Application of Asset Pricing Models: Evidence From Saudi Exchange

The Saudi Arabia Stock Exchange (Tadawul) is one of the biggest emerging Stock Exchanges in the Middle East region. Therefore, this research aims to apply Fama and French (2015) 5-factor model on Tadawul, and compares it with the Fama and French 3-factor model and CAPM to check the applicability of the models in Tadawul and the identity of the factors that can affect stock returns. Furthermore, the Generalized Method of Moments (GMM) regression has been implemented to examine the impact between the variables in the models. Empirically, the results show that Fama and French (2015) 5-factor model is the most consistent model in comparison to the other two models in terms of explaining the cross-section of average stock returns in Tadawul. However, it is not the best according to the intercepts results of all the regressions in 2x3, 2x2, or 2x2x2x2 sorts. Besides, Fama and French (2015) 5-factor model has the highest explanatory power in most of the portfolios based on the adjusted R2 regardless of the sort (2x3, 2x2, or 2x2x2x2). Finally, the results conclude that Fama and French (2015) 5-factor model can be an applicable model in Tadawul but only market and size can affect the stock returns, while the value, profitability, and investment cannot. Accordingly, the author recommends that, as a continuation of this research, further research can be done, which investigates a model with additional factors like momentum and illiquidity.


INTRODUCTION
The Modern Portfolio Theory was established around 1950 by Markowitz. Its main objective was to consider the asset return through its risk adjustment. Markowitz's contributions paved the way to Sharpe and others to construct the famous Capital Asset Pricing Model (CAPM). This single index model describes the linear adjusted relationship between the asset or portfolio return and the market risk beta.
The Arbitrage Pricing Theory (APT) was introduced around 1970 by Ross and Roll. It was a multiple independent micro or macro variables model to present the asset return (R i ) without determining the identity of the variables. The Size factor presented by Banz (1981), Jegadeesh and Titman (1993) introduced the momentum factor. Fama and French (FF1992, FF1993) models were mainly concerned with the milestone models (market, size and book-to-market (B/M)). Carhart (1997) 4-factor model consisted of FF1993 3-factor model and momentum. Moreover, Amihud (2002) introduced the illiquidity factor. Denial and Titman (1996) tested the independent variables as a characteristic excluding risk factor. The Profitability factor was identified by Novy-Marx (2013). The Investment factor was documented by Alharoni et al. (2013). Consequently, Fama and

LITERATURE REVIEW
To begin with, Markowitz could show how to construct an efficient frontier of portfolios, while Sharpe developed the single index model in 1963and CAPM in 1964(Haugen, 1997. The introduction of the USA earliest articles concerning this topic was full of contradictions and agreements. Fama and Macbeth (1973) proved that the portfolio risk only affects the returns. On the other hand, Banz (1981) found that smaller firms had a higher "risk-adjusted returns on average" than large firms. Reinganum (1982) totally agreed with Banz. However, Horowitz, Loughran, and Savin (1996) and Roll (1981) came to a contradiction with Banz. From Roll's (1981) perspective, the problem with Banz's study was in the methods and ways used to measure riskiness of small firms.
Many debates were concerned with the microeconomic risks. This includes a couple of FF statements. In 1992, they stated that Size and B/M are used with market β to capture the variation in the returns. In 1993, they stated that stock returns have shared variation due to Market, Size, B/M factors. In 1995, they also stated that many anomalies disappeared in FF1993 model. On the other hand, Davis, Fama, and French (2000) showed that FF1993 model explains the value premium better than the hypothesis that B/M characteristic is compensated irrespective of risk loadings. In 2003, Fama and French indicated that CAPM has been widely used in multiple applications. In 2007, they provided a framework for the disagreement among investors on probability distributions of future payoffs on assets. In 2012, Fama and French proved that there are value and momentum in average returns. As a result, a new milestone was introduced in FF2015 model by capturing size, value, profitability, and investment patterns in average stock returns. In 2017, Fama and French showed that average stock returns increase with B/M and profitability, and it is also negatively related to investment.
As a further contribution to the debate, Daniel and Titman (1997) indicated that the characteristics appear to explain the variation in returns, but not the covariance structure of returns. Daniel, Titman, and Wei (1999) could reject FF1993 model, but not the characteristics model. Also, Kim (1997) found that size, B/M, earnings price, and βs have explanatory power on the returns. In 2003, Gomes suggested that size and B/M can be consistent with conditional CAPM. However, Jegadeesh and Titman (1993) added the momentum factor. Jensen (1972) indicated that risk premium on an asset is not relative to its β. Griffin (2002) showed that the 3F model has the best performance on a country-specific basis and supported domestic factors. In contrast, Bartholdy and Peare (2005) found poor performance for CAPM and FF models. Liu (2006) showed that market and liquidity model explains returns effectively so as B/M. From his side, Chen, Novy-Marx, and Zhang (2011) explained that market, investment, and return-on-equity model reduce magnitude of abnormal returns to insignificance. Blitz (2016) il-lustrated how FF2015 model improved explanatory power. Bianchi (2016) also showed that FF2015 is the best. Wahal (2017) showed that profitability is similar in magnitude in pre and post 1963 periods. He also observed no relation between investment and returns. Hühn (2016) supported momentum factor.
Similarly, in Europe, Bhatnagar and Ramlogan (2012) compared CAPM's performance and evaluation in the UK using different approaches than the previous FF. Staying in the UK, Gregory and Michou (2009) showed that FF1993 model is better than CAPM, and they proved that size and value factors have an +impact. In further discussions on this issue in Italy, Brighi et al. (2013) found that market and size are confirmed for local investor. On the contrary, value factor has a weak proof. Let us consider the same issue in Turkey. Eraslan (2013) found that large size firms have more excess returns than small firms. In general, low B/M firms have better performance than high ones. Staying in Turkey, Unlu (2013) indicated that CAPM, 3F, 4F, and 5F models are applicable. Furthermore, Faff and O'Brien (2001,2007)  Moving the discussion to Middle East, Al-Zubi and Salameh (2009) indicated that FF1993 model is applicable in Amman Stock Exchange, and they stated that market and size variables had a significant impact. Aldaarmi, Abbod, and Salameh (2015) also showed the same results in Tadawul, but only market variable had an impact. Staying in Saudi Arabia, Habib (2016) found that Proxy Asset Pricing specifications are scant due to a lack of theoretical frameworks and misguided significance tests of factor loadings. To best of our knowledge, this research definitely is one of few supervene researches that apply the FF2015 methodology in Tadawul among Arab exchanges.

Data and sample
The period herein extended from January 2014 to August 2017, monthly stock prices of Tadawul firms were used (44 observations). The source of data is the Tadawul's website (http://www.tadawul.com.sa/).

Models
This author tested the factors of three models to find out if the factors in each model affect the portfolio returns. Moreover, the models were tested by using Generalized Method of Moments (GMM) regression (it does not need information about the exact distribution of the disturbances). In fact, many common estimators in econometrics can be considered as special cases of GMM, and time series (HAC) GMM is a robust estimate with regard to the heteroskedasticity and autocorrelation of unknown form was used to find out if the value of the intercept = 0, which means that the model cap-tures the cross-sectional variation in stock returns. The models with the intercept that is closer to zero would capture the cross-sectional variation in the stock better than other models. SMB t : is the difference between the return on portfolios of small and big size.
HML t : is the difference between the return on portfolios of high and low B/M. RMW t : is the difference between the return on portfolios of robust and weak profitability.
CMA t : is the difference between the return on portfolios of conservative and aggressive investment.
Risk-free rate R f : is the 4 weeks' interest rate on SAMA bills (Saudi Arabia Monetary Authority website).

Monthly return
The monthly return is a function of the price of the stock in the current month and the price of the stock in the previous month and can be represented by the following equation:

Methodology of forming the independent variables portfolios
To examine whether the specifics of factor construction are important to be used in the tests of asset pricing model, the author used three sets of factors to capture the patterns in average returns (depend-ent variables).On the other hand, three approaches were used in constructing the independent variables: Size (SMB), Book-to-market (HML), Profitability (RMW), and Investment (CMA), which were used in three different sorts (2x2x2x2, 2x3, and 2x2) ,which were further described formally and in detail.
The author uses the independent sorts to assign stocks in different groups at each sort.    HML, RMW, and CMA from the 2x3 or 2x2 sorts weigh small and big stock portfolio returns equally; they are roughly neutral with respect to size. The HML is constructed without controls for OP and Inv.; however, it is not neutral with respect to Profitability and Investment. This likely means that the average HML return is a mix of premiums related to B/M, Profitability, and Investment. Similar comments apply to RMW and CMA.

2x2x2x2 sort
In this sort, the author should better isolate the premiums in average returns related to Size, B/M, OP, and Inv. The final candidate factors use the four sorts illustrated above to construct the dependent variables so that it can jointly control four variables. Further explanation of the methodology of FF in constructing the four independent var-iables according to these sorts will be discussed further. Sixteen (16) portfolios formed for the dependent variables in the previous section were constructed using the following four sorts. The measurements of the independent variables are as follows: In 2x2x2x2 sort, SMB is equal to the weights high and low B/M, robust and weak OP, and conservative and aggressive Inv. portfolio returns. Thus, the Size factor is roughly neutral with respect to the value, profitability and investment, and this is what the author means by Size factor jointly controlling for the other three variables. Likewise, HML factor is roughly neutral with respect to the size, profitability, and investment, and similar comments could apply to RMW and CMA. As a comment, neutrality with respect to the characteristics does not imply low correlation between factor returns. Moreover, factor exposures are more important in the eventual inferences, since multivariate regression slopes measure marginal effects, the five factors slope for HML, RMW, and CMA produced by the factors from 2x3 or 2x2 sorts may isolate exposures to the value, profitability and investment effects in returns as effectively as the factors from the 2x2x2x2 sort.

Regressions results of 2x3 sort
Cross-section of stock returns: Table C1 in Appendix C shows that FF1993 and CAPM regressions do a better job in explaining the cross section of the average stock returns (R i ), which can be explained by the intercepts in all the regressions, which are insignificantly different from zero, but only in 14 regressions for FF2015 model, while BHWC, BLRA regressions are significant different from zero at 5% and 10%, respectively.

Regression results of 2x2 sort
Cross-section of stock returns:

Regressions results of 2x2x2x2 sort
Cross-section of stock returns:  12,9,9) for FF2015 portfolios in 2x3, 2x2, 2x2x2x2 sorts, respectively. Accordingly, there is good evidence that R m and R SMB significantly affect (R i ). R HML significantly affects (R i ) in 9, 6, 5 for FF1993, 9, 6, 3 for FF2015 portfolios for 2x3, 2x2, 2x2x2x2 sorts, respectively. R RMW significantly affects (R i ) in 2, 4, 1 portfolios in 2x3, 2x2, 2x2x2x2 sorts, respectively. R CMA significantly affects (R i ) in 3, 7, 6 portfolios for 2x3, 2x2, 2x2x2x2 sorts, respectively. Accordingly, there is no evidence that R HML , R RMW, and R CMA significantly affect (R i Finally, the author adds the following financial implications: the positive sign of Size variable in the paper contradicts FF2015 results. Fama and French illustrated the negativity of this variable as a result of neglected, mispriced, and insufficient analysis of small firms. The positive sign in Tadawul (the US's stocks are much larger than Tadawul) indicates a well-analyzed, not neglected, and correctly priced small firms. Moreover, the negative sign of Book-to-market variable in this study also contradicts FF2015 results. Fama and French illustrated the positivity of this variable due to making high Book-tomarket firms have higher returns so that it protects the investors from high risk. The negative sign in Tadawul is forcing the CEOs to take financial, investment, and operational activities to raise the stock price since they are not facing enough corporate governance procedures from the board of directors. Furthermore, the sign of Profitability variable in this study does not have any clear indication; some portfolios are positive, while others are negative and insignificant. Fama and French illustrated the positivity of this variable since robust profitability corporations have higher returns. The insignificant elusory sign in Tadawul is an indicator that robust profitability of the firms does not have any effect on raising the stock price because of poor implementation of corporate governance. Finally, the Investment variable sign in this study is also unclear same as profitability factor. Fama and French illustrated the positivity of this variable because conservative asset investments lead to higher returns. The positive insignificant sign in Tadawul also leads to higher returns but it is not significant due to poor implementation of corporate governance procedures.
Adding SMB, HML and SMB, HML RMW, and CMA to FF1993 and FF2015 regressions, respectively, has an effect on the market βs for stocks. In some regressions, it collapses the βs for stocks toward 1.0, low βs move up, and high βs move down toward one. This behavior is due to correlation between market and SMB or HML and correlation between markets in FF1993 and SMB or HML or RMW or CMA in FF2015.