Asset Pricing and Cost of Equity in the Tunisian Banking Sector: Panel Data Evidence

Authors


  • Earlier versions were presented at the 9th conference of ERF in Sharjah (UAE), 26–28 October 2002, the conference on Financial Development in Arab Countries in Abu Dhabi, 31 March–2 April 2003, and at the University of Rome Conference on Financial Markets and Banks, 9–12 December 2004. We thank Mahmoud A. El-Gamal of Rice University and Rania Al-Mashat from University of Maryland for their comments and suggestions.

*Corresponding author: Samy Ben Naceur, Laboratoire d'Economie et Finance Appliquées and Institut des Hauts Commerciales, University 7 at Carthage, 2016 Carthage, Tunisia. E-mail: sbennaceur@lycos.com

†Laboratoire d'Economie et Finance Appliquées, Institut Supérieur de Comptabilité & d'Administration des Entreprises (ISCAE), Campus Universitaire de Manouba, 2010 Manouba, Tunisia. E-mail: samir.ghazouani@fsegt.rnu.tn

Abstract

In spite of popularity and theoretical simplicity of the one-factor Capital Asset Pricing Model (CAPM) used in the valuation of financial assets, researchers are more concerned with the important extension proposed by Fama and French (1993), that is, the Three-Factor Pricing Model (TFPM). Alongside beta, average stock returns could be explained by some size and book-to-market supplementary effects. With these two complementary models, estimation of the cost of equity is carried out for the Tunisian banking sector. In order to account for inter-individual heterogeneity, estimation of parameters is conducted according to random coefficient specifications within the context of panel data analysis.

1. Introduction

The Capital Asset Pricing Model (CAPM), initiated by Sharpe (1964) and Lintner (1965), posits that the covariance of a stock's return with the excess return to a market portfolio and the variance of the latter are sufficient to explain its excess return over the risk-free rate. However, a large body of literature has identified many patterns in average stock returns that cannot be explained by the one-factor CAPM. These studies have documented that alongside beta, average stock returns in the US are related to size (Banz, 1981), earning price (Basu, 1983), past long-term returns (De Bondt and Thaler, 1985), leverage (Bhandari, 1988), past short-term returns (Jegadeesh and Titman, 1993), past sales growth (Lakonishok et al., 1994) and book-to-market equity (Rosenberg et al., 1985; Chan et al., 1991; Fama and French, 1992). Since these patterns in average stock returns are not explained by the CAPM, they are typically called anomalies.

Among these anomalies, size and book-to-market equity have been found to be the most significant in capturing the cross-section of average stock returns (Fama and French, 1992, 1993). Fama and French (1993) argue that the expected return on a portfolio in excess of the risk-free rate is explained by the sensitivity of its returns to three factors: (i) the excess return on a broad market portfolio; (ii) the difference between the return on a portfolio of small stocks and the return on a portfolio of large stocks; and (iii) the difference between the return on a portfolio of high book-to-market stocks and the return on a portfolio of low book-to-market stocks.

The Three-Factor Pricing Model (TFPM) captures most market anomalies except the momentum anomaly (Fama and French, 1996; Asness, 1997). Jegadeesh and Titman (1993) were the first to show that taking a long (short) position in well (poorly) performing stocks on the basis of past performance over a short period of time (3 to 12 months) tends to yield significantly positive abnormal returns for the following year. The results are confirmed by other tests in the US (Fama and French, 1996, Chan et al., 1999; Jegadeesh and Titman, 2001), in European markets (Rouwenhorst, 1998), in Asian markets except Japan and Korea (Chui et al., 2000) and in emerging markets (Rouwenhorst, 1999).

Estimating the cost of equity is crucial for many financial decisions of privately owned companies such as capital budgeting, capital structure, performance valuation using EVA,1 valuation and pricing of services in some regulated industries. In a survey, Bruser et al. (1998) find that the most common method favoured by practitioners for estimating the cost of equity is the CAPM. This widespread use of the CAPM in practice is no doubt due to its strong theoretical foundation and its simplicity. The approach of Fama and French, which has addressed size and book-to-market issues, challenges the validity of the CAPM because under the CAPM the only risk factor is beta (security's systematic risk). But some argue that the TFPM is empirically inspired and lacks strong theoretical foundations. As Fama and French (1996) suggest, ‘we do not take a stance on which is the right asset pricing model’; we use both the CAPM and the TFPM in order to estimate bank costs of equity.

The purpose of this study is to estimate the cost of equity of the Tunisian commercial banks using both CAPM and TFPM. Our research is characterized mainly by three contributions:

  • • It is the first paper that focuses on the estimation of the cost of equity of Tunisian banks using two models, that is, CAPM and TFPM. The econometric approach is also interesting because it is based on a random coefficient model in the context of panel data analysis.
  • • It is done during a period where the Tunisian banking industry is undergoing huge reforms (mergers, disinvesting, recapitalization, and so forth). The results of the paper will give Tunisian banks a benchmark for all their ongoing restructuring financial decisions.
  • • It will pave the way for estimating the cost of equity of banks in other Middle Eastern and North African (MENA) countries according to similar nice methodological and technical approach.

The paper is organized as follows. Section 2 presents the Tunisian financial system with an emphasis on the banking sector. Section 3 outlines the data and methodology. The findings are reported in Section 4 and the paper concludes with a summary and policy implications.

2. The Tunisian Financial System: An Overview

In the early 1980s, the inefficiencies and distortions of the Tunisian financial system were exacerbated by the emergence of severe macroeconomic difficulties. In order to tackle their mounting financial problems and enhance growth prospects, the Tunisian government reformed several times the financial system in the framework of the Tunisian's structural adjustment effort of the late 1980s and early 1990s. These reforms involved a liberalization of the financial sector under the auspices of the IMF. Besides, these reforms were intended to improve the capacity of financial institutions in order to mobilize domestic savings, lead to more efficient allocation of financial resources, increase competition among banks and strengthen their financial soundness.

The initial phase of financial reforms during the period 1987–1993 aimed at gradual dismantling of the debt economy. It involved a gradual liberalization of interest rates, a gradual suppression of planned policies of credit and a reinforcement of the prudential regulations in line with international standards. Thereafter, financial reforms aimed at paving the way for the strengthening of a financial market economy from 1994 until now.

The implementation of these reforms was articulated around the following pillars:

  • • Liberalizing interest rates and credit allocation decision by commercial banks: interest rates were liberalized in 1987 and were allowed to be set freely within a spread of three percentage points of the money market rate except for lending rates to priority sectors. By 1996, deposit and lending rates were fully liberalized, although limited controls on some deposit rates remained. A gradual relaxation of the requirements on which the banks lend to the treasury, to public enterprises and priority sectors was sustained by the move to a more market-based financing of the budget. In addition, the requirement for prior authorization by the Central Bank (BCT)2 for credit decisions was eliminated in 1988.
  • • Promoting the equity market: the Tunisian Stock Exchange (TSE) was first created in 1969, but not until 1994 when it was privatized did it become an integral part of the Tunisian financial market (the capital is split equally among the 28 brokerage firms in the market). The financial market was reformed according to international standards in 1994. The CMF3 was set up in order to reinforce the transparency of the market. Parallel to this, the STICODEVAM4 was created in order to clear transactions and to act as the central depository for the market. After experiencing two difficult years in 1996 and 1997, the TSE regained strength in 1998 as reforms were put in place in order to increase efficiency and transparency. They included the introduction of a new trading system based on the SuperCAC electronic trading system (Paris Bourse electronic system) and the implementation of new accounting standards consistent with the best international norms. In parallel with legal and technical consolidation, the Tunisian government has recently established fiscal advantages in order to incite companies listing their stocks on the TSE and the investors to buy securities. Finally, foreigners can participate within the limits of 50 per cent of the offering of a company. Above 50 per cent, an authorization is required. Foreigners currently account for 25 per cent of the total capitalization.5
  • • Introducing new indirect monetary policy: treasury bills were redesigned in order to make them more liquid and attractive to investors. At the same time, the legal framework for new private investments such as certificates of deposit, commercial papers, mutual funds and corporate bonds was reinforced, although many of these instruments are scarcely used.
  • • Moving to more market-based government financing: in 1991, the treasury stopped issuing low-interest, long-term government bonds, and the amount of Treasury bill that banks were required to hold was reduced. Besides, the government securities market (85 per cent of the stock of bond instruments) was modernized with the introduction of standardized instruments (‘bon du trésor assimilable’) and the establishment of systematic auction-based issuance and a group of primary dealers.
  • • Opening the financial sector to foreign financial institutions: this is done by opening banks' capital to foreign participation, by allowing foreign banks to open branches and operate onshore, and by allowing offshore banks to collect deposits in local currency from residents with some restrictions.
  • • Strengthening prudential regulations and banking supervision: domestic banks were required to meet the Basel risk-weighted adequacy ratio by 1999. Moreover, the authorities implemented a plan in order to restructure Non-Performing Loans (NPLs) to public enterprises,6 but the continuing high level of NPLs suggests the need for further improvements in bank credit policies.

Table 1 summarizes all the reforms undertaken by the Tunisian government from 1997 to 2006. All these reforms have contributed to strengthening the financial sector and its main characteristics today according to the IMF (2002). The commercial banks (14 institutions) dominate the financial sector with 64 per cent of the total assets of the financial institutions, and the state-controlled banks dominate the banking sector (the state controls the three largest banks and more than half the banking system's asset). These banks are allowed to collect deposits of any maturity, provide short- and medium-term credit and may engage in long-term credit operations. The extension of their networks gives to them an operational advantage in accordance with development banks. The development banks (6 institutions) represent only 4 per cent of total financial assets and suffer from high levels of NPLs. For these reasons, BDET7 and BNDT,8 two Tunisian development banks, merged in 2000 with the commercial bank STB.9 They are joint ventures between the Tunisian government and governments of other Arab states. The initial mission was to finance investment projects over the medium and long term and to participate in the capital of private firms. Their importance in the financial sector decreased gradually because of the wider scope of activity permitted to commercial banks by the 1994 amendments to the banking law (commercial banks are allowed to grant medium- and long-term credits) and the development of non-bank financial markets (the increase in the activity of the stock exchange after the 1994 reform). Offshore banks (8 institutions) represent less than 5 per cent of the total assets of the financial institutions and were initially created to provide financial services to offshore companies. They also extend limited loans in foreign currency to Tunisian residents and their ability to raise deposits from residents is strictly limited. The security market is still small relative to the banking industry and constitutes only a small portion of the financial system's assets. The number of firms listed on the TSE increased from 13 to 46 between 1990 and 2006. Despite a sharp increase of the volume of trading and capitalization since the implementation of 1989 and 1994 reforms, market capitalization represented only 8.8 per cent of GDP and the annual value of trading amounted to 1 per cent of GDP, which is very small compared to other emerging markets. Moreover, the bond market is dominated by government securities, which represent over 85 per cent of the outstanding bond instruments and the secondary market is in its infancy. The other main bond issues are banks and leasing companies. Finally, non-bank financial institutions (insurance companies, pension funds, collective investment institutions and investment companies) play a relatively small role in the Tunisian economy. Their assets represent only 22 per cent of GDP.10

Table 1.  Main Reforms in the Monetary and Financial Sectors
YearMonetary sectorFinancial sector
  1. Source: IMF (2002)+ updated.

1987- Lending rates are liberalized (except for priority sectors) but retention of ceiling of 3 percentage points above the money market rate (TMM).- Introduction of comprehensive bank prudential regulations.
- Rates for deposits of at least three months are free. 
 
1988- Rediscount operations limited to priority sectors.- Merger of two banks (BNT and BNDA).
- BCT introduces credit auction; refinance standing facility; and end-of-day repo operations.- Reform of legislation on investment and collective investment institutions.
- BCT approval for granting bank loans is eliminated.
- Introduction of inter-bank transactions.
 
1989- Reactivation of non-remunerated reserve requirement.- Introduction of treasury bill auctions.
1991 - Relaxation of mandatory bank holding of government securities.
 - Minimum term for CDs increased from 10 to 90 days and introduction of treasury bills with maturity over one year.
 
1992- Ceiling on individual lending rates replaced by ceiling on average lending rates per bank set at TMM+3.- Reduction of scope of credits at preferential rate.- Strengthening of prudential regulations.- New financial instruments are introduced (investment trusts, priority shares and equity loans).
 
1993 - Adoption of new auditing standards for the financial statements of banks.
 
1994 - Commercial banks are allowed to grant medium- and long-term credits.
 - Development banks are allowed to grant short-term loans.
 - New stock exchange legislation sets private stock market and creates independent supervisory body (CMF).
 - Introduction of negotiable treasury bill and investment trusts.
 
1995 - Venture capital companies are authorized.
 
1996- Lifting of all restrictions on lending rates. 
- Elimination of mandatory lending requirements for priority sectors. 
 
1997- BCT intervention in money market becomes main monetary instruments.- Implementation of a plan to restructure NPLs on public enterprises.
 - BTS is created (microfinance).
 - Implementation of a ‘mise à niveau program’.
 - Adoption of general regulations of BVMT.
 - Creation of Maghreb Rating.
 
1998 - Minimum capital ratio rises from 5 to 8%.
 - Issue of fungible treasury bonds.
1999 - Exposure to a single group reduced to 25% of the capital.
 - New statute for market intermediaries.
 - Adoption of CMF regulation covering public offer of securities.
 
2000 - Merger of two development banks with a commercial bank.
 - Enactment of a new business corporation code.
 
2001 - Enactment of a new banking law and law on collective investment institutions.
 - Preparation of draft laws on holdings.
 
2002–2006- Amendment of the code of commercial and civil procedure to facilitate the court-ordered sale of assets and shorten debt collection delay.- Enactment of a law to improve the security of financial relations, which aims to consolidate financial transparency and engender good corporate governance.
- Continuation of the gradual withdrawal of the government from the banking sector with the privatization of UIB and BS.- Prohibition of banks from distributing dividends when they have insufficient provisions.
 - The full tax deductibility of provision in the banking sector.

The Tunisian-listed commercial banks are the biggest companies in the TSE. Nine out of the ten biggest firms in the TSE come from the banking industry. Besides, 50 per cent of the banks are state-owned and only two have significant foreign participation in capital (ATB and UBCI). Only two banks are specialized (BNA in agriculture and BH in real estate). Comparing the banking sector to other sectors in the TSE, some comments must be made. First, the banking sector is one of the most represented sectors in the TSE (10 of the 14 banks are listed in the TSE). Second, banks are one of the least liquid sectors in the TSE (the turnover ratio11 is 5.7 per cent in the banking sector compared to the 9 per cent average rate in the TSE in 2004). Third, banks represent 50 per cent of the total market capitalization and more than 25 per cent of the number of listed companies in the TSE in 2005. Table 2 gives some statistics of the Tunisian banks in December 2004.

Table 2.  Some Statistics on the Tunisian Banks in December 2004
BanksSizeOwnershipForeign OwnershipSpecialization
  1. Note: Size is computed as the product of the share price by the number of outstanding shares in the 31 December 2004. The number is expressed in millions of Tunisian Dinars (local currency).

AB119Private 0.20%No specialization
ATB108Private64.24%No specialization
BH138State 6.47%Real estate
BIAT193Private27.36%No specialization
BNA 98State 0.11%Agriculture
BS164State17%No specialization
BT326Private26.08%No specialization
STB160State10.97%No specialization
UBCI200Private50.38%No specialization
UIB 76Private52.08%No specialization

3. Data and Econometric Modelling

3.1. Data Sources

We examine the monthly returns from the three factors RMRf, SMB (Small minus Big) and HML (High minus Low) on the TSE over the period (July 2000–June 2005). Data relative to financial statements, monthly stock returns and firm market equity (number of shares outstanding times the stock price) come from the TSE electronic database. The market return is a value-weighted return computed from the Tunindex index. Returns from the risk-free asset are estimated from the “TMM" (Money market rate),12 which is the smallest rate.13 Book equity is computed as the book value of the stockholder's equity. All observations with negative book equity are excluded from the sample since negative BE/ME14 can only be due to negative book value. Finally, all stock returns are adjusted for stock splits, right offerings and dividend payment.

3.2. Portfolio Formation

The construction of the size and book-to-market portfolios is similar to those of Fama and French (1993, 1995). To be included in a portfolio, a company must be listed in the TSE both in Decembert−1 and in Junet. Also, it must have a fiscal year end of 31 December, which is the case of all listed companies in the TSE. The number of firms that fulfils the data requirements ranges from 30 in 1995 to 31 in 2005. Market capitalization of equity is computed as the stock's price times the number of shares outstanding in Junet. In Tunisia, the listed firms must publish their financial statements within three months, but some financials are not disseminated until May or June. Since the TSE is likely to be less efficient than the developed markets, a time period of six months, from Decembert−1 to Junet, is fixed as sufficient for the investors to react to the information made public in the annual reports.

The market value and book value of equity used to compute BE/ME for the year t are the Decembert−1 values. Accordingly, the stock returns from July 1t to June 30t+1 are calculated for portfolio based on Decembert−1 BE/ME values and Junet sizes. We have constructed the size and book-to-market portfolios in keeping with Fama and French (1993). The stocks in the sample are first sorted each year from the smallest to the largest in terms of market capitalization. We then use a 50 per cent break point for size to allocate stocks in two groups that is S (for small) and B (for big). The firms are then sorted, again each year, into three book-to-market equity partitions designated as L (for low), M (for medium) and H (for high). The BE/ME partitioning is based on the break points for the bottom 30 per cent, middle 40 per cent and the top 30 per cent of the book-to-market equity values for the TSE stocks. We form six size-BE/ME portfolios, that is, S/L (small size and low book-to-market equity), S/M (small size and medium book-to-market equity), S/H (small size and high book-to-market equity), B/L (big size and low book-to-market equity), B/M (big size and medium book-to-market equity) and B/H (big size and high book-to-market equity). The ranking is redone each year and the portfolio composition changes due to the modifications in the size and book-to-market equity values of the TSE firms. The six portfolios are used to compute the risk premiums related to small size and high book-to-market equity, which are used as exogenous variables in the TFPM of Fama and French explained below. SMB is the difference, for each month, between the average of the 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). HML is the difference between the average of the returns of the two high BE/ME portfolios (S/H and B/H) and the average returns on the two low BE/ME portfolios (S/L and B/L).

3.3. Theoretical and Econometric Modelling

As mentioned earlier, we are interested in the more common theoretical models used in relation to the valuation of the financial assets. The CAPM argues that there is always a positive linear correlation between expected returns on securities and their market returns. Even more, the slopes of those simple regressions (βs) suffice to explain the cross-section of expected returns. In this case, the expected return on stock i, which means the cost of equity for bank i, i= 1, … , n, is defined by the following expression:

image(1)

where Rf15 and RM indicate, respectively, the risk-free interest rate and a weighted value of market portfolio. The coefficient βi is the risk of stock i. It is indeed the slope of regression of its excess return on the market excess return. A simple regression could be considered for each bank i as follows:

image(2)

We saw that the more important extension of this initial model was proposed by Fama and French (1993) raising the TFPM.16 According to this new formulation, the expected return on stock i, i= 1, … , n, is defined by the following expression:

image(3)

where βi,  si  and  hi are the slopes in the following multiple regression:

image(4)

Estimation of equations (2) and (4) will be conducted according to the random coefficient model of Swamy (1970).17 This kind of econometric models is interesting because when the coefficients of the regression are assumed to be random, one is able to account for inter-individual heterogeneity. So we have the possibility of looking for the variation of the parameters across cross-sectional units. This heterogeneity is due to a stochastic variability. In this sense, the errors ɛi are assumed to be both contemporaneously and serially independent but heteroscedastic across banks with different variances σ2i, i= 1, … , n. Coefficients αi, βi, si  and  hi, i= 1, … , n, could be estimated efficiently within an appropriate context of panel data analysis. We can put these coefficients into a vector named δi, which contains two coefficients in the case of CAPM and four coefficients in the case of TFPM. These vectors of coefficients are assumed to be identically and normally distributed with mean vector δ and covariance matrix Γ of the dimension k×k.18

In order to validate the random coefficient structure of Swamy, we adopt the indirect test of variation of the coefficients across the cross-sectional units. An important question is now to prove, according to the empirical application, that the regression coefficients so obtained are really varying across cross-sectional units. The appropriate procedure consists of testing whether the coefficient vectors δi are all equal to the mean vector δ. This corresponds to the following null hypothesis:

image(5)

If the null hypothesis is true, this signifies that the individual coefficient vectors must be considered as fixed and they are all equal to the mean. Rather, acceptance of the alternative hypothesis is interesting because it leads to the confirmation of the randomness assumption of the coefficient vectors. Swamy (1970) has constructed the appropriate statistic of the test, which is asymptotically distributed as χ2 with kx(n− 1) degrees of freedom under the null hypothesis and is defined as follows:

image(6)

where

image(7)

Xi determines the matrix of time series observations of explanatory variables of bank i. This matrix is defined by inline image for the CAPM and is of dimension T× 2 whereas it has the dimension T× 4 in the case of the TFPM and is defined by inline image. S is a T× 1 vector of ones.

A specification test could be conducted in order to verify which methodology has been proven to apply from a statistical point of view which is either the CAPM or the TFPM. This corresponds to the following null hypothesis:

image(8)

Since the estimator of the mean vector inline image is asymptotically efficient and normally distributed when T is high and n fixed,19 one could derive the appropriate statistic of the test that is distributed as χ2 with two degrees of freedom under the null hypothesis and is defined as follows:

image(9)

where R is a matrix of two restrictions defined as follows:

image(10)

4. Empirical Results

Table 3 documents the monthly average excess returns for the dependent and the explanatory variables of both CAPM and TFPM for the 60 months between July 2000 and June 2005, that is, the monthly average excess returns for all the deposit banks (RiRf), the monthly excess market returns (RMRf), the difference in average returns to the three small and three big firm portfolios (SMB), and the difference in average returns to the two high and two low book-to-market equity portfolios (HML). Mean values and standard deviations of these monthly excess returns are shown at the bottom of the table. The premiums for market risk, small size and relative distress are expected to be positive. Surprisingly, Table 3 reports that the three risk factors of (RMRf), SMB and HML are negative in about 60 per cent, 47 per cent and 47 per cent, respectively, of the 60 observations under study. These relatively high proportions of negative monthly excess returns are explained by the high volatility of the TSE and highly depressed market during the period of study.20 In comparison, Fama and French (1996) report that (RMRf) returns are negative in only 10 of the 30 years they studied. On the other hand, Aksu and Önder (2003) report 27 negative monthly excess returns of the 52 months under study (about 52 per cent of the total sample), which are inferior to those obtained for the TSE. The high number of negative excess returns for the risk factors suggests that there is no perfect effect of size and BE/ME in the TSE. However, the equally weighted mean values of the monthly market, size and distress premiums are still positive only for SMB and HML (5 per cent and 3.5 per cent per year, respectively), but negative for (RMRf) (−3.5 per cent per year) with the lowest premium observed for excess market returns and the highest for the distress risk factor. The SMB premium in the TSE is higher than those observed in the US market (Fama and French, 1993) but lower than those reported in the emerging markets (Fama and French, 1998). Conversely, market and value premiums are inferior to all results obtained in developed and developing countries except France. A description of the results on the determination of risk premiums in some developed and developing countries appears in Table 4.

Table 3.  Monthly CAPM and TFPM Explanatory Returns and Monthly Excess Returns over the Period 2000–2005
YearMonthsRiRfSMBHMLRMRf
  1. For the variable RiRf, mean value over the ten banks is considered for each month. t-value is obtained by dividing the mean of monthly returns (Mean) by its standard error that is (Std .  Dev)/(T− 1)0,5. The number of negative observations is in fact the number of negative monthly returns. We give also the proportions of these observations in the total sample.

2000–2001July0.007490.0178−0.07510.0447
August−0.00492−0.0183−0.003040.00816
September0.01410.03630.007310.0111
October−0.02440.006470.0046−0.063
November−0.01360.003290.0004730.0224
December0.0208−0.0124−0.02410.0172
January−0.08570.1780.137−0.026
February−0.04150.02740.0358−0.0651
March0.0070.006310.0003−0.00243
April0.0257−0.01760.01730.00382
May0.06770.04530.03020.0275
June−0.0258−0.04350.0537−0.0575
 
2001–2002July−0.01560.0221−0.008360.00533
August−0.0175−0.000210.0258−0.0942
September−0.0397−0.06750.0127−0.00218
October0.0354−0.00211−0.0349−0.0277
November−0.00886−0.03540.010.00845
December−0.006430.002620.01950.00186
January−0.00678−0.02040.043−0.00796
February−0.004080.003820.0927−0.00796
March−0.006850.02410.0299−0.0179
April0.00567−0.0195−0.0797−0.0516
May0.0633−0.02920.0171−0.00552
June0.01770.02810.0203−0.012
 
2002–2003July−0.01110.0112−0.0227−0.0109
August−0.02820.0124−0.0403−0.0395
September0.004560.0279−0.006460.0425
October−0.053−0.00085−0.0234−0.0557
November−0.0254−0.00188−0.0225−0.0153
December−0.00585−0.004570.0205−0.0113
January−0.05650.033−0.0503−0.0647
February−0.0296−0.0125−0.0113−0.0127
March−0.0230.0315−0.0695−0.00964
April0.0931−0.0460.1120.122
May0.01780.0341−0.0388−0.0263
June0.0337−0.0127−0.009950.00445
 
2003–2004July0.05490.03990.03260.0507
August−0.007840.0183−0.0028−0.0131
September0.0152−0.009090.0407−0.00604
October−0.01410.0217−0.0288−0.00615
November−0.001870.01490.01390.00231
December0.0223−0.0238−0.001830.017
January−0.02850.01850.01850.00245
February−0.01−0.00359−0.001−0.00193
March0.0465−0.009640.03330.0279
April0.0320.003980.02260.00953
May0.03820.02110.03830.00422
June0.003680.023−0.0305−0.00933
 
2004–2005July−0.02190.008920.0647−0.00479
August−0.01030.01730.0141−0.00446
September0.01460.0156−0.00238−0.0102
October0.0343−0.001860.04680.02
November−0.001140.00774−0.0192−0.018
December0.000659−0.02670.0196−0.00215
January−0.01090.0349−0.0288−0.00211
February0.00333−0.023−0.0324−0.00957
March0.0087−0.0084−0.08280.00677
April0.0899−0.0379−0.06950.0814
May0.072−0.04830.0340.0346
June0.0135−0.00839−0.07450.0128
 
Mean0.003710.004210.0029−0.0031
Standard deviation0.0340.03340.04350.0341
No. of negative observations31282836
Proportion in the sample51.6646.6646.6660
t-value0.840.9680.511−0.7
Table 4.  Annual Mean Premiums Obtained by Comparable Studies (in Percentages)
StudyCountryPeriodRMRfSMBHML
  1. Note: The means are annualized in order to make comparable the results across studies.

Fama and French (1996)USA1964–19935.944.926.33
Davis et al. (2000)USA1929–19978.342.435.66
Bauman et al. (1998)Canada1986–19965.401.20
Arshanapalli et al. (1998)Canada1975–19960.683.43
Liew and Vassalou (2000)Canada1978–19964.857.44
Molay (2000)France1992–19975.884.80.84
Aksu and Önder (2003)Turkey1993–199727.2418.2410.32

The standard deviation for HML is the largest with a value of 4.35 per cent, while it is 3.41 per cent per month for the average market premiums and 3.34 per cent per month for SMB. The high volatility implies substantial uncertainties about the true expected premiums. Unfortunately, all these premiums are not significantly different from zero. Therefore, no premium presents an arbitrage opportunity in the TSE, while the size premium seems to fulfil that role in the Turkish Stock Exchange (Aksu and Önder, 2003). However, the high number of negative monthly returns and their high standard deviations imply that these premiums do not present a perfect arbitrage opportunity.

Table 5 presents the results of the estimation for the CAPM and TFPM specifications carried out using the econometric methodology presented in the preceding section.21 First, the random coefficient specification is adopted according to the empirical results issued from the test (expressions (5)–(7)), which confirms the significant variation of the coefficients across the cross-sectional units.22 Therefore, the coefficient vectors δi could not be assumed as fixed and are not all equal. Refuting the null hypothesis means that the sample units under study are heterogeneous with a sensible random varying behaviour. For both the CAPM and TFPM, the estimated value for the statistic of the test (expression (6)) is, respectively, 24 and 149.29. This last value is largely above the corresponding critical value of χ2 at the 1 per cent level.

Table 5.  Random Coefficient Estimates and Predictors of CAPM and TFPM
BanksCAPMTFPM
InterceptRMRfInterceptRMRfSMBHML
  1. Figures given in parentheses are the estimated standard deviations of the estimates.

  2. ***, **, and * indicate significance levels at 1, 5, and 10%, respectively.

AB0.00610.45***0.0069**0.494***0.0292−0.0943
(0.0042)(0.142)(0.0035)(0.115)(0.156)(0.126)
ATB0.0079*0.625***0.0108***0.646***0.158−0.188
(0.0044)(0.154)(0.0036)(0.119)(0.171)(0.139)
BH0.00370.589***0.00380.56***−0.487***−0.0463
(0.0044)(0.151)(0.0035)(0.116)(0.159)(0.128)
BIAT0.011***0.669***0.0097***0.653***−0.1420.0934
(0.0043)(0.144)(0.0035)(0.115)(0.157)(0.127)
BNA−0.000310.403***−0.00050.341***−0.07750.263**
(0.0039)(0.126)(0.0032)(0.104)(0.129)(0.104)
BS0.00630.543***0.00530.524***−0.1520.137
(0.0046)(0.169)(0.0038)(0.126)(0.203)(0.165)
BT0.0118***0.579***0.0125***0.621***0.298−0.0447
(0.0045)(0.162)(0.0037)(0.122)(0.184)(0.15)
STB−0.0010.801***−0.00350.558***−0.796***0.58***
(0.0046)(0.165)(0.0035)(0.114)(0.155)(0.125)
UBCI0.00370.877***0.0087**1.115***−1.531***−1.0346***
(0.0043)(0.181)(0.0041)(0.135)(0.279)(0.226)
UIB0.0092**0.718***0.0084**0.592***0.2180.446***
(0.0047)(0.172)(0.0038)(0.125)(0.197)(0.16)
Mean vector0.0058*0.625***0.0062**0.61***−0.2480.0113
(0.0032)(0.118)(0.0029)(0.105)(0.211)(0.168)
Statistic χ2124 149.29*** 

The results presented in Table 5 show that the mean beta for the banking sector is highly significant (around 0.625 for CAPM and 0.61 for TFPM), but less than the usual values obtained for banks, which are greater than one. This could be attributed to the low turnover rate of financial institutions in Tunisia of less than 10 per cent in the period 1999–2005 compared to 20 per cent and 25 per cent, respectively, for industry and services. Another reason for this low beta is that the banking sector in Tunisia was protected from international competition during the period of study where only two international banks were allowed to operate in Tunisia (City Bank and Arab Banking Corporation). Last, but not least, the explanation for this low beta is the concentration of the Tunisian banks on traditional and not risky activity—that is, taking deposit and allowing credit. Although the average betas are the same in the two specifications, the individual bank coefficients (the individual predictors) differ sensibly from one model to the other. The two main reasons for this difference are the relative instability of the coefficient (instead of using sectors as individuals, we included firms) and the introduction of two new risk factors in the Fama and French model (TFPM). The coefficients associated with SMB are on the whole negative and relatively small, indicating that the banking industry is represented by big firms compared to the other companies that are listed on the TSE. Negative coefficients are obtained, especially for big-sized banks such as BH, BIAT, BNA, BS, STB and UBCI.23 In other words, it means that these banks are less exposed to risk than other smaller companies on the TSE. The other banks in the sample are small-sized. Therefore, the sign of the coefficients associated with SMB is positive, but not statistically significant. On the other hand, the coefficients associated with HML are positive but small, which again implies that Tunisian deposit banks have value stocks that under-performed during the period under study. For banks with a positive sign, this signifies that they are experiencing financial difficulties. It is the case, for example, of BS and UIB, which have been privatized, and BNA which suffers from the structural problems of the agriculture sector (insolvency of farmers, rescheduling of debts, etc.).

The cost of equity could be estimated either for each bank i or for the whole sector. To do this, we will use the estimated predictors for banks i, i= 1, … , n and the GLS estimator of the mean vector for the whole sector, which appear in Table 5. According to the CAPM approach, the used formulae are defined as follows:

image(11)
image(12)

where Ri0  and  Rs0 are, respectively, the cost of the equity of bank i and that of the banking industry both computed in June 2005. On the other hand, Rf0 is the money market rate (TMM) observed also in June 2005, that is, Rf0= 5%. inline image is the total market risk premium.24

For the TFPM approach, we obtain in a similar fashion the following formulae:

image(13)
image(14)

We now add inline image as the annualized average SMB and HML premiums, respectively, over the period of study.

Table 6 reports the estimated costs of equity for the 10 deposit banks on 30 June 2005. It shows that CAPM and TFPM give different costs of equity on average, since we obtain 8.38 per cent and 7.04 per cent, respectively. It means that investing in banking industry stocks is not a very risky activity since market risk premiums are only about 3.38 per cent for the CAPM and 2.04 per cent for the TPFM. When banks are individually compared, the CAPM specification gives individual values that are approximately around the average value of the whole banking sector and range from 7.18 per cent (BNA) to 9.74 per cent (UBCI). For the TFPM, the dispersion is more important with some individual costs under the TMM value of 5 per cent and the other reaching 10.90 per cent. The evidence surprising is the negative cost of equity of UBCI. It is the bank that is most sensitive to market risk with a beta over 1 but its loading on HML and SMB is very high compared to other banks but in the opposite direction. The negative and significant coefficient of HML is linked to the high performance and strong growth perspectives of UBCI under the control of the French ‘Banque Nationale de Paris’. In addition, UBCI is the second largest bank in terms of market capitalization in the TSE, which enables it to obtain a negative premium on the size factor. The differences between the CAPM and TFPM costs of equity are largely determined by the SMB and HML slopes in the three-factor regressions. Part of the dispersion of the TFPM cost of equity is caused by an estimation error in SMB and HML slopes. But the risk loadings are in fact a small part of the cost of equity estimation problem. Uncertainty about the market and SMB and HML premiums in CAPM and TFPM are more important (Fama and French, 1997). Thus, the choice of CAPM or TFPM costs of equity will have a large impact on the valuation of investments.

Table 6.  Estimated and Predicted Costs of Equity for the 10 Deposit Banks on 30 June 2005
BanksCAPMTFPM
βiCost of equityβisihiCost of equity
AB0.457.43%0.4940.0292−0.09437.49%
ATB0.6258.38%0.6460.158−0.1888.65%
BH0.5898.18%0.56−0.487−0.04635.33%
BIAT0.6698.61%0.653−0.1420.09348.12%
BNA0.4037.18%0.341−0.07750.2637.37%
BS0.5437.93%0.524−0.1520.1377.52%
BT0.5798.13%0.6210.298−0.04479.75%
STB0.8019.33%0.558−0.7960.585.92%
UBCI0.8779.74%1.115−1.531−1.0346−0.23%
UIB0.7188.88%0.5920.2180.44610.90%
 
Sector0.6258.38%0.61−0.2480.01137.04%

Finally, considering CAPM as a nested model within the TFPM and applying the statistical test developed by expressions (8)–(10), we can conclude from an econometric point of view that the CAPM could be rejected in favour of the more general TFPM. In this sense, the estimated value for the statistic of the test (expression (9)) is 19.8, so as to be above the corresponding critical value of χ2 at the 1 per cent level. This proves the importance of the presence of the variables SMB and HML in the model. But as mentioned above, the statistical significance of TFPM against CAPM is confirmed despite the lack of theoretical foundations for this specification. Further, one could not neglect the preponderant effect of other factors such as size and book-to-market equity in the valuation of financial assets.

5. Conclusions

This paper has explored the empirical feasibility of the two important theoretical models used for the valuation of financial assets and the direct implications of evaluating the cost of equity in the Tunisian banking sector. The period considered for this study is of interest since it coincides with the vast reforms undertaken by the Tunisian government in order to improve the performances of the whole financial system.

The empirical methodology developed in this study is based on the econometrics of panel data, especially the random coefficient model of Swamy (1970), which invokes the variability of the coefficients taking into account a possible heterogeneity across cross-sectional units.

Empirical results from this study argue that Tunisian banks are less exposed to market risk than the average companies on the TSE. Therefore, investing in banking securities seems not to be a risky activity since, as it is known, most of the banks operating in Tunisia are big in size and contribute a large share to the national economy as a whole. Also, the empirical results must emphasize the importance of calculating the cost of equity, which constitutes a good tool for improving the allocation of funds and the valorization of assets. Depending on the model specification, stockholders in the TSE require a 2 to 3 per cent risk premium to invest in the Tunisian banking sector.

Footnotes

  • 1

    Economic Value Added.

  • 2

    Banque Centrale de Tunisie.

  • 3

    Conseil du Marché Financier. It is a regulatory body equivalent to the SEC in the US. CMF could be translated as Financial Market Council.

  • 4

    Société Tunisienne Interprofessionnelle pour la Compensation et le Dépôt des Valeurs Mobilières. It is a national organization that provides highly automated record keeping and depository services and facilitates the clearing and settlements of transactions.

  • 5

    BVMT (2004).

  • 6

    NPLs were reduced in half between 1992 and 1999.

  • 7

    Banque de Développement Economique de Tunisie.

  • 8

    Banque Nationale de Développement Touristique.

  • 9

    See the list of the ten commercial banks which constitute the individual cross-sectional units in the sample with the corresponding abbreviation (French initials) in the Appendix.

  • 10

    Statistical information in Section II are found either in BVMT (2004) or the website of the TSE (http://www.bvmt.com.tn).

  • 11

    The turnover ratio is computed as the ratio of exchanged capital over total market capitalisation.

  • 12

    Interest rates in Tunisia are free since 1996 but the TMM is regulated by the BCT and changes by decree like the other interest rates which are defined according to the TMM plus a risk premium.

  • 13

    To match monthly return data with monthly money market-rate, we use the rates for the month in which the return is calculated.

  • 14

    This is the ratio of book value equity (BE) to market value equity (ME).

  • 15

    In the empirical study, the risk-free interest rate is the TMM (Money market interest rate). Such rate has been chosen because it is the smallest interest rate in the market.

  • 16

    More recently, a new generation of models are those that introduce a forth factor. We speak about the FFPM models. The additional variable introduced is called Winners Minus Losers (WML). See for the moment L'Her et al. (2004).

  • 17

    See also Greene (1993), Hsiao (1986), and Swamy (1971).

  • 18

    For the empirical analysis, we have k= 2 in the CAPM case and k= 4 in the TFPM case.

  • 19

    In the empirical study, the test will be conducted only on the mean vector δ because inline image is normally distributed which permits to constitute a statistic of the test with a usual distribution.

  • 20

    We observe negative returns on the TSE index in 2001 (−30%) and 2002 (25%), and zero return in 1998 and 2004.

  • 21

    Estimations were conducted on STATA8 software.

  • 22

    For CAPM, variation of the coefficients across the cross-sectional units is significant at only 15%.

  • 23

    Significance at the 99% level is observed only for BH, STB and UBCI.

  • 24

    “You can estimate an adjusted country risk premium by multiplying the default spread by the relative equity market volatility for that market (Standard deviation in country equity market/Standard deviation in country bond). I have used the emerging market average of 1.5 (equity markets are about 1.5 times more volatile than bond markets) to estimate country risk premium. I have added this to the historical premium for the US of about 4.8% to get the total risk premium. Then, the long term Tunisian market risk premium is 6.6% in US dollar” (Damodaran, 2006). To convert the premium in Tunisian dinar, the US premium was multiplied by (1 + the 2005 US inflation rate) and divided by (1 + the 2005 Tunisian inflation rate).

Appendices

Appendix: List of Abbreviations

ABAmen Bank
ATBArab Tunisian Bank
BCTBanque Centrale de Tunisie
BDETBanque de Développement Economique de Tunisie
BEBook Equity
BHBanque de l'Habitat
BIATBanque Internationale Arabe de Tunisie
BNABanque Nationale Agricole
BNDABanque Nationale de Développement Agricole
BNDTBanque Nationale de Développement Touristique
BNTBanque Nationale de Tunisie
BSBanque du Sud
BTBanque de Tunisie
BTSBanque Tunisienne de Solidarité
BVMTBourse des Valeurs Mobilières de Tunis
CAPMCapital Asset Pricing Model
CMFConseil du Marché Financier
EVAEconomic Value Added
FFPMFour-Factor Pricing Model
HMLHigh Minus Low
IMFInternational Monetary Fund
MEMarket Equity
MENAMiddle East and North Africa
NPLNon Performing Loans
SMBSmall Minus Big
STBSociété Tunisienne de Banque
STICODEVAMSociété Tunisienne Interprofessionnelle pour la Compensation et le Dépôt des Valeurs Mobilières
TFPMThree-Factor Pricing Model
TMMTaux du Marché Monétaire
TSETunisian Stock Exchange
UBCIUnion Bancaire pour le Commerce et l'Industrie
UIBUnion Internationale des Banques
WMLWinners Minus Losers

Non-technical Summary

Estimating the cost of equity is crucial for many financial decisions of privately owned companies such as capital budgeting, capital structure, performance valuation and the pricing of services in some regulated industries. Several asset pricings have been devised by financial scholars to explain the expected returns of stocks, namely the Capital Asset Pricing Model (CAPM), the Three-Factor Pricing Model (TFPM), the Four-Factor Pricing Model (FFPM) … . In a survey, Bruser et al. (1998) find that the most common method favoured by practitioners for estimating cost of equity is the CAPM. However, Fama and French (1993) addressed the size and the book-to-market anomalies detected in testing the CAPM by proposing a model that includes three factors to explain the movements of average excess stock returns, that is the excess return on a broad market portfolio, the difference between the return on a portfolio of small stocks and the return on a portfolio of large stocks and the difference between the return on a portfolio of high book-to-market stocks and the return on a portfolio.

The purpose of this study is to estimate the cost of equity of the Tunisian commercial banks using both CAPM and TFPM. Our research makes three contributions to the literature. It is the first paper that focuses on the estimation of cost of equity of banks using the CAPM and the TFPM. In addition, econometric approach is also novel in the field based on the random coefficient model in the context of panel data analysis. In addition, the estimation is done during a period where the Tunisian bank industry is undergoing substantial reforms (mergers, disinvesting, recapitalization and so forth) and the results of this study will give Tunisian banks a benchmark for all their ongoing restructuring financial decisions.

In our sample period, the size and book-to-market premium are positive as expected whereas the market premiums are negatively linked to the high proportion of negative monthly excess return recorded in the period. The SMB premium in the TSE is higher than those observed in the US market (Fama and French, 1993) but lower than those reported in the emerging markets (Fama and French, 1998). Conversely, market and value premiums are inferior to all results obtained in developed and developing countries except France.

In addition, the results show that the mean beta for the banking sector is highly significant (around 0.625 for CAPM and 0.61 for TFPM), but less than the usual values obtained for banks, which are greater than one. This could be attributed to the low turnover rate of financial institutions in Tunisia of less than 10 per cent in the period 1999–2005 compared to 20 and 25 per cent, respectively, for industry and services. Another reason for this low beta is that banking sector in Tunisia was protected from international competition during the period of study where only two international banks were allowed to operate in Tunisia (City Bank and Arab Banking Corporation). Last, but not least, the explanation for this low beta is the concentration of the Tunisian banks in traditional and non-risky activities.

Although the average betas are the same in the two specifications, the individual bank coefficients (the individual predictors) differ sensibly from one model to the other. The two main reasons for this difference are the relative instability of the coefficient (instead of using sectors as individuals, we included firms) and the introduction of two new risk factors in the Fama and French model (TFPM). The coefficients associated to SMB are on the whole negative and relatively small, indicating that the banking industry is represented by big firms compared to other companies listed on the TSE. In addition, the results show that CAPM and TFPM give different costs of equity in average, since we obtain 8.38 per cent and 7.04 per cent, respectively. It means that investing in the banking industry stocks is not a very risky activity since market risk premiums are only about 3.38 per cent for the CAPM and 2.04 per cent for the TFPM. When banks are individually compared, the CAPM specification gives individual values approximately around the average value of the whole banking sector and range from 7.18 per cent (BNA) to 9.74 per cent (UBCI). For the TFPM, the dispersion is more important with some individual costs under the TMM value of 5 per cent and other reaching 10.90 per cent.

Evidence that is surprising is the negative cost of equity of UBCI. It is the most sensitive bank to market risk with a beta over 1 but its loading on HML and SMB is very high compared to other banks but in the opposite direction. The negative and significant coefficient on HML is linked to the high performance and strong growth perspectives of UBCI under the control of the French ‘Banque Nationale de Paris’. Besides, UBCI is the second largest bank in terms of market capitalization on the TSE, which enables it to obtain a negative premium on the size factor.

Ancillary