Finding Size Factor and Value Factor in Indonesia Stock Exchange

This study conducted by gathering data from Indonesia Stock Exchange (IDX) with 2 specifics model, Capital Market Pricing Model (CAPM) and Fama French 3 Factors Model (FF3FM). These model was estimated by classify 557 stocks in Jakarta Composite Index (JCI) to 6 classes: S/L class is class with small size and low Book to Equity (BE) to Market Equity (ME), S/M class is class with small size and medium in BE/ME, S/H class is class with small size and high in BE/ME, otherwise B/L class is class with big size and low in BE/ME, B/M class is class with big size and medium in BE/ME, B/H class is class with big size and high in BE/ME. With F test, t test and classic assumption test, best class and best model were B/L class and FF3FM. The result was confirmed size factor and value factor in Indonesia Stock Exchange (IDX). Size factor are confirmed in 3 classes (S/M, S/H and B/L), and value factor are confirmed in 4 classes (S/M, S/H, B/L and B/H). Therefore, classes with size and value factor are S/M, S/H and B/L. With BE/ME is 1/PBV and PBV indicating the stock price relative to its book value, so in Indonesia Stock Exchange the size factor and value factor confirmed in market with small market capitalization with low to medium in stock price relative to its book value and market with big market capitalization with high stock price relative to its book value.


Introduction
After risk and return concept was developed by Markowitz (1952), the era of modern portfolio had just been started.Later, Sharpe (1964), Lintner (1965) and Mossin (1966) developing first theory by Markowitz, known as CAPM model, years after perfected by Jensen (1967) that introduced Jensen's Alpha.Research from Al-Afeef (2017) proved that CAPM could be applied in US market to predict return from 2009-2016 where 20% of expected return change was caused by beta and other 80% from other factors.Zeeshan (2016) proved CAPM in Karachi Stock Exchange and Singh, Jain, and Yadav (2016) proved CAPM in Indian Stock Market.Moreover, Poornima and Swathiga (2017) told that with CAPM model, he found that automotive industry has positive return with lower risk compare to IT based industry that has negative return with higher risk.
In fact, based on Lam (2005), said that 73.5% CFO in United States using CAPM to modeling risk and return, but CAPM left some misunderstanding and misleading towards some special cases.Fama and French (2004) was found some weakness in CAPM such as : 1) CAPM failed to explain some high and low beta cases, 2) CAPM was simple model that just explain risk and return, 3) CAPM was left huge error, proved by high Jensen's alpha value in some special cases.Tanjung, Siregar, Sembel, & Nurmalina (2014) said that the Jakarta Composite Index (JCI) tend to move down after merger activity that affecting the JCI return and maybe lead to misfit in CAPM.
Later, Fama and French (1993) was developing the CAPM.This model has 3 factors compared to CAPM (just 1 factor), and known as Fama French 3 Factors Model (FF3FM).In this model, instead of portfolio return just explained by single market risk premium, the others 2 factors added to model, size factor and value factor.Size factor is stock market capitalization and value factor is defined by Book to Equity (BE) divided by Market to Equity (ME).This model has been proved by Al-zubi and Salameh (2009), Blanco (2012), Dah, et.al (2015), Kilsgård and Wittorf (2010) and Aldaarmi (2015).Their statements were lead to single conclusion, FF3FM is better than CAPM.However, Eraslan (2013) said that size factor doesn't exist in stocks that has big market capitalization but just exist in medium and low market capitalization.The value factor just appeared in stocks with high Book to Market Ratio.Rossi (2012) found that size factor and beta has strong power of explanation to the model, but no confirmation of value factor.This study has aim to prove the size factor and value factor in Indonesia Stock Exchange by comparing CAPM and FF3FM.This study will help the investor gather more information to value stocks, give company to strengthen their growth and give a brief explanation to regulator in order to bring a good investment regulations.
Jakarta Interbank Offering Rate (JIBOR) will be used as risk free according to Zaremba and Konieczka (2015).
JIBOR is bank's rate for lending or borrowing in Indonesia.In this study, 1 Month JIBOR used in monthly basis by interpolated yearly basis data gathered from Central Bank of Indonesia (BI).

Classic Assumption Test
The regression approach for this study is ordinary least square (OLS), and has to follow the individual t test and F test.The error model must be free from collinearity, has independence of error, normal assumption of error and no heteroskedasticity (Gujarati, 2004).

Choosing the Best Class and the Best Model
In this section, each class will be modeled by CAPM and FF3FM, comparing with R 2 , and the best class will be choose.After the best class has been choose, CAPM and FF3FM are compaing by paired t test, in accordance to show whether yfits of CAPM is statistically different from FF3FM.

Determined the Size Factor dan Value Factor
From the 6 different classes, the size factor and value factor will be determined by looking the significant of the coefficient of regression in 1%, 5% and 10% of error.
From Table 2 and Table 3

Best Class and Best Approaching Model
After t test, F test and classic assumption test conducted in 6 different classes with 2 deffirent models (CAPM and FF3FM), B/L class is the best class with R 2 in 91.17% and 93.07%, respectively.The result from these 2 models, show that FF3FM is better than CAPM.The CAPM just confirming 1 class (B/L), but FF3FM, confirming 3 classes (S/M, S/H and B/L).
Stock Selection and Finding 6 Different Classes Stocks are collected from IDX and must listed (not delisted) from June 2011 to June 2017 proved by the existing of Price to Book Value (PBV) and Market Capitalization, then 6 different classes formed by classify 557 different stocks to 2x3 matrix by 2 size categories (small and big) and 3 value categories (low, medium and high), These 2 model will be tested on 6 different class formed from 557 stocks in IDX, named by class S/L, S/M, S/H, B/L, B/M and B/H.S/L class is class with small size and low Book to Equity (BE) to Market Equity (ME), S/M class is class with small size and medium in BE/ME, S/H class is class with small size and high in BE/ME, otherwise B/L class is class with big size and low in BE/ME, B/M class is class with big size and medium in BE/ME, B/H class is class with big size and high in BE/ME.CAPM and FF3FM will be tested on 6 different classes to prove size factor and value factor with CAPM act like control model, with hypotheses are follows : H1: There is no size factor in 6 different class in IDX H2: There is no value factor in 6 different class in IDX2.2 Gathering of DataThe stocks data gathered from Bloomberg and Indonesia Stock Exchange from June 2011 to June 2017 (72 months).there after 6 different classes named by S/L class is class with small size and low Book to Equity (BE) to Market Equity (ME), S/M class is class with small size and medium in BE/ME, S/H class is class with small size and high in BE/ME, otherwise B/L class is class with big size and low in BE/ME, B/M class is class with big size and medium in BE/ME, B/H class is class with big size and high in BE/ME will be formed.The size factor formed by ascending size data by 50% percentile to small and big category, then value factor formed by ascending value data by 30% and 70% percentile to low, medium and high category

Table 1 .
Number of Stocks in Each Class to data gathered from IDX, 290 stocks were selected from 557 stocks and 6 different classes, S/L class is class with small size and low Book to Equity (BE) to Market Equity (ME), S/M class is class with small size and medium in BE/ME, S/H class is class with small size and high in BE/ME, otherwise B/L class is class with big size and low in BE/ME, B/M class is class with big size and medium in BE/ME, B/H class is class with big size and high in BE/ME were formed.

Table 3
, FF3FM bring better R 2 value especially in S/L, S/M, S/H and B/H.In S/L class R 2 rise from 12.11% with CAPM to 71.83% with FF3FM, then in S/M class R 2 rise from 42.44% with CAPM to 77.87% with FF3FM, then in S/H class R 2 rise from 49.16% with CAPM to 92.05% with FF3FM and then in B/H class R 2 rise from 50.07% with CAPM to 77.49% with FF3FM.From this finding, show that with R 2 calculation, FF3FM alone can bring better the R 2 value than CAPM.So, in Indonesia Stock Exchange, the return of individual stock are not only explain by market risk premium (RMF) only, but also with size factor and value factor.

Table 4
From B/L class, the best class among 6 classes, CAPM and FF3FM must be tested to show, are there any significant difference from yfits modeled by CAPM dan FF3FM with paired t-test.Tablebelowshowed that yfits modeled by CAPM is significantly different in 5% of error from FF3FM, so the best model is FF3FM.