4. Methodology

#### 4.1. Model definitions

In this study, I test three models, namely, CAPM, 3F-FF model and 5F-FF model for BIST. The model definitions are given below:

$$\mathbf{R}\_{\rm it} - \mathbf{R}\_{\rm ft} = \mathbf{a}\_{\rm i} + \left(\mathbf{R}\_{\rm Mt} - \mathbf{R}\_{\rm ft}\right) + \mathbf{c}\_{\rm it-CAPM} \tag{5}$$

$$\mathbf{R}\_{\rm if} - \mathbf{R}\_{\rm f} = a\_{\rm i} + \left(\mathbf{R}\_{\rm Mt} - \mathbf{R}\_{\rm f}\right) + \mathbf{s}\_{i} \mathbf{S} \mathbf{M} B\_{\rm t} + h\_{i} \mathbf{H} \mathbf{M} L\_{\rm t} + e\_{\rm i} (\mathbf{3F} \text{-FF model}) \tag{6}$$

$$\mathbf{R}\_{\overline{t}} - \mathbf{R}\_{\overline{\rho}} = \mathbf{a}\_{\overline{t}} + \left(\mathbf{R}\_{\mathbf{M}\overline{t}} - \mathbf{R}\_{\overline{\rho}}\right) + \mathbf{s}\_{\overline{t}} \mathbf{S} \mathbf{M} \mathbf{B}\_{\overline{t}} + h\_{\overline{t}} \mathbf{H} \mathbf{M} \mathbf{L}\_{\overline{t}} + \mathbf{r}\_{\overline{t}} \mathbf{R} \mathbf{M} \mathbf{W}\_{\overline{t}} + \mathbf{c}\_{\overline{\mathbf{r}}} \mathbf{C} \mathbf{M} \mathbf{A}\_{\overline{t}} + \mathbf{e}\_{\overline{\mathbf{r}}} (\mathbf{S} \mathbf{F} \mathbf{-} \mathbf{F} \mathbf{F} \mathbf{m} \mathbf{o} \mathbf{d} \mathbf{d}) \tag{7}$$

where Rit is the return of portfolio i at time t (portfolio creation procedure is given in the following topic); Rft is the risk-free rate approximated by 3-month TRY Libor rate at time t; Rit�Rft is the excess return of portfolio i at time t; RMt is the monthly market return approximated by natural log difference of BIST-100 Index at time t; SMBt, HMLt, RMWt and CMAt are defined in details in the following topic; ai is the intercept; β<sup>i</sup> is the coefficient of RMt�Rft for portfolio i; si is the coefficient of SMBt for portfolio i; hi is the coefficient of HMLt for portfolio i; ri is the coefficient of RMWt for portfolio i; and ci is the coefficient of RMWt for portfolio i.

#### 4.2. Construction of Fama-French factors

The next step in the analysis is to create sorted portfolios from which the Fama and French factor return series could be calculated. The factors used in the analysis were constructed in a manner similar to the process described in [19], relying solely on 2 � 3 sorts for creating the factors. Other sorting choices might have been used; however, [19] finds no differences in model performance when testing differing sorting methods.

My first data point is at the 31st of December 1999, and the investment variable is calculated as in Eq. (4); the first available year of accounting data used in the sorting process is at the end of fiscal year 2000. The portfolios were sorted at the end of May each year, and therefore the first available return observation in the final analysis is the return of June 2000, sorted according to accounting data at the end of fiscal year 1999. Thus, the time period for the actual analysis is June 2000 to May 2017 or 204 months of return data.

The sorting process is as follows:

(1) First of all, stocks are sorted according to their market cap to define small-sized and bigsized stocks. Fifty percent of the market cap was used as the breakpoint for size. (2) For all other factors, yearly sample 30th and 70th percentiles were used as breakpoints in the sorting method. (3) After the determination of the breakpoints, the stocks in the sample were independently distributed for every year into six size-B/M (where B/M is book-to-market ratio) portfolios, six size-OP (where OP is operational profits divided by book equity showing profitability) portfolios and six size-Inv (where Inv is yearly increase in total assets) portfolios created from the intersections of the yearly breakpoints. (4) All portfolios are value-weighted according to their market cap. (5) Monthly returns were calculated for each of the 18 portfolios. (6) After calculating the sorted portfolio returns, the actual factor returns were calculated.

There are two size groups and three book-to-market (B/M), three operating profitability (OP) and three investment (Inv) groups. The resulting groups are labelled with two letters. The first letter describes the size group, small (S) or big (B). The second letter describes the B/M group, high (H), neutral (N) or low (L); the OP group, robust (R), neutral (N) or weak (W); or the Inv group, conservative (C), neutral (N) or aggressive (A). Stocks in each component are valueweighted to calculate the component's monthly returns (Figure 1).


Figure 1. Sorted portfolio groups to construct Fama-French factors.

Eqs. (8)–(14) define calculations of the Fama-French factors:

My first data point is at the 31st of December 1999, and the investment variable is calculated as in Eq. (4); the first available year of accounting data used in the sorting process is at the end of fiscal year 2000. The portfolios were sorted at the end of May each year, and therefore the first available return observation in the final analysis is the return of June 2000, sorted according to accounting data at the end of fiscal year 1999. Thus, the time period for the actual analysis is

(1) First of all, stocks are sorted according to their market cap to define small-sized and bigsized stocks. Fifty percent of the market cap was used as the breakpoint for size. (2) For all other factors, yearly sample 30th and 70th percentiles were used as breakpoints in the sorting method. (3) After the determination of the breakpoints, the stocks in the sample were independently distributed for every year into six size-B/M (where B/M is book-to-market ratio) portfolios, six size-OP (where OP is operational profits divided by book equity showing profitability) portfolios and six size-Inv (where Inv is yearly increase in total assets) portfolios created from the intersections of the yearly breakpoints. (4) All portfolios are value-weighted according to their market cap. (5) Monthly returns were calculated for each of the 18 portfolios. (6) After calculating the sorted portfolio returns, the actual factor returns

There are two size groups and three book-to-market (B/M), three operating profitability (OP) and three investment (Inv) groups. The resulting groups are labelled with two letters. The first letter describes the size group, small (S) or big (B). The second letter describes the B/M group, high (H), neutral (N) or low (L); the OP group, robust (R), neutral (N) or weak (W); or the Inv group, conservative (C), neutral (N) or aggressive (A). Stocks in each component are value-

weighted to calculate the component's monthly returns (Figure 1).

Figure 1. Sorted portfolio groups to construct Fama-French factors.

June 2000 to May 2017 or 204 months of return data.

74 Financial Management from an Emerging Market Perspective

The sorting process is as follows:

were calculated.

$$\text{SMB}\_{\text{B/M}} = (\text{SH} + \text{SN} + \text{SL})/\text{3} - (\text{BH} + \text{BN} + \text{BL})/\text{3} \tag{8}$$

$$\text{SMB}\_{\text{OP}} = (\text{SR} + \text{SN} + \text{SW})/\Im - (\text{BR} + \text{BN} + \text{BW})/\Im \tag{9}$$

$$\text{GMB}\_{Inv} = (\text{SC} + \text{SN} + \text{SA})/\mathfrak{3} - (\text{BC} + \text{BN} + \text{BA})/\mathfrak{3} \tag{10}$$

$$\text{SMB} = \left( \text{SMB}\_{\text{B}/M} + \text{SMB}\_{\text{OP}} + \text{SMB}\_{\text{inv}} \right) / \text{3} \tag{11}$$

$$\text{HML} = (\text{SH} + \text{BH})/2 - (\text{SL} + \text{BL})/2 \tag{12}$$

$$RMW = (SR + BR)/2 - (SW + BW)/2\tag{13}$$

$$\text{CMA} = (\text{SC} + \text{BC})/2 - (\text{SA} + \text{BA})/2 \tag{14}$$

#### 4.3. Regression portfolios and other data used in the regression analysis

Regressions were run on three sets of 16 left-hand-side regression portfolios. Monthly returns for the portfolios were calculated in a manner similar to constructing the factor portfolios;


For example, S1BM1 shows average of the monthly excess returns of stocks included in the smallest size and lowest bookto-market portfolio.

Table 1. Construction of dependent variables: each notation of a dependent variable in this table shows the monthly excess return of the corresponding sorted portfolio.


Table 2. Average number of stocks in regression portfolios.

equal-weighted portfolios were created from independent 4 4 sorts with 25th, 50th and 75th yearly sample percentiles as breakpoints for both sorting variables. Table 1 shows the constructed dependent variables.

Panels A through C in Table 2 show the average number of stocks in each of the regression portfolios. It is evident from Panel A that high B/M companies are often smaller companies, while low B/M is tilted towards bigger companies. A similar phenomenon can be observed in Panel B, where low operating profitability is a feature of smaller companies and high operating profitability is more often found in stocks with higher market capitalisations.
