CHAPTER I INTRODUCTION 1.1 Background
Theories of pricing model have been developed for years by many academicians. Each of those pricing model has different variables, considerations, and factors to be put into the the mode models ls deve develo lope ped. d. Thos Thosee prici pricing ng mode models ls have have been been used used by acad academi emici cian anss and and practitioners in explaining, assesing, and defining the expected returns that assets can have in relevant with the risk that investors should consider when they want to conduct investments activities. The first model to be developed to explain returns of assets (especially stocks) is Capital Asset Pricing Model (known as CAPM), developed by Sharpe (1964), Lintner (1965), and Mossin (1966). This model is widely use because of its simplicity. After Capital Asset Pricing Model was being developed to explain asset return (usually stocks), many asset pricing models come up with different approaches to advance the explanation of expected assets return in relevant with different risk proxies that investors should consider when making a decissionabout investment activities. From those many assets pricing model, some of them are, Inter-temporal Inter-temporal Capital Asset Pricing Pricing Model, Model, developed developed by Merton (1973), (1973), The Arbitr Arbitrage age Pricin Pricing g Model Model develo developed ped by Chen Chen and Ross Ross (1986) (1986),, and Three Three factor factor model model developed by Fama and French (1993). ( 1993). Different Different variables variables are being used by those those pricing pricing models models to explain assets (stocks) (stocks) return. return. Many researches researches and journals, journals, compared compared two of them which are, the Capital Capital Asset Pricing Model and Three Factor Model. The main reason is that, those two pricing models are generally applicable in different stock market circumstances across countries in the world, and in any economic conditions and characteristics that attached to a country being examined in the research.
The well-known prediction of CAPM is that, the expected excess return on an asset equals the beta of the asset times the expected excess return on the market portfolio, where the beta is the covariance of the assets’ return with the return on the market portfolio divided by the variance of the market return. John (2007) explained the simplicity of CAPM in explaining expected return on an asset. He explained that the expected rate of return on an asset is a function of the two components of required rate of return-the risk free rate and the risk premium. Thus,
K i = Risk-free rate + Risk Premium = RF + β [E(RM ) – RF] Equation 1.1
The use of only one risk factor in explaining expected return, makes this pricing model also being known as single single factor model. Dhamodaran Dhamodaran (2001) also explained CAPM with an analogy of an asset. He explained that in CAPM world, where all investors hold market portfolio, the risk to an investors’ individual asset will be the risk that this asset adds to the market portfolio. Intuitively, if an asset move independently in relevant with market portfolio, it will not add mcuh risk to the market portfolio. In other words, most of the risk in this asset is firm-specific and can be diversified. In contrast, if an asset tends to move up when the market portfolio moves up, and move down when market portfolio moves down, it will add risk to the market portfolio. It implies that this asset has more market risk and lessfirm specific risk. Statistically, this added risk is measured by the covariance of the asset with market portfolio. Under Under CAPM, CAPM, invest investors ors adjust adjust their their risk risk prefere preference ncess by using using their their alloca allocatio tion n decission, whther they want to invest more in riskless assets or more in market portfolio.
The well-known prediction of CAPM is that, the expected excess return on an asset equals the beta of the asset times the expected excess return on the market portfolio, where the beta is the covariance of the assets’ return with the return on the market portfolio divided by the variance of the market return. John (2007) explained the simplicity of CAPM in explaining expected return on an asset. He explained that the expected rate of return on an asset is a function of the two components of required rate of return-the risk free rate and the risk premium. Thus,
K i = Risk-free rate + Risk Premium = RF + β [E(RM ) – RF] Equation 1.1
The use of only one risk factor in explaining expected return, makes this pricing model also being known as single single factor model. Dhamodaran Dhamodaran (2001) also explained CAPM with an analogy of an asset. He explained that in CAPM world, where all investors hold market portfolio, the risk to an investors’ individual asset will be the risk that this asset adds to the market portfolio. Intuitively, if an asset move independently in relevant with market portfolio, it will not add mcuh risk to the market portfolio. In other words, most of the risk in this asset is firm-specific and can be diversified. In contrast, if an asset tends to move up when the market portfolio moves up, and move down when market portfolio moves down, it will add risk to the market portfolio. It implies that this asset has more market risk and lessfirm specific risk. Statistically, this added risk is measured by the covariance of the asset with market portfolio. Under Under CAPM, CAPM, invest investors ors adjust adjust their their risk risk prefere preference ncess by using using their their alloca allocatio tion n decission, whther they want to invest more in riskless assets or more in market portfolio.
Investors who are risk averse will choose to put more or even all their wealth to riskless assets. Conversely, investors who are risk taker will invest more, or even all of their wealth in market portfolio. Investors who invest their wealth in market portfolio and desired to bear more risk, would do so by borrowing at the riskless rate and investing in the market portfolio as anyone else. However some researches argue that the market beta itself is not sufficient to explain expected stock return. As quoted by Fama and French (1992); Basu (1977), shows that when common stocks are sorted on earning price ratio (E/P), future return of high E/P stock are higher than those predicted by CAPM. Moreover, Banz (1981), documented size effect , which revealed the statistical fact that stocks with low market value (market capitalization), earned higher return than what is predicted by CAPM; stocks with low market value have higher beta and higher average returns than those stocks with higher market value, but the difference is higher than those predicted by CAPM. Fama and French (1992), study the joint roles of market β, size, E/P, leverage, and book to market equity in the cross section of average stock return. return. They find that used alone, or in combinatio combination n with other variables, variables, β (the slope in the regression of a stock’s return on a market return) has little information about average return. Used alone, size, E/P, leverage, and book-to-market equity seem to absorb the apparent roles of leverag leveragee and E/P in averag averagee return return.. Briefly Briefly,, their their researc research h resulte resulted d in the statis statistic tical al conclusion that, two empirically determined variables, size and book-to-market equity, do a good job in explaining the average returns. Thus, Thus, concerning other factors that might be able to explain explain stocks stocks return, Fama and French (1993) developed a model called three factors model. This model is not only using the return of market portfolio to explain expected return, but also the other two factors, which are size and book-to market ratio. Mathematically, the model can be written as follow:
E(R ) ) – R f ) + si E(SMB) + hi E(HML) +e i - R f =c + β i (E(R M
Fama and French three factors model captures the performance of stock portfolios grouped on size and the book-to-market ratio. Fama and French (1993,1996), have interpreted that their three factors model as evidence of risk premium or "distress premium” . Small Stocks with high book-to-market ratios are firms that have performed poorly and are vulnerable to financial distress, and investors recognized a risk premium for this reason. Using the monthly stocks return data in NYSE, AMEX, and NASDAQ, from 1963 to 1991, Fama and French (1993) started their analysis by sorting stocks based on their size and their book-to-market ratio. They break the stocks based on size, into two groups, those stocks with small capitalization, and those stocks with big capitalization. Individually, they also break the stocks to be observed based on their book-to-market ratio, based on the breakpoints into three groups, those with low book-to-market ratio (30% of stocks), those with medium book-to-market ratio (40%), and those with high book-to-market ratio (30%). Their decision to break stocks into three groups on book-to-market ratio and only two groups on book-tomarket ratio, is based on their previous findings in Fama and French (1992), revealed that book-to-market equity has stronger role in average stock r eturns than size. Then six portfolios are formed based on the interception of the two size groups and the three book-to-market group, they are S/L, S/M, S/H, B/L, B/M, B/H (i.e S/L is portfolio consist of those stocks with small capitalization and low book-to-market ratio). The returns of those six portfolios are then being used as dependent variables. They use the excess market return (E(RM ) – R f ), which is the difference between the return on market portfolio, with risk free rate, as proxy for the market factor in stock return. To capture the size effect , they use the return of portfolio named under SMB (Small Minus Big). SMB meant to mimic risk factor in returns related to size. It is the difference (each month) between the simple averages of the return of the three small-stock portfolios (S/L, S/M, and S/H) and the simple average returns of three big-stock portfolios (B/L, B/M,
B/H). Thus, SMB is the difference between the returns on small and big stock portfolios with about the same weighted average book-to-market equity. To mimic capture the risk factor in returns related to book-to-market ratio, they use the return of portfolio named under HML (High Minus Low). It is the difference, each month, between the simple average of the returns on the two high book-to-market portfolios (S/H and B/H) with the simple average returns on the two low book-to-market portfolios (S/L and B/L). The two components are return on high and low book to market portfolio with about the same weighted average size. But, there also many research doubt about the strong relationship between book-tomarket ratio, and size toward return. Kothari, Shanken, and Sloan (1995), as quoted by Fama and French (1996), found that the relationship between book-to-market ratios toward return is relatively weak and not consistent with the findings of Fama and French (1992). The relationship between book-to-market ratio and return were partly caused by a certain bias on data. Bias on the data happened when there are data that cannot be obtain because the firms did not publish its financial reports, or the data from previous period are being used to fill the missing data that happen in the current period. There are also many explanations about size and book-to-market anomalies. Lakonishok, Shleifer, and Vishny (1994), Haugen (1995), and McKinlay (1995) , as quoted by Fama and French (1996), argue that the premium of financial distress is irrational. Three arguments justify it. First, it can express an over-reaction of the investors. Second argument is relative to the empirical observation of low stock return of firms with distress financial situation, but not necessarily during period of low rate of growth of GNP or of low returns of all stocks in the market. Lastly, diversified portfolios of stocks with, as well high as low, book-to-market ratio; have the same variance of return
From the discussion above it can be implied that the research about stock return and pricing model is worth to be reviewed, mainly in emerging market stock exchange. The new findings of Fama and French becomes an identification of risk factors that explain the statement and phenomenon that return is the trade-off between risk and return. This research is an empirical research about models that theoretically and empirically are commonly used to explain stock return. The consideration of using those two pricing model in the research is that, although both pricing model has different approach in assessing expected return, they actually have similarities. Both of the models are using market premiums as one of the variable. The use of market premium will be able to capture risk regarding market factor. This market factor will be able to capture the non-diversifiable risk, or risk that cannot be diversified by using portfolio. Hence, Indonesian Stock Market risk premium can be traced down and being put into consideration in the analysis to recognize the non-diversifiable risk which exist in the market . As Indonesian Stock exchange is considered as young Stock market (established in 1985). The use of both pricing model will be beneficial to reveals, whether the factors that are proposed by these two pricing models are applicable, robust, and reliable enough to be used as consideration and justification regarding the expected return that investors willing to get by investing on equity market. Thus, to serve the aim, this research will hopefully discuss deeply and comprehensively about “The factors Affecting Portfolio Return in Indonesia Stock Exchange : Fama three Factors model vs Capital Asset Pricing Model” 1.2 PROBLEM STATEMENT
Based on issues discussed in the background, the problem statements of this research are stated as follows:
1. Does market factor positively affecting stocks portfolio consist of stocks listed in Indonesian stock market. 2. Does the difference between the return of stocks portfolio consist of small-sized firm and big sized firm (SMB), affecting positively toward the return of portfolio consist of small size firms. 3. Does the difference between those firms included in high book to market ratio and those firms included in low book to market ratio, affecting the return of equity portfolio positively. 4. Which one of those pricing models (CAPM or Fama and French Three factor model) can explain stock returns better, especially under Indonesian stock market return.
1.3 LIMITATION OF THE RESEARCH
This research is being conducted by observing the monthly changes of individual stock price that are listed in Indonesian stock exchange, the changes of Indonesian Composite Index (IHSG). Stocks that are included in this research are only the stocks of non-financial firms, from 2007-2010 1. This research will compare the robustness of fama and French three factor models with CAPM, in terms of its slopes and coefficients, and to test the significance of market factor, SMB and HML factor. 2. Data that are being used are the data of non-financial firms that are listed in Indonesian stocks exchange from 2007-2010, with no missing observation, and the stock should not have minus book to market ratio during the time period of the research. 3. Both CAPM and Fama and French Three factors are model designed to calculate expected return. This model cannot be tested because expectation is an
unobservable value. Those that can be observed and then can be tested is historical value (ex post). Hence for the two pricing models are able to be tested, all data that are being used are historical data, and the empirical model will change the expected notion (e.g E(r)) to historical return ( R ).
1.4 PURPOSE OF THE RESEARCH
This research is aim to: 1. Which one of those two pricing theories describes the factors affecting equity price more effectively? 2. Test whether the market factor affecting stocks return at Indonesian stock market 3. Test whether the difference between the return of small sized firms and big sized firms (SMB) positively affecting the return of portfolio consisted of small sized firms. 4. Test whether the difference between the return high book to market ratio firms and the return of low book to market ratio firms (HML), positively affecting the return of portfolio consist of stocks that are listed in Indonesian stocks exchange.
CHAPTER II THEORIES AND HYPOTHESIS DEVELOPMENT 2.1 The concept of risk and return
Every investor invests their money in a particular asset with the expectation that their wealth will grow for some defined future period. The gain that the investors have by investing their wealth in some particular assets for some defined future period is called
return. John (2007) differentiates between two kinds of return, which are expected return and
realized return. Expected return is defined as the anticipated return expected by investors over some future holding period, while Realized return is defined as actual return on an investment for some previous period of time. There are two components of return as explained by Jones (2007). 1. Capital gain (loss): it measures the appreciation or depreciation in the price of the asset, or simply addressed as the price change. In the case of long position, it is the difference between the purchase price and the price at which the asset can be, or, is sold; for the case of short position, it is the difference between the sale price and the subsequent price at which the short position is closed out. In either case, gain or loss can occur. 2. Yield : it measures the periodic cash-flows (or income) on the investment either in terms of interest or dividend.
Risk, defined in statistical terms as the variance in actual returns around expected returns (Dhamodaran,2001). The greater is the variance, the more risky is the asset. Commonly, considering portfolio construction, investors decomposed risk related into two types of risks: diversifiable and non-diversifiable risk .
Diversifiable risk as defined by Brigham and Houston (2007), is that part of a security’s risk associated with random events that can be eliminated by proper diversification, usually called firm-specific risk (risk that attach to a specific firm); while non-diversifiable
risk defined as that part of a security’s risk that cannot be eliminated by diversification, usually addressed as market risk (e.g interest rate, war, inflation, ect). The rule of thumb that usually being used by investors is that, they want to get compensated by bearing more risk in their investment activities. Thus, the higher the risk, the higher the expected return
2.2 Capital Asset Pricing Model
Capital Asset Pricing Model (CAPM), was developed by William Sharpe (1964), John Lintner (1965) and Jan Mossin (1966), independently. Brigham and Ehrhardt (2005) as quoted by Nophbanon et al (2009) , stated that, this pricing theory was developed based on these assumptions •
All investors focus on a single holding period, and seek to maximize the expected utility of their terminal wealth.
•
All investors can borrow or lend an unlimited amount at a given risk-free rate of interest.
•
Investors have homogenous expectation
•
All assets are perfectly divisible and perfectly liquid
•
There are no transaction cost
•
There are no taxes
•
All investors are price takers
•
The quantities of all assets are given and fixed
By holding those assumptions above, it allows investors to keep diversifying without additional cost. Dhamodaran (2001) argued that, at the limit, their portfolios will not only include every traded assets in the market but also will have identical weights on risky assets (based on their market value). With that explanation above then it can be implied that at the limit, all investors in the world of CAPM will formed a market portfolio , that is, a portfolio that consist of all assets that are available in the market place. Considering the market portfolio, the concept of CAPM can easily be explained using Security Market Line (SML). E(Ri)
E(RM)
M
Security Market Line
RBR
Beta 0
1.0 Fig 2.1
Beta determined the value of additional expected return for individual security with the argument that portfolio that is perfectly diversified the non-systematic risk (diversifiable risk) tend to disappear, and left Beta measuring systematic risk (non-diversifiable risk) as the only relevant risk to be considered in the model. This argument is based on assumption that
for homogenous expectation, all investors will formed a market portfolio that is perfectly diversified, thus the only relevant risk for every securities is measure by Beta In figure 2.1, point M, representing a market portfolio with Beta equals 1.0 and expected return as big as E(R M). For riskless asset with 0 Beta, the expected return is R BR which is the interception between the Security Market Line and E(R i). Assuming that Security Market Line is linier, thus the equation of this linier line can be expressed as the intercept with the value of R BR and the slope will have the value of [E(R M) - R BR ] / βM. Because βM = 1, thus the slope of Security Market Line will have the value of [E(R M) - R BR ]. Thus the equation for i th securities can be written as:
E(R i) = R BR + βi . [E(R M) - R BR ]
Equation 2.1
Equation 2.1 is the equation that being recognized as Capital Asset Pricing Model. With that equation, the expected return of an equation can be determined. Jogiyanto (2007) explained that if Beta for market portfolio is equal one, thus for those securities with Beta less than one will have less systematic risk, and will be expected to have return less than the market return. Conversely, those securities with Beta more than 1 will have bigger systematic risk, and will be expected to generate return more than the market portfolio does. The model in equation 2.1, is the model to calculate expected return and cannot be tested for the sake of this research, because ex-ante return is not observable and obviously the data is not available. Thus this research will use ex-post return, and change the CAPM equation to:
R it = R BRt + βi . [R Mt - R BRt]
Equation 2.2
Equation 2.2 is the ex-post model of CAPM, which recognize the use of historical data. (Jogiyanto, 2007).
2.3 The relationship between stock return and firms’ characteristics 2.3.1 Firm’s size
The relationship between stock return and size is still debatable. There are several researches that tried to examine the relationship between firm’s sizes (represented by market capitalizations) with stock return. Banz (1981) and Reinganum (1981) were among the first to examine the relationship between size and stock return. They found that firm size or capitalization, measured as the market value of equity, possess significant influence on stock returns, smaller size firm, earn higher return than the bigger size firm. Banz (1981), concluded in his research considering size effect, that on average, small NYSE firms had significantly larger risk adjusted returns, than large NYSE firms over a forty year period (his study used time period from 1931-1975). However, they stated that this size effect is not linear in the market proportion, but is most affected the smallest firms in the sample. He also admitted that there is no theoretical foundation for size effect. The research conducted did not specified the fact whether the factor is the size itself or it’s just the proxy for one or more true but unknown factors correlated with size. Reinganum (1980) as noted by Banz (1981), has eliminated one possible candidate for the unknown factor, which is P/E ratio. He reported that P/E effect disappears for both NYSE and AMEX stocks when he controls for size, but there is a significant size-effect when he controls for P/E ratio, thus it
proves that P/E effect is the proxy of size effect and not vice versa. Stattman (1980) as noted by Banz (1981), also eliminated one of the possible candidate which is book to market ratio. Banz (1981) refers to Klaim and Bawa (1977) as one of the most possible explanation that can justify the relationship between size and stock return. They find that if insufficient information is available for a subset of securities, investors will not hold these securities because of estimation risk, i.e because of the uncertainty about the true parameters that justifies return distribution. If investors differ in the amount of information available, they will limit their diversification to different subsets of all securities in the market. It is likely the amount of information generated, is related to the size of the firm. Therefore many investors would not desire to hold the common stock of very small firms. Thus, lack information about small firms leads to limited diversification and therefore for higher returns for “undesirable” stocks of small firms. Since this informal logic resulted in the same logic as with the empirical test, he argued that it was just a coincidences or conjecture. In the continuance of those findings above, Fama and French (1992) observed that firm size capture much of the cross-sectional empirical relation with average stock return. Fama and French (1993) showed that size proxy for sensitivity to risk factor that capture strong common variation in stock return and help explain the cross-section of stock-return. However size remain arbitrary indicator variable related to risk factor in explaining average return due to unexplained economic reason. Thus, Fama and French (1995) conducted a research to clarify this issue, and they found that size factor in fundamentals, (earning and sales), is similar to those in stock returns, which lead to the strong presumption that the common factor in fundamentals, drive the risk factors in returns. Thus the evidence show that size is related to profitability.
2.3.2 Firms’ Book-to-Market ratio
Stattman (1980) and Rossenberg, Reid and Leinstein (1985) as noted by Fama and French (1992) find that average returns on U.S stocks are positively correlated with book-tomarket ratio. Chan, Hamao and Lakonishok (1991), as quoted by Fama and French (1992) also find that book-to market ratio has a strong role in explaining the cross-section of average returns on Japanese Stocks.
Fama and French (1992) noted that it is possible that the risk
captured by book-to-market ratio is the relative distress factor of Chen and Chan (1991). They stated that the earnings prospects of firms are associated with a risk factor in return. Firms that the market judges to have poor prospects, signaled by low stock price and high book-to-market ratio, have higher expected return (they are penalized with higher cost of capital) than firms with strong prospects. In Fama and French (1992) they documented that book-to-market ratio is related to economic fundamentals. Firms that have high B/M ratio (a low stock price relative to book value) tend to have low earnings on assets and the low earnings persist at least five years before and five years after the B/M ratio is calculated. Conversely those firms with high B/M ratio (a high stock price relative to book value) are associated with persistently high earnings. Auret and Sinclair (2006), tried to explain the logic behind the recognition of book-tomarket ratio as risk factor. The book value of the firm is the difference between total assets (resources expected to results in inflows economic benefits) and liabilities (obligation expected to result in outflows of economic benefit), or a measure of net expected inflows of economic benefits, or earnings. However, there is inherent uncertainty surroundings those earnings. Investment in two firms, each with similar book value to the other, are likely to be valued differently, if there is more uncertainty surrounding the return of one versus another. The investment with lesser uncertainty (less risk) is likely to be preferred, to the investment with grater uncertainty (higher risk), since the marginal utility of risk is assumed to be always
negative, as mentioned by Markowitz (1956). As a result, the market value of the less risky investment is likely to be higher than the market value of the more risky investment. Since book-to-market ratio is the ratio of the book value and the market value of the firm, the less risky investment is therefore likely to have lower book-to-market ratio than a more risky investment. Given that higher returns are necessary to induce investors to purchase a riskier investment, a positive relationship between book-to-market ratio and returns emerged.
2.4 Fama and French three factors model
Several of the return anomalies in CAPM were being affiliated by three factor model (Fama and French, 1993). This model stated that excess return of a portfolio [ E(R ) i - R f ], can be explained by return sensitivity toward three factors, they are: excess return of market portfolio [ E(RM ) – R f ], the difference between the average return of portfolio consist of stock with small capitalization, with those who have big capitalization (SMB), and the difference between the average returns of portfolio consist of stocks with high book-to-market ratio, with those stocks with low book-to-market ratio (HML). Those variables can be expressed as following equation.
E(R ) ) – R f ) + si E(SMB) + hi E(HML) +e i - R f =c + β i (E(R M Equation 2.3
Where E(RM ), E(SMB), and E(HML) are expected premiums; β i , si , and hi are factors sensitivity, which represent the slope of time-series regression. As stated previously in the background, the details of their research are as follows. Using the monthly stocks return data in NYSE, AMEX, and NASDAQ, from 1963 to 1991, Fama and French (1993) started their analysis by sorting stocks based on their size and
their book-to-market ratio. They break the stocks based on size, into two groups, those stocks with small capitalization, and those stocks with big capitalization. Individually, they also break the stocks to be observed based on their book-to-market ratio, based on the breakpoints into three groups, those with low book-to-market ratio (30% of stocks), those with medium book-to-market ratio (40%), and those with high book-to-market ratio (30%). Their decision to break stocks into three groups on book-to-market ratio and only two groups on book-tomarket ratio, is based on their previous findings in Fama and French (1992), revealed that book-to-market equity has stronger role in average stock r eturns than size. Then six portfolios are formed based on the interception of the two size groups and the three book-to-market group, they are S/L, S/M, S/H, B/L, B/M, B/H (i.e S/L is portfolio consist of those stocks with small capitalization and low book-to-market ratio). The returns of those six portfolios are then being used as dependent variables. They use the excess market return (E(RM ) – R f ), which is the difference between the return on market portfolio, with risk free rate, as proxy for the market factor in stock return. To capture the size effect , they use the return of portfolio named under SMB (Small Minus Big). SMB meant to mimic risk factor in returns related to size. It is the difference (each month) between the simple averages of the return of the three small-stock portfolios (S/L, S/M, and S/H) and the simple average returns of three big-stock portfolios (B/L, B/M, B/H). Thus, SMB is the difference between the returns on small and big stock portfolios with about the same weighted average book-to-market equity. To mimic capture the risk factor in returns related to book-to-market ratio, they use the return of portfolio named under HML (High Minus Low). It is the difference, each month, between the simple average of the returns on the two high book-to-market portfolios (S/H and B/H) with the simple average returns on the two low book-to-market portfolios (S/L and
B/L). The two components are return on high and low book to market portfolio with about the same weighted average size. The same with the case of CAPM, the equation above was meant to predict the expected return, by which will be unable to be tested statistically, because the expected return is unobservable. Thus, to be able to be statistically tested, the equation above will be change into:
Ri - R f =c + β i (RM – R f )t + si E(SMB ) t + h i E(HML)t +e Equation 2.4
However, their findings in their earlier research still could not explain the economic fundamentals’ explanation of size and book-to-market ratio in relation to stock return. Thus, Fama and French (1995), conducted a study, to find out whether the behavior of stock prices, in relation to size and book-to-market ratio is consistent with the behavior of earnings. They confirmed that Book-to-market ratio is related to persistent properties of earnings. High book-to-market ratio (a low stock price relative to book value) signals sustained low earnings on book equity. In brief, firms with high book-to-market ratio is firms that are relatively distress, while those firms with low book-to-market ratio (a high stock price relative to book value) is typical of firms with high average return on capital (growth stocks). They also confirmed that size is also related with profitability. Controlling for Book-to-market ratio, small stocks tend to have lower earnings on book equity than do big stocks. The results further shows that the common factors in returns mirror the common factors in earnings, and it suggest that the market, size and book-to-market factors in earnings are the source of the corresponding factors in returns. The tracks of the market and size factors in earnings are clear in returns.
2.5 Previous studies
Fama and French (1992) conducted a research using stocks that are listed in New York Stock Exchange (NYSE), American Stock Exchange (AMEX), and NASDAQ stock market. They found that there is no cross-sectional relationship between beta and return when other variables being considered, which are, size and book-to-market ratio. Fama and French concluded that book-to-market ratio have a positive relationship with return, which means, the higher the book-to-market ratio, the higher the return of a firm’s stock. In the continuance of their research, Fama and French (1996), conducted a research using stocks listed in NYSE for the period 1928-1993. In the research, they stated that their three factor model, gives a better description compare to single-factor CAPM, and accommodate most of average return anomalies that are abandoned by CAPM. In this three factor model, it is stated that the expected return of a portfolio, can be explained using three factors. The first factor, is the excess return of market portfolio, the second factor is the difference between the return of portfolio consist of stocks with small capitalization with those consist of big capitalization (SMB), and the third factor is the difference between the return of portfolio consist of stocks with low book-to-market ratio with those consist of high book-to-market ratio. In the case of emerging market, Nophbannun et al (2009) conducted a study to compare Fama and French three factor model with CAPM. Their samples are stocks that are listed in Thailand ctock exchange during 2002-2007. Their study found that Fama and French three factors model can describe the expected stock return in Thailand Stock market better than the CAPM does.
2.6 Hypotheses development
Both Fama and French Three factors model and CAPM use the excess return on market portfolio as explanatory variable to explain expected return of stocks. Both theories proved that there is a positive relationship between the excess return on market portfolio, with the average return of portfolio they have constructed. Bodie et al (2003) explained the logic behind the positive relationship between the excess return of market portfolio (the equilibrium risk premium of the market portfolio), with average return on stocks (stocks portfolio). They explained that when investors purchase stocks, their demand drives up prices, thereby lowering expected rates of return and risk premium. But if risk premium (excess return of market portfolio) fall, then relatively more risk-averse investors will pull their funds out of the risky market portfolio, placing them instead in risk-free assets. In equilibrium, the risk premium on the market portfolio must be just high enough to induce investors to hold the available supply of stocks. If the risk premium is too high compared to the degree of risk aversion, there will be excess demand for securities and price will rise; if it is too low, investors will not hold enough stock to absorb the supply and price will fall. Concisely, Brigham and Houston (2007) stated that, considering risk premium is the premium demanded by investors for investing in the market portfolio, which includes all risky assets in the market, instead of investing in risk-free assets, then the positive relationship between risk premium and expected return that the investors willing to get is positive. Thus, based on the logic described previously, then the first hypothesis to be developed is:
Ha1: There is a positive relationship between market risk premium and average return on portfolio
Fama and French (1992, 1993, 1995,1996) use the return of SMB (Small Minus Big) portfolio to mimics the risk factors in returns related to size. SMB is the difference between the average return of portfolio consist of stocks with small capitalization, and portfolio consist of stocks with big capitalization. Their results show that the slope of SMB is positive for those portfolios consist of small capitalization. In their research, Fama and French (1993), shows that SMB as a factor used to mimic risk related to size, had significant effect on stocks grouped on smaller size portfolio. Their findings show that SMB, the mimicking return for the size factor, clearly captures sharedvariation in stocks return that is missed by market and by HML. . For every book-to-market quintiles, the slopes of SMB decrease substantially from smaller size quintile to bigger size quintiles (1.46 to –0.17 for the lowest book-to-market ratio quintile). The empirical evidence provided, shows that SMB only had positive effect toward firms with small size. However, they admitted that the return test still could not tell the full economic story. To explain the economic fundamentals of the relationship between size and stock return, Fama and French (1995), study the behavior of stock price, in relation to size and book to market equity to find out whether it consistent with the behavior of earnings. Using the percentage change in, EI/BE (Equity income over Book value of equity), EBI (Earning Before interest) and S (Sales) as dependent variables, they found that the common factors in fundamentals (earning and sales), drive the risk factor in returns, in this case, size. .
As mentioned previously, in relation with the discussion of size effect, Banz (1981)
refers to Klaim and Bawa (1977) as one of the most possible explanation that can justify the relationship between size and stock return. They find that if insufficient information is
available for a subset of securities, investors will not hold these securities because of estimation risk, i.e because of the uncertainty about the true parameters that justifies return distribution. If investors differ in the amount of information available, they will limit their diversification to different subsets of all securities in the market. It is likely the amount of information generated, is related to the size of the firm. Therefore many investors would not desire to hold the common stock of very small firms. Thus, lack information about small firms leads to limited diversification and therefore for higher returns for “undesirable” stocks of small firms. Since this informal logic resulted in the same logic as with the empirical test, he argued that it was just a coincidences or conjecture. Dhamodaran (2001), also described about small firm effect. He stated that there are at least two explanations regarding size effect, in this case, small firm effect, which are: First, the transaction cost of investing in small stocks are significantly higher than the transaction cost for investing in larger stocks, and the premiums are estimated prior to these cost. Second, the capital asset pricing model may not be the right model for risk, and betas underestimate the true risk of small stocks. Thus, the small firm premium is really a measure of the failure of beta to capture risk. Moreover, he also mentioned that the additional risk associated with small stocks may come from several sources, which are: First, the estimation risk associated with estimates of beta for small firms is much greater than the estimation risk associated with beta estimates for larger firms. The small firm premium may be a reward for this additional estimation risk. Second, in line with Klaim and Bawa (1977), he argued that there may be additional risk in investing in small stocks because far less information is available on these stocks. Thus, based on the empirical evidence mentioned above, the smaller the market capitalization of the stock, the higher the risk related with size (SMB), thus investors will require higher return to compensate the risk. Then the hypothesis to be proved is:
Ha2: SMB has a positive effect toward return on portfolio consist of small stocks
Fama and French (1992, 1993, 1995, 1996) also used HML (High Minus Low) to mimic the risks factor in returns related to book market ratio. They found that the slope of HML increased in every classification of book-to-market ratio. The logic behind the positive relationship between HML and stock return was explained by Fama and French (1993, 1994,1995). They stated that low book-to-market ratio is typical of firms that persistently have strong earnings, while high book-to-market ratio is typical of firms that persistently have low earnings. In Fama and French (1993), they showed that the slopes of HML increase substantially for the lowest book-to-market equity quintiles to the highest (-0.29 to 0.62 for the smallest size quintile). The empirical evidence shows that there is a positive relationship between portfolio return formed on size and book-to-market ratio, with HML as a factor used to mimic the risk associated with book-to-market ratio. Auret and Sinclair (2006), tried to explain the logic behind the recognition of bookto-market ratio as risk factor. The book value of the firm is the difference between total assets (resources expected to results in inflows economic benefits) and liabilities (obligation expected to result in outflows of economic benefit), or a measure of net expected inflows of economic benefits, or earnings. However, there is an inherent uncertainty surroundings those earnings. Investment in two firms, each with similar book value to the other, are likely to be valued differently, if there is more uncertainty surrounding the return of one versus another. The investment with lesser uncertainty (less risk) is likely to be preferred, to the investment with grater uncertainty (higher risk), since the marginal utility of risk is assumed to be always negative, as mentioned by Markowitz (1956). As a result, the market value of the less risky
investment is likely to be higher than the market value of the more risky investment. Since book-to-market ratio is the ratio of the book value and the market value of the firm, the less risky investment is therefore likely to have lower book-to-market ratio than a more risky investment. Given that higher returns are necessary to induce investors to purchase a riskier investment, a positive relationship between book-to-market ratio and returns emerged. Moreover, Fama and French (1992) noted that it is possible that the risk captured by book-to-market ratio is the relative distress factor of Chen and Chan (1991). They stated that the earnings prospects of firms are associated with a risk factor in return. Firms that the market judges to have poor prospects, signaled by low stock price and high book-to-market ratio, have higher expected return (they are penalized with higher cost of capital) than firms with strong prospects. Thus, by the expected relationship is that, the higher the book-to-market ratio, the higher the risk associated with book-to-market ratio (HML), and the higher the return on portfolio expected from investors. Then, the hypothesis to be proved is:
Ha3 : HML has a positive relationship with average return on portfolio
Many researches compare the effectiveness and the robustness of Fama and French three factor model and CAPM. Nophbannun et al (2009) conducted a study to compare Fama and French three factor model with CAPM. Their samples are stocks that are listed in Thailand stock exchange during 2002-2007. By taking into account the adjusted R 2 obtained by conducting time series regression on portfolio return from 2002-2007, their study found that Fama and French three factors model can describe the expected stock return in Thailand Stock market better than the CAPM does, by generating higher adjusted R 2. The average adjusted R 2 of six portfolios obtain from Fama and French three factors model is 62.42%
equally higher than the average adjusted R 2 of six portfolios obtained from CAPM which is 29.47%. Ajili (2001) also compare the use of Fama and French three factor models and Capital asset pricing model, in the case of France stock market. On the basis of R 2 criterion, they affirm that the three factor model, compared with CAPM, captures better common variation in stock return. They constructed 6 portfolios same with Fama and French (1992,1993 , 1994,1996), and added two more portfolios based on only book to market ratio. For the eight portfolios, they obtained a higher average adjusted R 2 with Fama and French three factor models (90.05%) compare to the average adjusted R 2 obtained by CAPM (71.4%). Thus, by considering the finding of those researches, then the last hypothesis can be developed as:
Ha4 : Fama and French three factors model, can explain portfolio return better than CAPM in Indonesian Stock Market.
CHAPTER III RESEARCH METHODOLOGY
3.1
Data and Sample
This research will take the samples consist of companies that are listed in Indonesian Stock Market from period 2007-2010. Companies that are being taken into consideration are all non-financial companies. This research will not use financial companies because their leverage characteristics are different. Financial companies tend to have high leverage, where for financial firms, it will implies that the companies is in distress, or having a high risk; thus if financial companies are included in the research, it will be resulted to bias. Sampling method that will be used is purposive sampling in which samples that are being taken into the analysis already have a certain specification so that it can give the required information needed for the research. . Type of purposive sampling that are being used is judgment sampling where the choice of subjects which are being taken into the research are those subjects that will most advantageously placed or in the best position to provide the information required (Sekaran, 2003) Thus, under judgment sampling, this research will use the monthly closing price of all stocks in Indonesian stock exchange which are to be constructed as portfolios and being used as dependent variable, with the same requirement as Fama and French (1993) used in their research: •
There is no missing observation of the stock being observed during the period of research (2007-2010)
•
The stock does not have the track record of negative book-to-market ratio during the period of the research (2007-2010)
•
Stocks being used in the research are common stock, so this research will not use prefer stocks
•
Non-financial firms
After sorting all stocks available in Indonesian stock exchange, the data that are being used in this research consists of 227 stocks (can be seen in appendix 1).
3.2
Data and source of the data
The type of the data that are being used is secondary data that refers to Indonesian Stock Market Monthly statistics, Indonesian Composite index (IHSG), and risk-free rate (1-month SBI). 3.3 Identification and variables measurement a. Return of common stock
Returns of common stocks are calculated by the percentage change in stock’s price from July (t), to June year (t+1). The formula to calculate the percentage change is as follow:
R t =
CP(t) – CP (t-1) CP(t-1)
Where R t is the return of the individual stock in period t, CP(t) is the closing price of the individual for period t, and CP (t-1) is the closing price of the individual stock for period t-1. The monthly closing price is being taken from Indonesian stock exchange monthly statistics, that can be seen in www.idx.co.id . Returns are calculated from July (t) to June (t+1) for each stock.
b. Risk free rate
Risk free-rate is the rate that an investor can earn by leaving their money in risk-free assets such as T-bills, money market funds or the bank (Bodie et al, 2008). Thus, the risk free rate that is being used in this research is 1 month-SBI rate (the rate of Indonesian central bank’s certificate). The data of 1-month SBI is being taken from the website of Indonesian central bank, www.bi.go.id
c. Market return
Market return is calculated using monthly closing price of Indonesian Composite Index (IHSG) taken from www.idx.co.id . The return will be calculated as monthly percentage change of Indonesian composite index, calculated as: IHSG(t) – IHSG(t-1)
R M =
IHSG(t-1) Where R M is market return, IHSG (t) is Indonesian composite index for period t, and IHSG(t-1) is Indonesian composite index for period t-1.
d. Book to Market ratio
To calculate book-to-market ratio, book value per share and market value per share have to be calculated first. Book value per share is calculated as assets minus liabilities of the company, divided by number of shares outstanding, while market value per share is calculated as the market capitalization of the stocks, divided by numbers of share outstanding. (Dhamodaran,2001). Then after finding the book value per share and market value per share, book-to-market ratio can be calculated as: Book value/share
Market value per share
As being conducted by Fama and French (1993), this research also use the accounting data of December (t-1) each year, gained from Indonesian stock exchange monthly statistics. (www.idx.co.id ). Book to market ratio is being used to group portfolio based on three groups, which are, those with low book to market ratio, those with medium book-to-market ratio, and those with high book-to-market ratio.
e. Portfolio return
This research will use six portfolios grouped based on its size and book-to-market ratio, by which the formation will be explained in the next session. The returns of the six portfolios as stated by Ajili, (2001) are calculated as follow:
Where: R p,t
= is the value-weight monthly return of portfolio p in month t
R i,t
= is the monthly return of stock I of portfolio p in month t
Wi,t
= is the ratio of market value of stock i on total market value of portfolio p in month t
N
= is the number of stocks in portfolio p
f. size
Size of firms, can be judge by its market capitalization. Dhamodaran (2001), suggested the calculation of market capitalization of a stock as follow:
The numbers of company’s shares outstanding X Market value of the company’s stock
Following the research conducted by Fama and French (1993) and the other research refer to them; the market capitalizations that are being used in this research is the market capitalization of each stock\ in every June (t) for 3 years. Market capitalization is being used as the basis to group stocks into two portfolio categories, one consist of those stocks with big capitalization, and another one consist of stock with small capitalzion (Fama and French, 1993).
g. Market Factor
Mkt is the excess return between market return and risk free rate. Mkt is being used to prove that under time series, whether the excess return on portfolio was caused by the difference in size and book-to-market ratio, or merely because the change in risk free rate that happen in the market (Fama and French; 1995,1996). Mkt is being used to test the sensitivity of portfolio return toward Market return. Mkt is calculated as follow:
Mktt = R Mt - R ft
Where: Mktt = excess return of market portfolio for period t R Mt = Market return for period t R ft
= Risk free rate proxied by 1-month SBI rate for period t
h. SMB (Small Minus Big)
Fama and French (1992,1993,1996) used variable SMB (Small Minus Big) to mimic the risk factor in returns related to size. It is the difference, each month between the simple average of the returns on three small-stock portfolios, and the simple-average of three bigstock portfolios. Fama and French (1993) showed the calculation of SMB as follows:
[(S/H + S/M + S/L)] – [(B/H + B/M + B/L)] 3 Where:
S/H, S/M, S/L = portfolio of stocks with small capitalization, with low, medium and high book to market ratio.
B/H, B/M, B/L = portfolio of stock with big capitalization, with low, medium, and high book-to-market ratio.
i. HML (High minus Low)
HML is the variable used by Fama and French (1992,1993,1996), to mimic the risk factor in returns related to book-to-market ratio. HML is the difference, each month, between the simple average of the returns on the two-high book-to-market ratio-stocks portfolio, with the two low-book-to-market-ratio- stock portfolio. Fama and French (1993) showed the calculation of HML as follows:
[(S/H + B/H)] – [(S/L + B/L)] 2
Where: S/H, B/H = the portfolio of stocks with high book-to-market ratio, with small and big capitalizations. S/L, B/L = the portfolio of stocks with low book-to-market ratio, with small and big capitalizations.
3.4 Methodology and hypothesis testing a. First Step
This research is started by forming six portfolios that are formed based on size and book-to-market ratio, that later on will be used in the identification of SMB variable and HML. Then the stocks are grouped based on size, into two groups, those stocks with small capitalization, and those stocks with big capitalization. Individually, stocks are also being grouped based on their book-to-market ratio and based on the breakpoints, into three groups, those with low book-to-market ratio (30% of stocks), those with medium book-to-market ratio (40%), and those with high book-to-market ratio (30%). The decision to group stocks into three groups on book-to-market ratio and only two groups on book-to-market ratio, is based on their previous findings in Fama and French (1992), revealed that book-to-market equity has stronger role in average stock returns than size. Then six portfolios are formed based on the interception of the two size groups and the three book-to-market group, they are S/L, S/M, S/H, B/L, B/M, B/H (i.e S/L is portfolio consist of those stocks with small capitalization and low book-to-market ratio). The returns of those six portfolios are then being used as dependent variables.
After stocks are being grouped, the next step is applying regression model to the formed portfolios to see the effect of market factor (as suggested by CAPM), and the effect of the three factors which are market, SMB and HML as suggested by Fama and French three factors model.
b. Second step
The regression model that is being used to test Capital Asset Pricing Model, is as follow: R it- R ft = R ft + βi . [R Mt – R ft]
The purpose of the empirical model is to test Capital Asset Pricing Model in time series. Capital Asset Pricing Model stated that the expected return of portfolios is a function of the two components of which are the risk free rate and market factor (John 2007). Technical analysis that is being used to estimate the regression in this step is Ordinary Least
Square Method with the use of Eviews 4.0 statistical software. Then hypothesis testing is being conducted under t-test , to test the significance of independent variable toward dependent variable. Since in this regression model there is only one variable, then F-test is not being conducted in this step. c. Third Step
In the third step, the regression model that is being used is: R i - R f =c + βi (R M – R f) t + si E(SMBt) + hi E(HML)t +e
The purpose of the regression in this step is to test Fama and French three factor model in time series manner. Fama and French three factors model suggest that the expected return on portfolio can be explained by return sensitivity on three factors, which are Mkt (market factor), SMB, and HML. Technique of analysis that is being used is Ordinary Least
Square using E-views 4.0 statistical software. Hypothesis then will be tested using t-test to test the significance of independent variable toward the dependent variable (partial test). F-
test is also being used to test whether all independent variables that are being put into the model, together affecting the dependent variable,
d. Fourth Step
To compare the effectiveness of Capital Asset Pricing model and Fama and French three factors model, adjusted R 2 of both regression in the second and third step are being compared.
3.5 Classic Assumption test a. Autocorrelation
Autocorrelation is the existence of relationship between the residual of one observation, with the residual of other observation. Autocorrelation is easily emerge in the case of time-series data, because based on the characteristics, current data is affected by the previous data (Winarno, 2006). One of the ways to identify autocorrelation that disturbing the regression analysis is using Durbin Watson (DW test). DW test is only being used for first order autocorrelation, and required that there is an interception in the regression model and there is no lag variable in independent variable. Whether there is autocorrelation problem or not within the model, is based on the criterion below: •
If the value of DW is higher than upper bound (U), then the coefficient of autocorrelation is equal to zero, means there is no autocorrelation.
•
If the value of DW-statistics is lower than lower bound (L) the coefficient of autocorrelation is bigger than zero, means there is a positive autocorrelation.
•
If the value of DW statistics fall between Upper and Lower bound, then autocorrelation cannot be conclude.
b. Multicolennierity
Muliticoliniearity is the existence of linear relationship between independent variable (Gujarati,2003). According to Gujarati (2003), if the correlation between two independent variable is higher than 0,8 then multicolinierity exist.
c. Heteroskedasticity
Heteroskedasticity is a condition whereby the residual variables have different variance between one observation to another. It occurs when the residual does not have constant variance. If heteroscedasticity exist, the estimator of regression will not be efficient, either in small, or large population. To identify the existence of heteroscedasticity, scatterplot of the data can be examined between the predicted value of the dependent variable, and its residual, based on these assumptions: •
If the scatterplot forms a particular shape, it means that there is heteroscedasticity.
•
If the scatterplot does not form any particular shape, or evenly distributed, it means that there is no heteroscedasticity.
FACTORS AFECTING PORTFOLIO RETURNS IN INDONESIAN STOCK MARKET: CAPITAL ASSET PRICING MODEL VS FAMA AND FRENCH THREE FACTORS MODEL THESIS PROPOSAL
Submitted by HARLAN SETIADI 07/257781/EK/16810 INTERNATIONAL UNDERGRADUATE PROGRAM FACULTY OF ECONOMICS AND BUSINESS UNIVERSITAS GADJAH MADA
Table of contents: Chapter 1: Introduction
1.1 Background 1.2 Problem statement 1.3 Limitation of the research 1.4 Purposes of the research
Chapter 2: Theories and Hypothesis development
2.1 The concept of risk and return 2.2 Capital Asset Pricing Model 2.3 The relationship between stock return and firms’ characteristics 2.3.1 The relationship between stock return and firms’ size 2.3.2 The relationship between stock return and firm’s book to market 2.4 Fama and French Three Factor Model 2.5 Previous Research 2.6 Hypothesis development
Chapter 3: Research methodology
3.1 Data and sample 3.2 Data and source of the data 3.3 Identification and variable measurement 3.4 Methodology and Hypothesis testing 3.5 Classic Assumption test
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