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 models developed. Those pricing models have been used by academicians 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 Capital Asset Pricing Model, developed by Merton (1973), The
Arbitrage Pricing Model developed by Chen and Ross (1986), and Three factor model
developed by Fama and French (1993).
Different variables are being used by those pricing models to explain assets (stocks)
return. Many researches and journals, compared two of them which are, the 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,
Ki = Risk-free rate + Risk Premium
= RF + β [E(RM) – RF]
The use of only one risk factor in explaining expected return, makes this pricing
model also being known as single factor model. 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 less-
firm specific risk. Statistically, this added risk is measured by the covariance of the asset with
market portfolio.
Under CAPM, investors adjust their risk preferences by using their allocation
decission, whther they want to invest more in riskless assets or more in market portfolio.
Equation 1.1
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. They find that used alone, or in combination with other 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 leverage and E/P in average return. Briefly, their research resulted in the statistical
conclusion that, two empirically determined variables, size and book-to-market equity, do a
good job in explaining the average returns.
Thus, concerning other factors that might be able to explain 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(Ri) - Rf =c + βi (E(RM) – Rf) + si E(SMB) + hi E(HML) +e
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-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.
They use the excess market return (E(RM) – Rf), 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-to-
market 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).
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
ME(RM)
RBR
0 1.0Beta
E(Ri)
Security Market Line
Fig 2.1
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(RM). For riskless asset with 0 Beta, the expected return is RBR
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 RBR and the slope will have the value of [E(RM) - RBR] / βM.
Because βM = 1, thus the slope of Security Market Line will have the value of [E(R M) - RBR].
Thus the equation for ith securities can be written as:
E(Ri) = RBR + βi . [E(RM) - RBR]
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:
Equation 2.1
Rit = RBRt + βi . [RMt - RBRt]
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
Equation 2.2
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-to-
market 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-to-
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 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(Ri) - Rf], can
be explained by return sensitivity toward three factors, they are: excess return of market
portfolio [E(RM) – Rf], 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(Ri) - Rf =c + βi (E(RM) – Rf) + si E(SMB) + hi E(HML) +e
Where E(RM), E(SMB), and E(HML) are expected premiums; βi , 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
Equation 2.3
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-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.
They use the excess market return (E(RM) – Rf), 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 - Rf =c + βi (RM – Rf)t + si E(SMBt) + hi E(HML)t +e
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.
Equation 2.4
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 shared-
variation 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 book-
to-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 R2 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 R2. The average
adjusted R2 of six portfolios obtain from Fama and French three factors model is 62.42%
equally higher than the average adjusted R2 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 R2 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 R2 with Fama and French
three factor models (90.05%) compare to the average adjusted R2 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:
CP(t) – CP(t-1)
Where Rt 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
CP(t-1)
Rt =
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)
Where RM 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
IHSG(t-1)
Market value per share
RM =
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:
Rp,t = is the value-weight monthly return of portfolio p in month t
Ri,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 = RMt - Rft
Where:
Mktt = excess return of market portfolio for period t
RMt = Market return for period t
Rft = 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 big-
stock 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:
Rit- Rft = Rft + βi . [RMt – Rft]
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:
Ri - Rf =c + βi (RM – Rf)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 R2 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
References:
Sekaran, Uma (2003). Research Methods for Business 4th Edition. NJ: John Wiley & Sons, Inc.
Fama, Eugene F., and Kenneth R. French, (1992), The cross-section of expected stock returns, Journal of Finance 46, 427–466.
Fama, E. and K. French (1993), Common risk factors in the returns on stocks and bonds, Journal of FinancialEconomics 33, 3-56.
Fama, Eugene F., and Kenneth R. French, (1995), Size and book-to-market factors in earnings and returns, Journal of Finance 50, 131-155.
Fama, E. and K. French (1996), Multifactor explanations of asset pricing anomalies, Journal of Finance 51, 55-84.
Dhamodaran, Arswath (2001), Investment Valuation 2nd edition, NJ: John Wiley & Sons, Inc
Jones P. Charles (2007), investments 10th edition, NJ: John Wiley & Sons, Inc
Homsud, Nopbhanon et al (2009), The study of Fama and French Three Factors model and Capital Asset Pricing Model in the stock exchange of Thailand, International Research Journal of Finance and Economics.
Ajili (2001), The capital asset pricing model and the three factor model of Fama and French revisited in the case of france.
Auret C.J and Sinclair RA (2006), Book to market ratio and return. Investment analysis journal, no : 63.
Banz R. 1981. The relationship between return and market value of common stock. Journal of Financial Economics, 9:3-18.
Winarno W.W (2009), Analysis Eknometrika dan Statistika dengan E-views, edisi ke-2, Jogjakarta: UPP STIM YKPN
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