Asian Journal of Finance & Accounting
ISSN 1946-052X
2013, Vol. 5, No. 1
Evidence to Support Multifactor Asset Pricing Models:
The Case of The Istanbul Stock Exchange
Ulas UNLU
The University of Nevsehir, Department of Accounting and Finance
50300, Nevsehir/Turkey
E-mail: ulasunlu@gmail.com
Received: Feb. 4, 2013 Accepted: April 12, 2013 Published: June 1, 2013
doi:10.5296/ajfa.v5i1.3216 URL: http://dx.doi.org/10.5296/ajfa.v5i1.3216
Abstract
The objective of this study is to test, instead of the single factor CAPM, the power of three
factor, four factor and five factor models to explain stock returns for the Istanbul Stock
Exchange (ISE). The test results of all models in the ISE indicate that the models are
applicable. During the period covering July 1992-June 2011 it is consequently established
that, in addition to the market risk, size, book to market ratio, momentum and liquidity
factors also constitute significant risk factors that affect the expected stock returns in the ISE
and that the risk premiums belonging to these five factors are priced by the market.
Keywords: Fama and French Three Factor Model, Four-Factor Pricing Model, Five Factor
Pricing Model, Asset Pricing, Emerging Markets
JEL Cod: G11, G12
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1. Introduction
The validity of asset pricing models bears vital importance for individual and institutional
investors planning to invest in securities. As it is known, the most widely known and used
asset pricing model in capital markets is CAPM (Capital Asset Pricing Model) as developed
by Sharpe (1964), Lintner (1965) and Mossin (1966), which represents a balance model that
prices a certain asset relying on certain assumptions with consideration of the relation
between the risk and the expected return.
During the 1970’s, CAPM was widely advocated owing to the facilities it provided such as its
provision for measuring risks with a single variable. In parallel with the developing capital
markets during the 1980’s and 1990’s however, controversies appeared as to the adequacy of
CAPM to explain the stock returns. Nevertheless, many researchers show that the anomalies
they detected could not be foreseen by the model. Examples to these are size anomaly by
Banz (1981), Reinganum (1981), Keim (1983); Book to Market effect by Stattman (1980),
Rosenberg, Reid and Lanstein (1985), Chan, Hamao, and Lakonishok (1991); Price-Earning
effect by Basu (1983); and Momentum effect by Jegadeesh and Titman (1993).
The fact that no non-market factor (size, book to market ratio, momentum, liquidity, etc…)
other than market risk is included in CAPM, indicates that excessive returns created by such
variables, which are thought to lead anomalies, cannot be foreseen by the model either. Focus
switched towards multifactor models for capital markets as CAPM fell insufficient to explain
stock returns. These models present evidence that company specific characteristics are
usually very successful in explaining horizontal-section stock returns. The purpose of this
study is to test the power of the three factor, four factor and five factor models, which attract
intensive attention in international markets, to explain asset prices in the Istanbul Stock
Exchange (ISE). It is believed that testing alternative asset pricing models will fill an
important gap for the Turkish capital market. This study further represents an initial work for
the ISE that tests the five factor asset pricing model, which is created by adding liquidity as a
risk factor to the four factor model. In addition, it is considered that the study bears
importance in that it shows whether small company premium, value premium, momentum
and liquidity premium are priced in the ISE as far as the investors are concerned.
2. Literature Review
As CAPM fell insufficient to explain security prices, various studies were conducted on
multifactor models in capital markets and alternative asset pricing models were suggested to
remedy the deficiencies of CAPM.
Fama and French suggest a multifactor model to explain expected stock returns in the studies
they conducted in 1993 and 1996. In the three factor model by Fama and French, the Rm-Rf,
SMB and HML risk factors affect the expected return of stocks.
Fama-French (1993, 1996) predicted this model for the below equation:
E(Ri ) Rf i i [E(Rm ) Rf )] si E(SMB) hi E(HML) i
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The beta coefficients mentioned in the equation represent sensitivity coefficients that express
the slope of the multiple regressions that is made between E(Ri) – Rf and Rm-Rf, SMB and
HML. Here, SMB covers the size risk factor on the returns and HML covers the B/M ratio
risk factor in the returns.
The validity of the three factor model proposed by Fama and French (1993, 1996) was
supported by the studies conducted in many markets. Griffin (2003) tested the three factor
model for Japan, England and Canada for the period of 1981-1995 and found the power of
the model significant for explaining the change in of cross-section stock returns. Lam (2002)
reached findings that support the three factor model in the study he conducted during the
period of 1980-1997 for 100 companies that were traded in the Hong-Kong stock exchange.
Ajili (2003) tested the three factor model for the French market during the July 1976 – June
2001 period and the characteristic model of Daniel-Titman (1997). It was established that
power of 6 portfolios, which were determined as dependent variables, to explain the expected
returns was 90,5% on average. Cao, Leggio and Schniederjans (2005), included within the
model 367 stocks that were quoted in the Shanghai Stock Exchange (SHSE) during the period
of 01 December 1999 - 31 December 2002. The focus of the study is to compare the
explanatoriness of CAPM and the Fama – French three factor model with the artificial neural
network model and linear models. The result showed that the composed linear models
produced much mode significant results compared to the artificial neural networks. Iqbal and
Brooks (2007) compared two asset pricing models (CAPM and Fama and French three factor)
in Pakistan's Karachi Stock Exchange (KSE). They applied GARCH and EGARCH as the
method and used the daily, weekly and monthly data. The study used 89 stocks that were
traded in the Karachi Stock Exchange (KSE) during the period of 09 March 1999 – 08 March
2005. The KSE-100 index was used as the market index. It was concluded that the risk
factors in the Fama and French three factor model were more significant than the CAPM. In
the meanwhile, the authors recommend using daily data instead of monthly data. In their
study conducted for the Australian market, O’Brien, Brailsford and Gaunt (2008) took
1982-2006 as the sampling period and compared CAPM with the three factor model. It was
concluded that the three-factor model represented a very successful model for explaining the
change in returns and that it explained nearly 70% of the changes in returns.
3. The Four-Factor Model
The four factor model represents an asset pricing model developed by Carhart (1997) owing
to the fact that the three factor model of Fama-French (1993, 1996) could not explain the
momentum effect presented by Jegadeesh-Titman (1993).
During a study by Jegadeesh and Titman (1993), the portfolios created using a strategy, which
is based on the assumption that within a period of 3-12 months (short-term), the stocks that
made gains (led to losses) in the past will make gains (lead to losses) in the future, obtained
abnormal returns of 1% in each consecutive year. When the literature is examined, it is seen
that very small number of studies paid regard to the power of adding the momentum factor to
SMB and HML factors of Fama and French (WML-winners minus losers) in explaining stock
returns. (Carhart 1997, Jegadeesh 2000, Liew and Vassalou 2000, Kim and Kim 2003, L’Her;
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Masmoudi; Suret 2004, Bello 2007, Carmichael and Coën 2008, Lam; Li; So 2009; Unlu,
2012).
The four factor model was first tested by Carhart (1997). Carhart (1997) created the four
factor model by augmenting the momentum factor of Jegadeesh and Titman (1993) to the
three factor model of Fama-French. The four factor model is tested as follows (Carhart, 1997:
61):
riT iT biT RMRF siT SMB hiT HML piT PR1YR i
The thing involved here is the return of the RMRF; NYSE, AMEX and NASDAQ indexes on
the one month Treasury bill. These are SMB and HML Fama-French factors. On the other
hand, PR1YR represents the difference between the highest 30% returns 11 months ago and
the lowest 30% returns 11 months ago. As a conclusion, Carhart (1997) suggests that the four
factor model can be used in explaining stock returns.
Liew and Vassalou (2000) examined the relation between the macroeconomic risk factors and
the profitability of SMB, HML, WML transaction strategies for 10 developed markets
comprised of Australia Canada, France, Germany Italy, Japan, the Netherlands, Switzerland,
England and the USA. Whereas this study represents an evidence for the WML factor, the
findings obtained are not as strong as the SMB and HML factors. By using monthly data,
L’Her, Masmoudi and Suret (2004) looked into the power of four factors, which are Rm-Rf,
SMB, HML and WML, to explain stock returns during the period of 1960 – 2001 for the
Canadian equity market. It was concluded that the four-factor model was valid for the
Canadian Market. Naceur and Chaibi (2007) researched into the best asset pricing model in
the Tunisian Stock Exchange (TSE) for calculating the capital cost. The result of the study,
the four factor model of Carhart (1997) was the best model to estimate the capital cost for the
TSE. Lam, Li and So (2009) examined the power of the four factor model, which was
created by adding the momentum factor to the three factor model of Fama-French, in
explaining the change in stock returns concerning the Hong Kong market. The study
concluded that the coefficients of the four factor model are significant; alpha coefficients are
not significantly different from zero and thus showed that the model is applicable. Unlu
(2012) tested the four factor model in the ISE for the period of July 1992 – June 2008 and the
results showed that the four factor model was significant for the ISE.
4. The Five Factor Model
The liquidity of a stock means that it can easily be purchased and sold rapidly on lower costs
in the secondary market.
Pastor and Stambaugh (2003) added the liquidity factor to the four factor model in their
studies for the NYSE, AMEX, and NASDAQ stocks and tested the five factor model.
Amihud (2002) was used as the liquidity measurement method. The study concluded that
liquidity represented an important risk factor. On the other hand, Chan and Faff (2005) added
the liquidity factor as the four factor to the three factor model for the Australian market. The
study, which used turnover rate as the liquidity measurement, determined that the liquidity
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factor was priced by the market. In their studies, Nguyen and Tribhuvan (2009) added the
liquidity factor to the three factor model and examined the role of liquidity in stock pricing.
In the study where the NYSE and AMEX stocks were used, it was established that liquidity
could be used as an important systematic risk factor.
5. Data Structure and Method
The study took July 1992 – June 2011 as the sample period and used monthly data. Data on
stock returns, index closing and balance sheets was obtained from the ISE and Treasury bill
rates was obtained from the official website of the Turkey Undersecretariat of Treasury. Stock
transaction amounts and the number of stocks were taken from Datastream. The financial ratios
in the study were calculated from the 31 December 1991 and 31 December 2010 end-year
balance sheet data of the companies. Presuming that the company profits arrived to the investor
before the balance sheets were declared, results in look ahead bias. The returns were calculated
for the 01 July 1992 – 30 June 2011 period in order to prevent this (Fama and French 1993,
1996). The ISE-100 index was used as the index return. The annual compound reference
Treasury bill rates was converted into monthly values and used as risk-free interest rate in the
study. The portfolios were created using the Fama and French (1993, 1996) methodology and
factors of size and B/M ratio were used as criteria. Firm size was measured by market
capitalization or market value of equity. The B/M ratio is calculated by dividing the per-stock
book value into the stock’s market price.
The portfolios were created in the June of each t year and the balance sheet data in the t-1 year's
December were paired with the stock returns in the t year's June. As the firm size was
calculated as of the month of June, the B/M ratio was calculated by dividing the book value in
the t-1 year’s December into the market value in the t-1 year’s December.
The returns for the three factor model, four factor model and the five factor model are
monthly, and on the other hand, 6 pcs portfolios were created according to the B/M ratio and
these were used as dependent variable in the models. 2 pcs (small and large) portfolios were
determined for the size effect and 3 pcs (low, medium and high) portfolios were determined
for the B/M effect. A total of 6 intersection portfolios were created for the size effect and the
B/M ratio effect (Low = 30%, Medium = 40%, High = 30%) and (SMB and HML) were used
for the calculation of (S/L, S/M, S/H, B/L, B/M, B/H) risk factors.
The portfolios created were calculated in a manner to cover the period between each t year's
July until each t+1 year's June and they were revised in the June of each year.
In order to enable the calculation of the momentum factor, the stocks were sequenced as the t
year’s July and t-1 year’s June and their performances between the months of t-2 and t-12
were taken into consideration (Fama and French, 2007, L’Her; Masmoudi; Suret, 2004, Lam;
Li; So, 2009). The stocks were divided into two groups according to their size measurements,
which are S (small) for 50% and B (big) again for 50%. Later, 6 pcs equally weighted
portfolios were created, representing namely the 70% portion with the best return
(momentum) labeled as W (winner), the average 40% labeled as N (Neutral) and the lowest
30% portion labeled as L (loser), and these were used for the calculation of the “WML” risk
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factor.
“Turnover Ratio” was used the liquidity criterion as similar to Chan and Faff (2005) and
Eckbo and Norli (2005). The turnover ratio is found by using the monthly transaction amount
and the number of stock certificates present in the market. That is to say, the turnover ratio of
a stock was calculated by dividing the monthly transaction amount into the number of stock
present in the market. 6 pcs equally-weight portfolios were created in order to calculate the
liquidity risk factor.
Five pcs risk factors were determined in order to explain the stock returns. These are the risk
factors of Rm-Rf (the difference between the market return and the risk-free interest ratio),
SMB (the difference between the return of the portfolio that is composed of the small stocks
with low market values and the portfolio that is composed of large stocks with high market
values), HML (the difference between the return of the portfolio that is composed of the
stocks with high B/M ratio and the return of the portfolio that is composed of the stocks with
low B/M ratio) and WML (the difference between the return of the winner stocks portfolio
and the return of the loser stocks portfolio) and LMH (the difference between return on the
two portfolios with low turnover and return on the two portfolios with high turnover)
(E(Rm) – Rf) represents the market premium and it is the return of the market over the
risk-free interest ratio. SMB represents the size premium, HML represents the value premium,
WML represents the earning premium and LMH represents liquidity premium.
The returns of the 6 portfolios, which were created according to size and B/M ratio, on the
risk-free interest ratio were used as dependent variables in time series regressions. The
following regression models were created in order to estimate the stock returns:
E(Ri ) Rf i i [E(Rm ) Rf )] si E(SMB) hi E(HML) i (1)
E(Ri ) R f i i [E(Rm ) R f )] si E(SMB) hi E(HML) wi E(WML) i (2)
E ( Ri ) R f i i [ E ( Rm ) R f )] si E ( SMB) hi E ( HML) wi E (WML) li E ( LMI ) i
(3)
The beta coefficients mentioned in the equation represent sensitivity coefficients that express
the slope of the multiple regressions that is made between E(Ri) – Rf and Rm-Rf, SMB, HML,
WML, LMH.
As it is known, if the alpha value reached in the asset pricing models is significantly different
from zero, this means that there is a pricing error in the models and there is a factor or are
factors that cannot be explained by the models (Black; Jensen; Scholes 1972, Fama and French,
1993).
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The F (GRS) test of Gibbons, Ross and Shanken (1989) is usually recommended during studies
in order to determine whether the alpha value is significantly different from zero (Fama and
French 1996, Campel; Lo; Mckinlay 1997, Gregory; Tharyan; Huang 2009).
The GRS test statistic is;
(T N k )
J (1 k 1 k ) 1 1 FN ,T N K
N
H0 = All αi coefficients obtained from multiple factor models are equivalent to zero (αi =
0).
H1 Not all αi coefficients obtained from multiple factor models are equivalent to zero (αi ≠
0).
The acceptance of the zero hypothesis will also show that the multi-factor asset pricing
models, which constitute the basic purpose of the study, can be used for the ISE to explain the
stock prices (Fama and French 1996).
6. Findings
The regression results pertaining to the three factor asset pricing model have been given in
Table 1.
Table 1. Three factor regression of montly excess returns: from July 1992 to June 2011
E ( R ) R [ E ( R ) R )] s E ( SMB) h E ( HML)
Ri-Rf α Β s h Ad.R2 DW F
SL -0,003 0,694 0,618 -0,191 0,726 2,05 76,18
(-0,355) (13,803)* (5,434)* (-2,415)** [0,000]
SM -0,016 0,612 -0,618 -0,869 0,811 2,11 124,53
(-0,658) (10,642)* (-4,755)* (-9,610)* [0,000]
SH -0,009 0,759 0,388 0,235 0,719 2,12 73,75
(0,273) (14,848)* (3,369)* (2,936)* [0,000]
BL -0,013 0,733 -0,648 -0,887 0,868 2,09 187,65
(-0,455) (14,077)* (-5,505)* (-10,840)* [0,000]
BM -0,015 0,747 0,406 -0,030 0,737 2,22 80,562
(-0,751) (14,929)* (3,591)* (-0,385) [0,000]
BH -0,006 0,669 -0,418 0,685 0,763 2,19 88,03
(-0,766) (13,786)* (-3,810)* (8,983)* [0,000]
GRS-F Test: 0,955 [0,432]
The p value are in parentheses ***, **,* show significance at the 10, 5, and 1% levels,
respectively. Probability values of GRS-F test are in brackets.
When Table 1 is examined, the F values and probability values of all models, which were
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created according to the regression results of the Fama-French's three factor model, show that
the established models are meaningful. It is seen that not the entirety of the alpha values is
different from zero. In addition, the GRS F test result’s being 0,655 and that the probability
value’s being 0,432 mean that the zero hypothesis is accepted, in other words that the three
factor model is valid for the ISE.
Table 2. Four factor regression of montly excess returns: from July 1992 to June 2011
E ( Ri ) R f i i [ E ( Rm ) R f )] si E ( SMB) hi E ( HML) wi E (WML) i
Ri-Rf α β s h w Ad.R2 DW F
SL 0,006 0,677 0,558 -0,283 -0,271 0,748 2,15 64,105
(0,754) (13,915)* (5,018)* (-3,434)* (-2,844)* [0,000]
SM -0,009 0,600 -0,659 -0,931 -0,183 0,817 2,11 95,87
(-0,923) (10,457)* (-5,021)* (-9,554)* (-1,690)*** [0,000]
SH -0,000 0,741 0,332 0,148 -0,259 0,736 2,22 101,14
(-0,043) (14,920)* (2,923)* (1,760)*** (-2,627)* [0,000]
BL -0,007 0,723 -0,681 -0,937 -0,150 0,869 2,12 143,71
(-0,791) (13,877)* (-5,718)* (-10,606)* (-1,455) [0,000]
BM -0,004 0,728 0,340 -0,131 -0,300 0,764 2,23 69,50
(-0,786) (15,201)* (3,111)* (-1,614) (-3,154)* [0,000]
BH -0,000 0,659 -0,455 0,630 -0,166 0,760 2,15 68,38
(-0,048) (13,624)* (-4,116)* (7,677)* (-1,731)*** [0,000]
GRS F Test: 1,103 [0,295]
*** ** *
The p value are in parentheses , , show significance at the 10, 5, and 1% levels, respectively. Probability
values of GRS-F test are in brackets.
When regression results of the four factor model are examined, the F values and probability
values of all models show that the established models are significant. Not the entirety of the
alpha values is different from zero. It was established that the GRS F test result is 1,103 and
the probability value is 0,295. This result means that the zero hypothesis is not rejected,
meaning that the four factor model is also valid for the ISE.
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Table 3. Five factor regression of montly excess returns: from July 1992 to June 2011
E ( R ) R [ E ( R ) R )] s E ( SMB) h E ( HML) w E (WML) l E ( LMI )
Ri-Rf α β s h w l
Ad.R2 DW F
SL 0,006 0,346 0,589 -0,285 -0,264 0,332 0,753 2,17 52,83
(0,724) (1,748)* (5,271)* (-3,495)* (-2,758)* (-1,728)*** [0,000]
SM -0,010 0,096 -0,593 -0,935 -0,162 0,700 0,833 2,10 86,08
(-1,036) (12,405)* (-4,670)* (-10,665)* (-1,486)*** (3,001)* [0,000]
SH -0,001 0,145 0,387 0,144 -0,240 0,598 0,761 2,26 55,24
(-0,112) (17,365)* (3,522)* (1,792)*** (-2,546)* (2,958)* [0,000]
BL -0,008 0,096 -0,622 -0,942 -0,131 2,970 0,881 2,21 127,37
(-0,895) (10,774)* (-5,390)* (-11,155)* (-1,823)*** (1,059) [0,000]
BM -0,004 0,167 0,393 -0,135 -0,282 0,563 0,782 2,12 62,28
(-0,573) (11,243)* (3,694)* (-1,734)*** (-3,094)* (2,883)* [0,000]
BH -0,000 0,296 -0,421 0,627 -0,155 0,363 0,766 2,02 56,84
(-0,090) (12,235)* (-3,803)* (7,749)* (-1,741)*** (1,790)*** [0,000]
GRS F Test: 0,512 [0,725]
*** ** *
The p value are in parentheses , , show significance at the 10, 5, and 1% levels, respectively. Probability
values of GRS-F test are in brackets.
The examination of Table 3 established that just like the three factor and four factor models, F
values and probability values of the established models were significant for the regression
results yielded by the five factor model and that not the entirety of their alpha values was
different from zero. The GRS F test result was found to be 0,512 and the probability value
was found to be 0,725. This result shows that the five factor model can be used in explaining
securities’ returns in the ISE.
When the regression results are examined, it is seen that the R square vales of the three factor
and four factor models are close to each other. The addition of the liquidity factor to the four
factor model has meaningfully increased the R square value. It is seen that the coefficients of
the Rm-Rf, SMB, HML, WML and LMH, which constitute systematic risk factors, are
meaningful in almost all models.
The regression findings revealed the finding that the portfolio of the companies with small
market value (SL and SH) has a positive SMB slope whereas the portfolio of the companies
with large market value (BL and BH) has a negative SMB slope. This finding points to the
effect of company size. Furthermore, the fact that the portfolio of the companies with high
B/M ratio (SL and SH) has a positive HML slope and the portfolio of the companies with low
B/M ratio (BL and BH) has a negative HML slope points to the presence of the value effect.
The obtained results are consistent with the findings of Fama and French (1996). It was
nevertheless determined that all WML slopes are negative and all LMH slopes are positive.
This results shows that the WML and the LMH factors are not related with the firm size or
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the B/M ratio.
7. Conclusion
The purpose of the study is to test the alternative asset pricing models for the ISE. This paper
aims to fulfill this gap and contributes to empirical literature on this subject. The obtained
findings point to the existence of the size and value effects for the ISE. It is also determined
that the factors of momentum and liquidity should be preferred during the creation of asset
pricing models.
It is consequentially established that the three factor, four factor and five factor models are
valid in the ISE, and that in addition to the market risk, factors of firm size, B/M ratio,
momentum and liquidity also constitute significant risk factors that affects stock returns and
that the risk premiums belonging to these five factors are priced by the market.
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