Book-to-market equity and size as determinants of returns: evidence from the Tunisian stock exchange

Bergaoui Nejla

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BOOK-TO-MARKET EQUITY AND SIZE AS DETERMINANTS OF RETURNS: EVIDENCE FROM THE TUNISIAN STOCK EXCHANGE

Bergaoui Nejla

University of Manouba,

ESC (High School of Business), (Tunisia)

PhD applicant, Assistant of Finance Department, e-mail: nejberg@yahoo.fr

Abstract. Little, if any, has been published on the robustness of the Fama & French multi-factor model in emerging and little markets, such as the Tunisian Stocks’ market. This paper extends the existing literature and provides an out-of sample check on the performance of size and BE/ME factors proposed by Fama & French (1993). It firstly investigates the relation of stock returns with size and BE/ME ratio for equities listed in the Tunisian Stocks ‘market during the period July 1998-June 2004.The evidence we find support the presence of size and BE/ME effects in the Tunisian stocks’ market. We find that the mimic portfolio for size (SMB) and the mimic portfolio for BE/ME generate positive returns, which is consistent with a risk-based explanation for size and BE/ME effect. The second purpose of this paper is to examine the explanatory power of the three-factor model of Fama & French (1993) in the Tunisian stocks ‘market. We estimate a one factor model (CAPM) and the three-factor model of Fama & French (1993). The results give evidence on the additional explanatory power of SMB and HML factors of Fama & French, relative to the market factor, for cross-section of stock returns in the Tunisian Stocks’ market. Findings of this paper have implications for investors in the Tunisian stock market exchange. We suggest that investors must tilt their portfolios in favor of characteristics such as firm's BE/ME and size. Note that by tilting portfolios in favor of these characteristics investors are exposed to additional sources of risk.

Keywords: Size and BE/ME ratio effects, Tunisian stocks ‘market, CAPM, Three-factor model of Fama & French (1993).

INTRODUCTION

There is now, considerable evidence that a number of firm characteristics, such as size (Market equity ME) and Book equity to market equity (BE/ME), have more explanatory power for the cross section of average stock returns than do traditional measures of risk, such as market betas. Because the Capital Asset Pricing Model (CAPM) of Sharpe [24, p24] and Lintner [19, p24] does not explain these patterns in average returns, they are typically called anomalies. The existence of these anomalies may be due to several sources, which we can broadly grow into four common explanations. In line with rational asset pricing, Fama & French [12, 13, 14; p23] suggest that these variables proxy for additional non diversifiable risk factors. So, they have developed a three factor asset pricing model which relates the expected returns of a portfolio to excess returns on a market portfolio, a book-to-market equity

premium and size premium. They find that the CAPM average returns related anomalies disappear in their three factor model. The second sets of explanations are behavioral, suggesting that these anomalies arise due to investor overreaction to firm performance. Value stocks tend to be firms that are weak on fundamentals like earnings and sales, while growth stocks tend to have strong fundamentals. Investors overreact to performance and assign irrationally low values to weak firms and irrationally high values to strong firms. When the overreaction is corrected, weak firms have high stock returns and strong firms have low returns [18, p24]. The third set of explanations suggested by Daniel & Titman [7, p22], is that the expected returns of assets are directly related to their characteristics for reasons, that may have nothing to do with the covariance structure of returns. For example, a behavioral story that does not require overreaction is that investors like growth stocks (strong firms) and dislike value stocks (weak firms). The result is a premium (low prices and high expected returns for value stocks relative to growth stocks) that is not due to risk. The fourth possibility is that the explanatory power of the B/M ratio of equity or firm size for the cross section of stock returns is a chance result, unlikely to be observed out of sample [4, p22], [21, p24]. Kothari, et al [17, p23] argue that the B/M effect is spurious and is induced by data selection bias; which has a serious effect when the COMPUSTAT data are used. However, this set of explanations has been challenged by studies that have proved the findings of these anomalies on a hold out sample of financial firms [3, p22], outside the US markets [5, p22] and in pre-COMPUSTAT era [9, p21]. By referring to the literature, we notice that the bulk of the existing research on stock market anomalies relates to the United States and other developed capital markets. Little, if any, has been published on the robustness of the Fama & French multi-factor model in emerging markets, such as the Tunisian Stock Exchange (Bourse des Valeurs Mobilieres de Tunis BVMT). It seems that, to date, there is no evidence on the explanatory power of factors of Fama & French in the Tunisian Stock Exchange. Therefore, this paper extends the literature by investigating the explanatory power of an overall market factor, firm size and BE/ME of stocks listed on BVMT. This study must respond to the survivorship bias hypothesis, in that it provides out-of-sample check on the performance of size and BE/ME factors. The main purpose of this paper is to examine whether there is a size and BE/ME effect in the Tunisian Stock returns as well as the robustness of the multi-factor model of Fama & French [12, p23] in the BVMT. The remainder of the paper is organized as follows. Section 2 describes The Tunisian Stock Exchange. Section 3 is a review of the literature. The fourth section documents the size and BE/ME ratio effects in the Tunisian stocks ‘market. Section 5 examines the robustness of the Fama & French [12, p23] three-factor model in the Tunisian stocks ‘market and section 6 concludes main findings.

The Tunisian Stock Exchange (BVMT)

The Tunisian stock exchange (Bourse de Valeurs Mobilieres de Tunis) was founded in 1969 but remained dormant until 1989, date from which, Tunisia has been undertaking reforms of its financial sector as part of a broader macroeconomic adjustment program and structural reforms undertaken since 1987. Key elements of

the reform were the liberalization of interest rates, the improvement of banking supervision and the introduction of more market-based instruments of monetary policy.

The 1989 law had defined main features and rules of functioning of the Tunis Stock exchange. Nevertheless, this law had shortcomings that discourage the issue of new securities. It concentrates regulation and management in one public sector institution, it did not provide for a modern settlement system and brokerage activities were under the control of the banks. In 1994, another law was passed that included most features of OECD stock markets (a private bourse, private brokerage firms, and a modern settlement system and regulatory framework). These improvements encourage the test of size and BE/ME effect on Tunisian stock returns and whether the multi-factor alternative to CAPM is robust in this stock market.

Size (ME) and BE/ME effect: Literature Review

A large body of literature documents empirically observed predictable patterns in stock returns that cannot be explained by the one-factor CAPM and there has been growing international evidence on such asset pricing anomalies. The most prominent is the size effect of Banz [2, p21]. He finds that the market equity, ME, adds to explanation of the cross-section of average returns provided by market fi’s. Average returns on small (low ME) stocks are too high given their 1 estimates, and average returns on large stocks are too low. Another contradiction of CAPM, is the positive relation between average returns on American stocks and the ratio of firm's book value of common equity (BE) to its market value (ME) documented by Rosenberg et al [23, p24]. Similarly, Chan et al [5, p22] find that BE/ME also has a strong role in explaining the cross-section of average returns on Japanese stocks. For American stocks’ market, Fama & French [11, p23] document that BE/ME ratio of a firm capture significant variation in the cross section of returns and Fama & French [12, p23] show that small stocks tend to have higher returns than big stocks (size effect) and high BE/ME stocks have higher returns than low BE/ME stocks (BE/ME effect). Elfakhani et al [10, p23] report a significant size effect and a strong BE/ME effect in average stock returns in the Canadian stock market. Chui & Wei [6, p22] find that book-to-market equity can explain cross-section of returns in Korea, Hong Kong and Malaysia. Fama & French [15, p23] examines returns on value (high BE/ME) and growth (low BE/ME) portfolios for 12 major EAFE (Europe, Australia and the Far East) countries, and show that value stocks outperform growth stocks. On the French stock market, Molay [22, p24] confirms the negative relation between size and average returns for the period from July 1992 to June 1997. However, he doesn’t found any relation between BE/ME ratio and average returns. Nevertheless, Ajili [1, p21] confirms that the positive relation between BE/ME ratio and average returns is observed, in the French stock market, in the smallest size quintile for the period from July 1976 to June 2001.

Size and BE/ME effect in the Tunisian Stock Market

To examine whether there is a size and BE/ME effect in the Tunisian stocks' market, we used the methodology of Fama & French [12, p23].

Data description and methodology: Data sources

Consistent with prior research, the sample includes only non-financial firms that trade in the Tunisian stock exchange (BVMT) during 1998-2004. Monthly stock prices, ME, and accounting data are obtained from the (BVMT)s' electronic data base.

Portfolios construction

To test the existence of size and BE/ME effect, we have formed size and book-to-market portfolios, similar to that of Fama & French [12, 13; p23]. To be included in a portfolio, a firm must be trading in BVMT both in December (t-1) and in June (t) Stocks with negative BE/ME are eliminated as they do not have a meaningful explanations. The number of firms that fulfill the data requirements range from 15 in 1998 to 38 in 2004. At the end of June of each year (t), stocks are assigned to two portfolios of size (Small and big) based on whether their June market equity (ME) (defined as the product of the closing price times the number of shares outstanding as of June (t)) is above or below the median ME. The same stocks are allocated in an independent sort to three BE/ME portfolios. Designed as Low (L), Medium (M) and High (H). The BE/ME partitioning is based on the breakpoints for the bottom 30%, middle 40% and the top 30% of the BE/ME value in December (t-1), for the BVMT stocks. Since the Tunisian stock market is likely to be less efficient than the more developed markets, a time period of six months, from December (t-1) to June (t) could be sufficient for the market to react to any new information in the annual reports1.

Six size, BE/ME portfolios are formed at the intersection of the two firm size portfolios and three book-to-market equity portfolios. The six portfolios formed are: S/L, S/M, S/H, B/L, B/M and B/H. The ranking is redone each year and the portfolio composition change due the change in the size and BE/ME values of firms listed in BVMT. Monthly value weighted returns on the six portfolios are calculated from July of year (t) to June of year (t+1).

Performance of six portfolios: a detection of some size and BE/ME effect

Table (1) summarize average returns from 1998 through 2004 for six size, BE/ME portfolios. Value premium measured by the difference between High and Low BE/ME portfolios returns (H-L), and size premium measured by the difference between small and big size portfolios, are also reported in table (1).

1 Fama & French (1993) note that, to ensure that the accounting variables are known before the returns they are used to explain, they match the accounting data for fiscal year ends in calendar year (t-1) with returns for July of year (t) to June of year (t+1).

Table 1. Monthly average excess returns (in percent) for portfolios formed on size and BE/ME July

1998-december 2004

Monthly average excess returns

Ratio BE/ME

H M L H-L

S 1.22 0.406 0.212 1.008

B 0.807 0.398 0.322 0.485

S-B 0.143 0.008 -0.11 -

Table (1) reports that excess returns of the six stock portfolios considered are positive, they range from 0.212% per month for S/L portfolio to 1.22% per month for S/H portfolio. We find that the two stock portfolios with high BE/ME ratio produces returns in excess of the two stock portfolios with low BE/ME ratio. Table (1), reports that the difference between the average returns for the highest and the lowest BE/ME portfolio (H-L) range from 0.485% for big firms to 1.008% for small ones. This means that, book-to-market equity effect decrease with size. This result is consistent with findings of Fama & French [12, p23], Loughran [20, p24] and Daniel et al [8, p22]. The negative relation between size and average returns is observed only for portfolio with high BE/ME ratio. Table (1) shows that mean returns of small firms (S) (adjusted from BE/ME effect) is 0.6127 % compared to 0.509 % for big firms. Which confirms the presence of size effect in the BVMT during the period from July 1998 to December 2004. Consistently with results of Fama & French [12, p23], we have found that S/H portfolio has the highest returns .Results reported in table (1) have implications for investor in the Tunisian stocks’ market exchange. Indeed, to release higher returns, they can invest in the S/H portfolio or they can construct a strategy which is long on S/H portfolio and short on S/L portfolios.

The Three factor Model of Fama & French (1993): Case of the Tunisian Stocks’ Market

The basic idea of Fama & French [12, p23] is: the size and BE/ME ratio are considered as factors of risk that are remunerate. So they developed a three factor model, in which the expected returns on a portfolio in excess of the risk-free rate (E(R)-Rf) is explained by the sensitivity of its return to three factors :(i) the excess returns on a broad market portfolio (Rmt-Rf); (ii) The difference between the returns on a portfolio of small stocks and the return on a portfolio of large stocks (SMB: Small minus Big, size related factor) and (iii) The difference between the return on a portfolio of high BE/ME stocks and the return on a portfolio of low BE/ME stocks (HML: High minus Low, BE/ME ratio related facto). Specifically, the expected excess return on portfolio (i) is:

E(R)-Rj=Pi(E(Rm)-Rf) +SiE(SMB) +hi E(HML), (1)

where (E(Rm)-Rf); E(SMB) and E(HML) are expected premiums;

Pi, Si, hi are factor sensitivity or loadings. They are slopes in the time series regression.

Fama & French [12, p23] show that this model is a good description of returns on portfolios formed on size and BE/ME ratio in the American stock exchange.

The model predicts that smaller, riskier firms will tend to have positive slopes on the size premium (SMB) and hence have higher average returns. Similarly, relatively distressed firms with persistently high book-to-market equity ratios tend to load positively on the book-to-market premium (HML) that also implies higher expected returns.

In this section, we explore whether Fama & French [12, p23] three-factor model explain the Tunisian BE/ME and size effect. First, we estimate the one- factor model to see to what extend the market 1 can explain the higher return associated to value stocks (with high BE/ME ratio) and to small stocks.

Regression of the one-factor model (CAPM)

We have estimated the following specification over the period July 1998 -December 2004 for six portfolios sorted on size and BE/ME ratios.

RprRft=aP+Pp(RmrRfi)+ept, (2)

where Rpt - Monthly return of portfolio (p);

Rft - risk free rate: it is the monthly equivalent rate to monetary market rate;

Rmt - Monthly market return: is the return in the Tunisian stock market index (Tunindex)2 that includes stocks in the six portfolios and the negative BE stocks that were excluded from the sample while forming BE/ME portfolios;

Pp - sensitivity of portfolio (p) to market risk;

ap - the model constant. It underlines the market risk adjusted portfolio returns.

Results of estimation of the one-factor CAPM model are reported in table (2). Intercept values, the coefficients of the explanatory variable fip, their t-values and the adjusted R2 of the specification estimated are presented in table (2)

Table 2. Estimation of the one-factor CAPM for the period: July 1998- December 2004

А в Adjusted R2

S/H 1.025 0.61*** 0.092

(1.172) (2.96)

S/M 0.35 0.1272 0.0036

(0.547) (113)

S/L 0.077 0.542*** 0.093

(0.0837) (2.793)

B/H 0.634 0.555*** 0.072

(0.715) (2.655)

B/M 0.32 0.167 0.0022

(0.314) (1.073)

B/L 0.0438 0.750*** 0.123

(0.532) (3.428)

t-values of coefficients a et 1 are in parentheses. *** pc<1%.

2 Tunindex is the most popular index used in the Tunisian financial market. It regroups the 25 most liquid stocks. It is considered as the most representative of market evolution

Coefficient of the market factor fi, reported in table (2), have /-values that exceed 2. All fip are positive. Hence, returns of stocks listed in the BVMT are positively related to the market fi. Nevertheless, there is no monotonic relation of ME and BE/ME with market-fi.In value portfolios, small firms have higher market fi than big firms but in growth portfolio small firms have lower market fi than big firms. Also, in small firm’s portfolio, value stocks have higher market-fi than growth stocks, but in big firm’s portfolio, growth stocks have higher market-fi than value stocks. So classic measure of systematic risk cannot explain the difference of returns neither between small and big firms, nor between high and low BE/ME firms. Adjusted R are low, which range from 0.093 for S/L portfolio to 0.123 for B/L portfolio. The intercept a (which underlines the market risk adjusted portfolio returns), show BE/ME effect. Indeed, in every size quintile, the intercept increase with BE/ME. The intercepts for the highest BE/ME portfolio exceed those for the lowest BE/ME portfolio by 0.948 in small size quintile to 0.560 in the big size quintile. The intercepts for the smallest size portfolio exceed those for the biggest portfolio in every BE/ME quintile. So, the constant (a) show also a size effect. These results parallel the evidence in Fama & French [12, p23] that used alone, market fiS leave a cross-sectional variation in average stock returns that is related to BE/ME and size.

Regression of the three-factor model

HML and SMB factor construction and summary statistics

Using the methodology of Fama & French [12, p23], SMB and HML factor are defined as follows:

- SMB is the difference each month between the average of returns of the three small stock portfolios (S/L, S/M and S/H) and the average of the returns of the three big portfolios (B/L, B/M and B/H): SMB = {(HS +MS + LS) -(HB + MB + LB)}/3;

- HML is the difference between the average of the returns of the high BE/ME portfolios (S/H and B/H) and the average of the returns of the two low BE/ME portfolios (S/L and B/L): HML = {(HS + HB) - (LS + LB)}/2.

Table 3 shows average values and correlations of three factors: Rm-rf, SMB and HML.

Table 3a. Monthly average returns: from July 1998 to December 2004

Rm - rf SMB HML

Monthly average returns 0.31 0.106 0.75

Standard-deviation 4.26 4.57 8.69

Table 3b. Correlation

Rm - rf SMB HML

Rm 1 - -

SMB -0.0118 1 -

HML -0.0302 -0.139 1

Table (3 a) reports that the average value of excess returns of the overall market portfolio is 0.31% per month. This is close to the result of Fama and French [12, p23] in the US-case (0.43%).The average HML return is 0.75% per month (standard deviation = 8.69) or 9% per year. The size factor SMB produces an average premium of 0.106 % (standard deviation = 4.57), or 1.27% per year. The positive returns of HML and SMB is consistent with the hypothesis of Fama & French [12, 13, p23], that HML and SMB are risk premium and that high BE/ME firms (small firms) are riskier than low (big) ones. Like Fama and French [12, p. 23] table (3b) shows that HML portfolio returns have negative correlation with excess market and SMB portfolio returns (-0.0302 and -0.139 respectively). Unlike Fama and French [12, p23], SMB and market portfolio have negative correlation. Correlation among SMB and HML with the overall market factor are weaker than that observed in the study of Fama & French [12, p23] (-0.0118 and -0.0302 against 0.32 and -0.38 for SMB and HML respectively). Correlation among SMB and HML is more important (-0.139 against -0.08 in Fama & French [12, p. 23]3.

Results of estimation of the three-factor model of Fama & French (1993)

We have estimated the following time series regression over the period from July 1998 to June 2004:

Rpt -rf = ap + ftp (Rmt -rft) + hp HMLt + Sp SMBt +ept (3)

where : Rpt is the average returns of portfolio p formed on the basis of size and BE/ME criteria;

Rmt - Monthly market return is the return in the Tunisian stock market index (Tunindex);

Rft - risk free rate - it is the monthly equivalent rate to monetary market rate;

SMBt is the monthly difference between the return on a portfolio of small stocks and a portfolio of big stocks (neutral with respect to BE/ME ratio);

HMLt is the monthly difference between the return on a portfolio of high BE/ME stocks and the return on a portfolio of low BE/ME stocks (neutral with respect to size); ftp, hp, Sp are factor loadings; ap is an intercept.

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Results are reported in table (4).

Table 4. Estimation of the three-factor model of Fama & French (1993) over the periodfrom July

1998 tojune2004

А в H S Adjusted R2

S/H 0.633 0.645*** 0.438*** 0.498*** 0.342

(0.846) (3.675) (5.043) (3.018)

S/M 0.265 0.28 -0.053 0.878*** 0.191

(0.286) (129) (-0.49) (4.294)

S/L 0.30 0.526*** -0.418*** 0.586*** 0.476

(0.48) (3.581) (-5.76) (4.25)

3To make sure that correlations among SMB, HML and Rm are not significantly undistinguishable from zero, we have regressed SMB on HML and Rm, over the period from July 1998 to June 2004. Results show that slopes on the explanatory variables are statistically indistinguishable from zero at 1% level. This allows avoiding the problem of deceptive regression when we estimate the three factor model of Fama & French (1993). SMB = 0.178 - 0.049315 HML- 0.128635 Rm+e with (/=-0.73567) and (/=-0.89798).

B/H 0.242 (0.355) 0.585*** (3.662) 0.55*** (6.957) -0.274** (-2.825) 0.459

B/M 0.355 (0.384) 0.36 (1.656) 0.057 (0.567) -0.75 (-4.283) 0.210

B/L 0.574 (0.795) 0.705*** (4.15) -0.593*** (-7.069) -0.362** (-2.27) 0.469

^-values of coef icients a, ft, s, and h are in parent ieses. ***pc<1% and **pc<5%

Factors capture the cross-section of average stock returns the intercepts (ap) in the time-series regression should be indistinguishable from zero. Table (4) confirms that intercepts are statistically indistinguishable from zero, for six size-BE/ME sorted portfolios (t(ap) <2). On the basis of the adjusted R2 criterion, we can affirm a net improvement of explanatory power of the model when HML and SMB are included (compared to the one-factor model); although not in the same magnitude as those reported in studies using relatively larger markets4. The increase of adjusted R2 and the weak changes in values of ft give evidence of additional explanatory power of SMB and HML over the market factor. Moreover, HML slopes (h) are related to book to market ratio. For, as big as small, capitalizations; they increase from negative values for the lowest book to market quintile to positive values for the highest book to market quintile. Their t-statistics are greater than two. Similarly, SMB slopes (s) are related to size. In every book to market quintile (except for the median BE/ME portfolios)5. They decrease from positive values for small capitalization portfolios to negative values for big capitalization portfolios. Their t-statistics are greater than two. The behavior of the (h) and (s) coefficients is generally consistent with the findings of Fama and French [12, p23]. In other words, the outcome in terms of risk premium is consistent with the arguments of Fama & French [12, p23]. Indeed, the existence of positive returns of SMB combined with positive (negative) coefficient for size factor generates positive (negative) premium for small (big) firms (so higher returns for small firms). Also, positive returns of HML combined with positive (negative) coefficient for BE/ME factor generates positive (negative) premium for value (growth) stocks (so higher returns for value stocks). Considering these results, we suggest that multi-factor-mean - variance efficient investors in Tunisia should invest in some combination of small and high BE/ME firms in addition of the overall market portfolio to generate superior returns.

Conclusion

This paper provides an out-of sample check on the performance of size and BE/ME factors proposed by Fama & French [12, p23]. It firstly investigates the relation of stock returns with size and BE/ME ratio for equities listed in the Tunisian Stock Exchange (BVMT) during the period July 1998 - June 2004. From this investigation we stress that firms with high BE/ME ratio produce returns in excess of the stock portfolios with low BE/ME ratio. We also find that the mimic portfolio for

4 Adjusted R2 is of the order of 90% for the American stock market (Fama & French [11, p23]) and for the French stock market (Ajili [1, p21]).

5The weakness of results for the median BE/ME portfolios can be explained by a greater heterogeneousness of stocks composing them.

BE/ME (HML) generates positive returns suggesting that the high book-to-market equity ratio portfolio are more risky than low book-to-market ones. The evidence we find in this study relative to size effect support the finding of Fama & French [12, p. 23], who report that small firms generate superior returns because they are distressed. Indeed, we find that the mimic portfolio for size (SMB) generates positive returns, which is consistent with a risk-based explanation for size effect. The second purpose of this paper is to examine the explanatory power of the three-factor model of Fama & French [12, p23] in the BVMT. Firstly, we estimate a one factor model (CAPM) during the period July 1998 to June 2004. From this investigation, we note that the market factor is significant but not sufficient to explain variation in stock excess returns. When HML and SMB are included in the model, we note a net improvement of adjusted R2 and weak changes in values of ft. This gives evidence on the additional explanatory power of factors of Fama & French, for cross-section of stock returns in the BVMT. Findings of this paper have implications for investors in the Tunisian stock market exchange. We suggest that investors must tilt their portfolios in favor of characteristics such as firm' BE/ME and size. Note that by tilting portfolios in favor of these characteristics investors are exposed to additional sources of risk.

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РЫНОЧНАЯ СТОИМОСТЬ КАПИТАЛА И ЕГО РАЗМЕР КАК ФАКТОРЫ, ОПРЕДЕЛЯЮЩИЕ ДОХОДНОСТЬ (НА ОСНОВЕ ДАННЫХ

ФОНДОВОЙ БИРЖИ ТУНИСА)

Бергауи Нэйла

Университет Мануба (Тунис)

Аннотация. Имеется незначительное число публикаций по устойчивости мультифакторной модели Фама и Фрэнча на развивающихся и маленьких рынках, таких как фондовый рынок Туниса. Данная статья основана на анализе существующих литературных источников и приводится на вневыборочной проверке на выполнимость величины и BE/ME факторов предложенных Фама и Фрэнчем в 1993 году. Она, прежде всего, исследует связь на доходность акций с величиной ставки BE/ME для акций, котирующихся на фондовой бирже Туниса в период с июля 1998 по июнь 2004 гг. В доказательство мы находим поддержку наличия величины и BE/ME эффекта на фондовой бирже Туниса. Обнаружено, что имитированный портфель для величины (SMB) и имитированный портфель для BE/SE генерирует положительную доходность, которая согласуется с учётом риска объяснения величины и BE/ME эффекта.

Следующим направлением данного исследования является выяснение силы трёхфакторной модели Фама и Фрэнча в случае рынка акций Туниса Проанализирована однофакторная модель (CAPM) и трёхфакторная модель Фама и Фрэнча (1993 г.). Полученные результаты свидетельствуют о дополнительном объяснении силы SMB и HML факторов Фама и Фрэнча по отношению к рынку факторов по перекрёстной доходности акций на фондовом рынке Туниса. В итоге данной работы выделены последствия для инвесторов на тунисской фондовой бирже. Предложено, что инвесторам следует склонять собственные портфели в пользу таких характеристика как BE/ME фирм и сечения. Важно понимать, что склонение портфелей в пользу этих характеристик для инвесторов составляет дополнительные источники риска.

Ключевые слова: величина и BE/ME соотношение эффектов, фондовая биржа Туниса, CAPM, трёхфакторная модель Фама и Фрэнча.

Book-to-market equity and size as determinants of returns: evidence from the Tunisian stock exchange Текст научной статьи по специальности «Экономика и бизнес»

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