1. Introduction

Borsa Istanbul (BIST) stock exchange was established in 1985 and commenced stock trading on 3 January 1986. Acceptance of BIST as a full member to the World Federation of Exchanges (WFE) was in 1992. As elsewhere, obviously for all investors (institutional or individual), the main goal is to get the highest possible return in a stock market.

This study tests the capital asset pricing model (CAPM hereafter), the three-factor Fama-French model (3F-FF hereafter) and the five-factor Fama-French model (5F-FF hereafter) in the case of the Turkish stock market. This study extends the asset pricing tests in three ways: (a) this study is the first application of the 5F-FF Fama-French model for the Turkish stock market. (b) It expands the test of the 3F-FF model to the Turkish market for a longer period, and this is the first study that covers 17 years of the Turkish data. The main result is that the

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5F-FF model explains better the common variation and the cross section of stock returns than the 3F-FF model and the CAPM. (c) I test all the models (CAPM, 3F-FF and 5F-FF) with 48 different market portfolios. 5F-FF model portfolios capture the common variation in stock returns and can explain the cross section in returns.

In Section 2, I give a literature review on asset pricing models and applications. In Section 3, data selection, variable definitions, return periods and filtering data issues are given. Section 4 explains the methodology to apply the CAPM and Fama-French factor models to the Turkish stock market. In this section, explanatory variables and dependent variables are defined. First of all, Fama-French factors are constructed. Then, regression portfolios are constructed by sorting the stocks by their size, book-to-market ratios (B/M), profitability (OP) and investment (INV). In Section 5, I give regression portfolio statistics to see patterns in the behaviour of portfolios. Section 6 defines and estimates factor spanning regressions, which are important to see if an explanatory factor can be explained by a combination of other factors. Having estimated and tested factor spanning regressions, I go on testing of hypothesis of joint significance of portfolio regressions' alphas in Section 7. In this section, I conduct Gibbons-Ross-Shanken (GRS) test for the regression portfolios and give preliminary results of the performance of the CAPM, the 3F-FF and the 5F-FF models for the Turkish case. Section 8 is devoted to the detailed analysis of regressions, and the main messages of these regressions are presented. Section 9 concludes and presents the main findings of the study.

#### 2. Literature review

What kinds of factors determine the price of an asset? Since Markowitz formulated a model of asset pricing [1], the debate on this question continues. The main determinants of asset prices and risk factors that affect the demand for assets and asset prices have been an important issue in finance theory and practice. One can find enormous number of studies on this issue. Earlier studies in this area are by Markowitz, Sharpe, Ross, Fama and French [1–4].

Since the literature on asset pricing model (APM) is very well known and can be reached easily in finance textbooks, I do not go into a detailed explanation of evolution of APM. However, I would like to briefly state that all the asset pricing models developed so far have included risk as the most important determinant. For example, [1] defines the expected return and variance of returns on a portfolio as the basic criteria for portfolio selection.

Markowitz's model requires large data inputs. Because of input drawback, new models have been developed to simplify the inputs to portfolio analysis. William Sharpe's market model [2] is as follows:

$$R\_{it} = \alpha\_i + \beta\_i \, ^\*R\_{Mt} + \varepsilon\_{it\prime} \tag{1}$$

where Rit is the return of stock i in period t, α<sup>i</sup> is the unique expected return of security i, β<sup>i</sup> is the sensitivity of stock i to market movements, Rmt is the return on the market in period t and eit is the unique risky return of security i in period t and has a mean of zero and finite variance σ2 ei, uncorrelated with the market return, pairwise and serially uncorrelated. This equation explains the return on asset i by the return on a stock market index. β in Eq. (1) is a risk measure arising from the relationship between the return on a stock and the market's return.

5F-FF model explains better the common variation and the cross section of stock returns than the 3F-FF model and the CAPM. (c) I test all the models (CAPM, 3F-FF and 5F-FF) with 48 different market portfolios. 5F-FF model portfolios capture the common variation in stock

In Section 2, I give a literature review on asset pricing models and applications. In Section 3, data selection, variable definitions, return periods and filtering data issues are given. Section 4 explains the methodology to apply the CAPM and Fama-French factor models to the Turkish stock market. In this section, explanatory variables and dependent variables are defined. First of all, Fama-French factors are constructed. Then, regression portfolios are constructed by sorting the stocks by their size, book-to-market ratios (B/M), profitability (OP) and investment (INV). In Section 5, I give regression portfolio statistics to see patterns in the behaviour of portfolios. Section 6 defines and estimates factor spanning regressions, which are important to see if an explanatory factor can be explained by a combination of other factors. Having estimated and tested factor spanning regressions, I go on testing of hypothesis of joint significance of portfolio regressions' alphas in Section 7. In this section, I conduct Gibbons-Ross-Shanken (GRS) test for the regression portfolios and give preliminary results of the performance of the CAPM, the 3F-FF and the 5F-FF models for the Turkish case. Section 8 is devoted to the detailed analysis of regressions, and the main messages of these regressions are

What kinds of factors determine the price of an asset? Since Markowitz formulated a model of asset pricing [1], the debate on this question continues. The main determinants of asset prices and risk factors that affect the demand for assets and asset prices have been an important issue in finance theory and practice. One can find enormous number of studies on this issue. Earlier

Since the literature on asset pricing model (APM) is very well known and can be reached easily in finance textbooks, I do not go into a detailed explanation of evolution of APM. However, I would like to briefly state that all the asset pricing models developed so far have included risk as the most important determinant. For example, [1] defines the expected return and variance

Markowitz's model requires large data inputs. Because of input drawback, new models have been developed to simplify the inputs to portfolio analysis. William Sharpe's market model [2]

where Rit is the return of stock i in period t, α<sup>i</sup> is the unique expected return of security i, β<sup>i</sup> is the sensitivity of stock i to market movements, Rmt is the return on the market in period t and eit is the unique risky return of security i in period t and has a mean of zero and finite variance

<sup>∗</sup> RMt <sup>þ</sup> eit, (1)

Rit ¼ α<sup>i</sup> þ β<sup>i</sup>

presented. Section 9 concludes and presents the main findings of the study.

studies in this area are by Markowitz, Sharpe, Ross, Fama and French [1–4].

of returns on a portfolio as the basic criteria for portfolio selection.

returns and can explain the cross section in returns.

70 Financial Management from an Emerging Market Perspective

2. Literature review

is as follows:

Later on, the equilibrium models have been developed. The difference between the market model and the equilibrium model was that asset returns are related to excess market return rather than market return. The first and basic form of the general equilibrium model, which was developed by Sharpe, Lintner and Mossin [2, 4, 5] called capital asset pricing model (CAPM), is given in Eq. (2):

$$R\_{it} = R\_f + \beta\_i \, ^\* \left( R\_{Mt} - R\_f \right) + e\_{it} \tag{2}$$

where Rit is the return of stock i in period t, Rf is risk free rate, β<sup>i</sup> is the sensitivity of stock i to excess return on a market portfolio, Rmt is the return on the market in period t and eit is the unique risky return of security i in period t and has a mean of zero and variance σ<sup>2</sup> ei.

Black et al. [6] derived a new model of the CAPM by relaxing the assumption of risk-free lending and borrowing. Basu [7] considers a different time series model, which is written in terms of returns in excess of the risk-free rate Rf and shows that returns are positively and linearly related to β, as follows:

$$R\_{\rm it} - R\_{\rm ft} = \alpha\_{\rm i} + \beta\_{\rm i} \left( R\_{\rm Mt} - R\_{\rm ft} \right) + e\_{\rm it} \tag{3}$$

While the CAPM is still the most widely accepted description for security pricing, empirical studies found contradicting evidence (see [7–14]). Therefore, researchers concentrated on finding better models for the behaviour of stock returns and added more explanatory variables into CAPM.

In the early 1990s, one of the most influential researches was by Fama and French [15, 16]. Fama and French [15] reject the market beta associated with the CAPM and instead find that stock size and book-to-market (B/M) ratio better capture the cross-sectional variation in average stock returns. One year later the same researchers proposed that a 3F-FF asset pricing model augmenting the CAPM with size and book-to-market proxies for risk might be a superior description of average returns [16]. After these two influential studies, along with earlier evidence against the CAPM drove the finance community into investigating the reasons behind the anomalies found in [10–14].

Recent studies have found additional factors that seem to exhibit a strong relationship with average returns. Novy-Marx [17] finds that firms with high profitability generate significantly higher returns than unprofitable firms. Aharoni et al. [18] find that a statistically significant relation exists between an investment proxy and average returns. In the wake of these findings, Fama and French [19] expanded the 3F-FF model with profitability and investment. They reveal that the 5F-FF model performs better than the 3F-FF model in explaining average returns for their sample. The same model was tested using international data [20, 21], and they have found similar results.

This study adds to research conducted on CAPM, three-factor model and the new 5F-FF model by testing all these models on the Turkish stock market.
