077 Jarque-Bera 468.5430 Probability 0.000000 According to Cooper, Gulen and Schill (2008), we use total assets growth (TAG) as a measure of the overall growth of business investments and assets issuance. TAG is defined as the growth rate of total assets (TA) of the firm from year t-1 to year t. Table 3.5: Descriptive statistics of stacked series of total assets individual growth (TAG) 120 100 Series: TAG Sample 2009M01 2012M12 Observations 600 80 60 40 20 0-0.250-0.125-0.000 0.125 0.250 0.375 Mean 0.093400 Median 0.083459 Maximum 0.411494 Minimum -0.297254 Std. Dev. 0.092525 Skewness 0.230197 Kurtosis 7.199555 Jarque-Bera 446.2056 Probability 0.000000 70

International Journal of Empirical Finance The descriptive statistics in table (3.5) indicate that for the stacked series of total assets growth, skewness and kurtosis statistics are respectively different from 0 and 3. Moreover, the Jarque-Bera statistic shows zero probability below the 5% level, and therefore we reject the null hypothesis of the series normal distribution. This series presents first a skewness (S) of (0.230197) which is greater than 0 and it is skewed to the right. Second, the series has a kurtosis (K) of (7.199555) which is greater than 3, and therefore the distribution is leptokurtic. This table also shows a maximum growth of (0.411494) and a minimum growth of (-0.297254). The series mean growth is (0.093400) with a standard deviation of (0.092525). 240 200 Table 3.6: Descriptive statistics of the series individual monthly returns Series: RIT Sample 2009M07 2012M06 Observations 540 160 120 80 Mean 0.006656 Median 0.000000 Maximum 1.203125 Minimum -0.797361 Std. Dev. 0.109453 Skewness 2.245217 Kurtosis 36.77687 40 0-0.5-0.0 0.5 1.0 Table (3.6) indicates that for the series of individual monthly returns, skewness and kurtosis statistics are respectively different from 0 and 3. Furthermore, the Jarque-Bera statistic displays zero probability below the 5% level, and therefore we reject the null hypothesis of the series normal distribution. First, this series has a skewness (S) of (2.245217) which is greater than 0 and then it is skewed to the right. Second, the series has a kurtosis (K) of (36.77687) which is greater than 3, and therefore the series of individual monthly returns distribution is leptokurtic. This table also shows maximum returns of (1.203125) and minimum returns of (-0.797361). Mean returns of the series is (0.006656) with a standard deviation of (0.109453). Application of Lam and Wei (2011) model on the Tunisian stock market Jarque-Bera 26123.42 Probability 0.000000 In panel data studies, it seems necessary to choose in advance between a fixed effect and a random effects model. To this end, we use Hausman test (1978). The results of the Hausman test are reported in the following table: Table 3.7 : Test of cross-section random effect Test Summary Chi-Sq,Stastic Chi-Sq.d.f. Prob cross-section random 0.464565 2 0.7927 Table 3.8 : A comparative test of cross-section random effect Variable fixed random var (diff) Prob TAG 0.127720 0.180204 0.022791 0.7281 IVOL 1.782392 1.882553 0.025420 0.5299 In table (3.8), the differences between the TAG and IVOL variables are relatively high. Therefore, the null hypothesis of the Hausman test on the absence of a systematic coefficient is rejected. Then, we can conclude that the fixed effects model is the appropriate model for our regression. The results of the fixed effects model s estimation are reported in the following table: 71

S. Brahim et al. Table 3.9 Results of fixed effect model variable coefficient Std.Error t-stat Prob C -0.283583 0.283221-1.001281 0.3253 TAG 0.127720 0.239184 0.533984 0.5976 IVOL 1.782392 0.305397 5.836320 0.0000 R 2 0.725473 0.568601 F-Stat 4.624604 Prob (F-stat) 0.000205 D-W stat 1.108097 The table above indicates that the coefficient of determination R 2 is 72.54%. This means that 72.54% of returns variance is explained by the independent variables retained in our model (TAG and IVOL) and 27.46% of the returns variance is explained by residual factors, i.e. other factors. The overall significance test supports R 2. Table (3.9) shows a Fisher probability statistic of 0.000205, inferior to the 5% level. Therefore, we can conclude that the overall model quality is acceptable, i.e. the model is significant overall. Consequently, the independent variables (TAG and IVOL) generally influence the dependent variable R it. These results lead us to check individual quality of the independent variables. Testing the individual quality of these variables is done through the Student test. The results indicate that the variable IVOL is statistically significant at the 1% level. Student statistic is greater in its absolute value than its critical value which is 1.96. this means that individual returns are influenced by the variable IVOL. In order to improve the quality of our results while following Lam and Wei (2011), we saw it fit to use a weighted fixed effect model. The results are reported in the following table: Table 3.10 Results of weighted fixed effect model variable coefficient Std. Error t-stat Prob. C -0.378126 0.097073-3.895257 0.0006 TAG 0.267406 0.084882 3.150307 0.0039 IVOL 1.096382 0.244737 4.479848 0.0001 R 2 0.673657 0.487175 F-Stat 3.612455 Prob. (F-stat) 0.001449 D-W stat 1.117734 Table 3.10 indicates that the coefficient of determination R 2 decreased from 72.54% to 67.36%. despite this decrease, our model remains significant. Moreover, Fisher probability statistic (0.001) indicates that our model is significant overall at the 1% level. This means that the independent variables (TAG and IVOL) affect overall the dependent variable R it. In this table, we notice that the constant, the variable TAG and the variable IVOL are statistically significant at the 1% level. Moreover, we should point out that the coefficient C 2 is statistically significant at the 1% level indicating limits to arbitrage in the Tunisian stock market. In conclusion, against the above results, we may conclude that assets growth anomaly may be explained by arbitrage limits. 72

International Journal of Empirical Finance Arbitrage limits are due to presence of «noises traders» in the market. These arbitrage limits result from the inability to predict future stocks movements. If assets prices evolution is not consistent with arbitrageurs expectations, these latter are forced to liquidate their funds and wave their profits because of arbitrage. 4. Conclusion This paper attempted to show that arbitrage, an activity to which rational investors make recourse in order to bring assets prices to their fundamental values, is not a riskless and costless operation and therefore it is limited. In this regard, we focused on theoretical and practical limits of arbitrage. By opposition to Friedman approach, based on efficiency of arbitrage which assumes that any deviation between asset price and its fundamental value is temporary and should disappear during arbitrage process, the work of Shiller and Summers (1990) indicate that arbitrageurs tend to predict irrational investors behaviour, «noises traders», rather than bring assets prices to their fundamental values. Excess volatility and market instability result essentially when «feedback traders» engage in a series of feedback strategies. Our first empirical study consisted in highlighting limits to arbitrage in the Tunisian stock market using Lam and Wei (2011) model. The studies conducted by Santana and Wadhwani (1992), Bohl and Siklos 2004) suggest that in the presence of «positives feedback traders», arbitrageurs look for anticipating shortterm prices changes rather than reducing their deviation from their fundamental values. Nevertheless, our results point to the presence of «positives feedback traders» during prices volatility periods in the Tunisian stock market. These traders engage in a series of feedback strategies. It has been shown that in their presence, arbitrage operations destabilize the market as arbitrageurs make profits, not because of reducing the deviation between assets prices and their fundamental values but because of its temporary persistence. This latter phenomenon leads to excess volatility whose victims are irrational investors «positives feedback traders» Shiller (2000). References Lam F.Y.E.C., Wei K.C.J. 2011, Limits-to-arbitrage, investissment frictions, and the asset growth anomaly. Journal of Financial Economics, 102(1): 127-149 De Long, J. B., Shleifer A., Summers, L., and Waldmann, R., (1990a), Noise trader risk in financial markets, Journal of Political Economy 98, 703-738. Shleifer A (2000), Inefficient markets: An introduction to behavioral finance, Oxford University Press. Shleifer A. et Summers L. H. (1990), «The Noise Trader Approach to Finance», Journal of Economic Perspectives, 4, N 0 2, Pages: 19-33. Shleifer, A., Vishny, R., (1997). The limits of Arbitrage. Journal of Finance 52, pp. 35-55. Bohl and Siklos 2004, Empirical evidence on feedback trading in mature and emerging stock market, working paper, European University of Frankfurt. Santana. E and Wadhwani, 1992, Feedback traders and stock reteurns autocorreallations: evidence from a century of daily data, Economic Journal, Vol 102. De long J.B., Summers L. et Waldman R., (1990b), Positive feedback investment strategies and destabilizing rational speculation, Journal of Finance, 45, Pages: 375-395. Pontiff J., 2006, Costly arbitrage and the myth of idiosyuncratic risk, Journal of Accounting and Economics 42: 35-52 Duan, Y., Hu, G., McLean, R.D., 2010. Costly arbitrage and idiosyncratic risk : evidence from short sellers, Journal of Financial Intermediation 19, 564-579. 73

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