INTERNATIONAL JOURNAL OF BUSINESS POLICY AND ECONOMICS
Vol. 4, No. 2, (2011) : 241-276
AN EMPIRICAL TESTING OF CARHART MODEL IN INDIAN STOCK MARKET*
Santosh Kumar
Lecturer, Finance and Accounts Department, Amity Business School,
Amity University, Noida
Tavishi
Lecturer, Department of Economics, Mity Business School,
Amity University, Noida
Indian capital market has changed drastically in the past one decade. The ability
to predict the stock price movements based on a given set of information helps
investors and fund managers to frame suitable strategies for investment. CAPM,
Fama-French, Arbitrage, Carhart, are among the various models which are used
in investment decision making. This study examines the validity of Carhart Model
in Indian Stock market using the daily data on stock price, size, B/P, and the
market index S&P CNX 500 for the period ranging from 2009 to 2010 and
documents its pricing ability. Results indicate that the momentum factor WML
(winner minus loser) is not significant in Indian stock market while the factors
like SML (Small Minus Big), RM (Return of Market) and HML (High Minus
Low) reflects higher reliability and explanation capacity in the pricing of stocks.
It is also found that the size effect (SMB) is significant in almost all portfolios
except in the larger companies and the higher returns of the portfolio are attributed
to either medium or high Book value by Market value (B/P) and small size. It
implies that investors can rely on size, B/P and market index rather than ex post
performance.
Keywords: SMB, HML, WML, Carhart Model.
1.
INTRODUCTION
India is considered as one of the fastest emerging markets in the world and
these changes in the economy are directly reflected in capital market. Indian
capital market has changed rather drastically in the last few years. A capital
market in which stock prices fully reflect all available information can be termed
as efficient. The ability to predict stock price changes based on a given set of
information is behind the notion of stock market efficiency. Momentum
investment Strategy is based on efficient market hypothesis. It suggests that
“today’s winners will be tomorrow’s winners and today’s losers will be tomorrow’s
losers” and hence the investment strategy based on buying today’s winners and
selling today’s losers will generate superior returns. However, Contrarian
investments strategy claims that “Today’s losers are tomorrow’s winners and
today’s winners are tomorrow’s losers’ and thus the investment strategy based
This paper is presented and discussed in a National Finance Conference LBS, New Delhi.
242
Santosh Kumar & Tavishi
on buying today’s losers and selling today’s winners should generate superior
returns. This strategy is based on the idea that market is inefficient. It is also
known as overreaction hypothesis. Studies have shown sufficient evidence of
both overreaction and momentum hypotheses.
The Capital Asset Pricing Model (CAPM) oversimplifies the complex market
scenario by using a single factor market, to compare the excess returns of a
portfolio with the excess returns of the market as a whole. Fama and French in
1992 have extended the model to three factors viz. Market Return (Rm), Small
minus Big (SMB) and Highest minus Lowest (HML) and have observed that
stocks which are either small caps or higher Book Value to Market Price ratio
have relatively performed well. This model captures most market deviations
except the momentum effect. Carhart model in 1997 have augmented the Fama
and French three-factor model with a momentum factor Winners minus losers
(WML) constructed by the monthly return difference between the returns on
the high and low prior return portfolios, to capture the cross-sectional return
patterns.
2.
REVIEW OF LITERATURE
The Overreaction Hypothesis asserts that stocks which have underperformed
the market over a period of time will outperform the market over a subsequent
and similar time period. Till now many researchers have shown interest in the
functioning of overreaction hypothesis. De Bondt and Thaler (1985) reveal, using
monthly return data for New York Stock exchange common stocks from January
1926 and December 1982, loser’s portfolio outperforms the market by 19.26
per cent. They discover that overreaction hypothesis is asymmetric; it is much
larger for the losers than for winners. De Bondt and Thaler (1990) further studies
rationality of earnings forecasts, using analyst’s earning forecasts of New York
stock exchange between 1976 and 1984 and concludes that there exsists a strong
evidence of overreaction in the predictions of graduates as well as stock market
professionals by applying regression analysis. Paul, (1990) investigates that
tendency for losers to outperform winners is not attributed to investor
overreaction, but to the tendency for the losers to be smaller sized firms than
winners. They identify that when losers are compared with winners of equal
size, there is little evidence of any return discrepancy, and in period when
winners are smaller than losers, winners outperform losers.
Lawrence and Hao (1992) test the overreaction hypothesis using monthly
data for stocks listed on the Toronto Stock Exchange over the 1950-1988 period
and find significant continuation behavior for the next one (and two) year(s) for
winners and losers, and insignificant reversal behavior for winners and losers
over longer formation/test periods of up to ten years. Page & Way (1992), study
overreaction hypothesis on Johannesburg Stock exchange using data from July
1974 to June 1989 for 204 relatively well traded securities. They observe that
portfolios of prior losers significantly outperform portfolio of prior winners by
10-20per cent .Clare and Thomas (1995), analyzes overreaction hypothesis for
the UK stock market using data from 1955 to 1990 drawn from a random sample
of 1000 companies. They find that losers outperform previous winners over a
An Empirical of Carhart Model in Indian Stock Market
243
two year period by a statistically significant 1.7per cent per annum. On further
investigation they locate that such overreaction may in fact be a manifestation
of the small firm effect.
Aiyagari and Gertler (1997) study the overreaction of asset prices to
movements in short term interest rates, dividends, and asset supplies with the
help of a dynamic general equilibrium model of asset pricing. They analyze
that it is possible to have substantial departures of the market price from
the corresponding price under frictionless markets. Karan et.al. (2003),
test overreaction for the Istanbul Stock Exchange using price limits in two
sub-periods when the daily price limit is 10per cent and 20 per cent respectively.
They observe overreaction mainly in the second sub-period when the daily limit
is higher and changes in the trading volume that accompany overreaction in
prices. Up-limit hits are accompanied by increases in trading volume while
consecutive price falls are accompanied by decreasing trading volumes.
Antoniou et.al. (2005) investigate the existence of contrarian profits and
their sources for the Athenes Stock Exchange. Results indicate that contrarian
strategies produce statistically and economically significant profits even after
risk and market frictions are taken into considerations. Ali et.al. (2009)
investigate overreaction in the Malaysian stock market taking data for the period
from January 1987 to December 2006. They establish that loser has insignificantly
become loser and winner has significantly reversed in the subsequent period.
Du and Denning (2009) examine US and international stock price reaction to
common market-wide information over the period 1941-2006 and 1975-2006
respectively. They come across evidence of both under and over-reaction but it
is not systematic and further concludes that although investors might make
mistakes, they do not do so consistently. Rastogi and et.al. (2009) study
momentum and overreaction hypothesis in the Indian equity markets by taking
the adjusted monthly prices data for all NSE listed stocks for the period of 1996
to 2008 from the CMIE prowess database. S&P CNX 500 index is used as a
proxy for the market return. They find out strong substantiation for the presence
of momentum in all the categories, but weak evidence for the presence of
overreaction in the low and high cap stocks. The mid cap stocks demonstrate
strong overreaction. Thus in Indian Context there is dearth of literature
regarding overreaction hypothesis. This paper tries to bridge the above gap.
The objectives of the study is to test the impact of loser and winner portfolio in
the next period on the portfolio’s return and to test the importance of size, P/B
of the firm in their pricing .
3.
DATA & METHODOLOGY
Data: The closing prices of different stocks for a period 2009 and 2010 is taken
from www.nseindia.com historical data. Market returns of S&P CNX 500 of
the same period is taken from prowess database.
Portfolio construction: The three benchmark factors, i.e., HML, SMB, and
WML, from the 27 (3*3*3) three-way independently sorted size, book to market,
and momentum portfolios at each point in time t are calculated through the
following equations: This 3 way sorted benchmark factor portfolios, i.e. HML,
SMB, WML are created from the formulae given by Liew and Vassalon (2000).
244
Santosh Kumar & Tavishi
HML = 1/9 ((S1M1B3-S1M1B1) + (S1M2B3-S1M2B1)+ (S1M3B3-S1M3B1)+
(S2M1B3-S2M1B1) + (S2M2B3-S2M2B1) + (S2M3B3-S2M3B1) +
(1)
(S3M1B3-S3M1B1) + (S3M2B3-S3M2B1) + (S3M3B3-S3M3B1))
SMB = 1/9 ((S1M1B1-S3M1B1) + (S1M2B1-S3M2B1) + (S1M3B1-S3M3B)+
(S1M1B2-S3M1B2) + (S1M2B2-S3M2B2) + (S1M3B2-S3M3B2) +
(2)
(S1M1B3-S3M1B3) + (S1M2B3-S3M2B3) + (S1M3B3-S3M3B3))
WML = 1/9 ((S1M3B1-S1M1B1) + (S1M3B2-S1M1B2) + (S1M3B3-S1M1B3)
S1M1B3) + (S2M3B1-S2M1B1) + (S2M3 B2-S2M1B2) + (S2M3B3(3)
S2M1B3) + (S3M3 B1S3M1B1) + (S3M3 B2-S3M1B2) + (S3M3B3-S3M1B3))
In order to limit the number of test assets, the firms are assigned 27 (3*3*3)
portfolios based on the break points for the bottom 30 per cent , middle 40 per
cent and top 30 per cent of the ranked values where the first two characters of
the portfolio name indicate the size category the portfolio belongs to, the second
two characters indicate the momentum category, and the last two characters
the book value to market price category, with size, momentum and book to
market increasing from one to three.
The Table 1 presents the unique code of 27 portfolios and consequent features.
Table 1
Portfolio Construction and Description
Portfolio
Code
41
42
43
46
47
48
51
52
53
61
62
63
66
67
68
71
72
73
81
82
83
86
87
88
91
92
93
Market
Capitalization
Small
Medium
Large
Small
Medium
Large
Small
Medium
Large
Small
Medium
Large
Small
Medium
Large
Small
Medium
Large
Small
Medium
Large
Small
Medium
Large
Small
Medium
Large
BE/ME
High
High
High
Medium
Medium
Medium
Low
Low
Low
High
High
High
Medium
Medium
Medium
Low
Low
Low
High
High
High
Medium
Medium
Medium
Low
Low
Low
Cumulative
Return
Symbol
Loser
Loser
Loser
Loser
Loser
Loser
Loser
Loser
Loser
Moderate
Moderate
Moderate
Moderate
Moderate
Moderate
Moderate
Moderate
Moderate
Winner
Winner
Winner
Winner
Winner
Winner
Winner
Winner
Winner
S1B3M1
S2B3M1
S3B3M1
S1B2M1
S2B2M1
S3B2M1
S1B1M1
S2B1M1
S3B1M1
S1B3M2
S2B3M2
S3B3M2
S1B2M2
S2B2M2
S3B2M2
S1B1M2
S2B1M2
S3B1M2
S1B3M3
S2B3M3
S3B3M3
S1B2M3
S2B2M3
S3B2M3
S1B1M3
S2B1M3
S3B1M3
The Table 1 presents the unique code of 27 portfolios and consequent features.
An Empirical of Carhart Model in Indian Stock Market
245
The four factor model suggested by the prior macroeconomic asset pricing
literature is used in the analysis, which is as follows:
Rit = α1 + β1 (Rmt) + β2 (SMBit) + β3 (HMLit) + β4 (WMLit ) +ε
(4)
Where SMBit is the return on a zero investment portfolio long on large and
short on small market capitalization stocks. SMB is meant to mimic the risk
factor and returns related to size and SMB is largely clear of B/P effect, focused
on the different behavior of small and big stocks. HMLit is the return on a zero
investment portfolio long on high and short on low value book to market ratio
stocks. It is meant to mimic the risk factor in returns related to values (Book/
Market Price). It is relatively free of size effect. WMLit is the return on a zero
investment portfolio long on loser and short on winner stocks. The entire four
factor model is tested with the help of SAS programming in following major
steps: First the returns of stock price data is calculated , followed by computation
of cumulative return for each stock. Then the return is converted in to 30, 70
and 100 percentile and unique code is assigned to market’s return, P/B, size
and cumulative return of stock which is later added.then Segregation into
different portfolios on the basis of unique code and transposition into column
format with column variables as 27 portfolios and portfolio return and market
return takes place Atlast after computing SMB and HML and WML, all 27
portfolios are regressed to test the significance of coefficients of different factors.
4.
RESULTS AND DISCUSSION
4.1. Pricing Ability of the Carhart Model
The results presented in Table 2 indicate that in almost all 27 portfolios’ (3*3*3)
market return and size is significant in 100 per cent and 77 per cent of the
cases respectively and P/B is also significant in 75 per cent of the sampled
portfolios. The momentum (WML) factor is not significant in Indian scenario.
In all the 27 portfolios the Fama French model reflects higher reliability and
explanation capacity of the price of the firm. Thus the fourth factor (Winner
minus Looser i.e. momentum factor) is not significant in Indian stock market.
The market return estimate is significant in 100% sampled portfolios
indicating the reliability of fundamental CAPM model. Thus the movement of
benchmark or market has a deciding role in the portfolio return. The size effect
(Table 2) is pronounced in almost all portfolios except in the larger companies.
Thus the results exhibit consistency with the previous work that the small size
of the company leads to better return even more than 200 per cent in few cases.
The higher return of the portfolio (Table 2 and Table 3) is evident in the
cases of medium or high values of B/P. Thus the Three Factor Model represents
that the price of the stock can be well explained in the range of 60 to 80per cent
with the help of market return, size effect and B/P values. It is attributed to
higher significant in almost all portfolios except 3 or 4. Further it is also observed
that higher return of portfolio is mainly in higher B/P values.
Out of the 27 portfolios, 14 have insignificant value of WML indicating that
the overreaction is not justified in majority of portfolios. Thus it is evident that
WML is not a key attribute or factor in Carhart model.
246
Santosh Kumar & Tavishi
Table 2
Regression Coefficients of 27 Portfolios in Carhart Model
Four Factors of Carhart Model
Portfolio
Code
Portfolio
Symbol
Rm
HML
SMB
41
S1B3M1
0.90*
1.16574*
1.03303*
-0.73442*
42
S2B3M1
0.83*
0.47527*
0.85369*
-0.22211
43
S3B3M1
0.96*
0.77128*
-0.34916*
46
S1B2M1
0.83*
0.9697*
0.41665*
-0.30609*
47
S2B2M1
0.93*
0.47702*
0.3749*
-0.22103*
48
S3B2M1
0.86*
0.16309*
51
S1B1M1
1.16*
0.98812*
52
S2B1M1
0.83*
53
S3B1M1
0.94*
61
S1B3M2
62
-0.01134
0.18102
WML
-0.60796*
-0.4161*
-1.93312*
0.48828*
-0.1633
-0.85962*
0.06606
-0.13674*
-0.19695*
0.96*
1.10809*
0.82086*
-0.15828
S2B3M2
0.86*
0.57322*
0.58626*
-0.00055406
63
S3B3M2
1.05*
0.03955
1.09681*
-0.1758
66
S1B2M2
0.80*
1.02311*
0.69837*
-0.22935
67
S2B2M2
0.95*
0.54834*
0.25765*
-0.18577
68
S3B2M2
1.08*
0.07729
0.40804*
-0.25261*
71
S1B1M2
1.16*
0.97052*
-0.86022*
-0.3907
72
S2B1M2
0.90*
0.54916*
0.10532
-0.173
73
S3B1M2
0.93*
0.2021*
-0.07421
0.05858
81
S1B3M3
1.03*
1.12354*
0.72398*
0.05523
82
S2B3M3
0.94*
0.63582*
0.81524*
0.27306*
83
S3B3M3
1.01*
-0.16796*
0.49548*
0.10097
86
S1B2M3
0.84*
0.90682*
0.61022*
0.59184*
87
S2B2M3
1.01*
0.55691*
0.35082*
0.00233
88
S3B2M3
0.80*
0.04909
0.17677*
0.26235*
91
S1B1M3
1.06*
1.24116*
-0.13836
1.95827*
92
S2B1M3
0.72*
0.35762*
-0.08969
0.31153*
93
S3B1M3
0.83*
0.07893
-0.03004
0.01395
Significant at 5% level of significance.
Almost all 27 portfolios’ (3*3*3) market return and size is significant in 100 per cent and 77 per cent
of the cases respectively and P/B is also significant in 75 per cent of the sampled portfolios. The size
effect is pronounced in almost all portfolios except in the larger companies.
It is evident from the above results (Table 2 and Table 3) that the portfolios
which gave good returns consists majority of those companies which have low
to medium book to market ratio and are small to medium in size. These portfolios
consist of losers, showing that losers outperform in future and gives high returns.
On the other hand the portfolios which gave low returns, majority of them
consists of mediocre to winner companies, medium to large size and medium to
high book to market ratio. This shows that winners of the past underperform in
the future. This analysis again supports contrarian hypothesis for the Indian
247
An Empirical of Carhart Model in Indian Stock Market
Table 3
Annualized Return of 27 Portfolios
Portfolio Code
Portfolio
Annual Return (%)
41
S1B3M1
37.2
42
S2B3M1
64.4
43
S3B3M1
13.2
46
S1B2M1
60.7
47
S2B2M1
229.3
48
S3B2M1
87.5
51
S1B1M1
99.3
52
S2B1M1
204.0
53
S3B1M1
475.3
61
S1B3M2
74.5
62
S2B3M2
48.2
63
S3B3M2
20.0
66
S1B2M2
90.1
67
S2B2M2
186.9
68
S3B2M2
21.8
71
S1B1M2
29.1
72
S2B1M2
98.3
73
S3B1M2
37.2
81
S1B3M3
33.1
82
S2B3M3
32.4
83
S3B3M3
13.7
86
S1B2M3
38.4
87
S2B2M3
89.7
88
S3B2M3
25.8
91
S1B1M3
41.7
92
S2B1M3
75.2
93
S3B1M3
59.8
Out of the 27 portfolios, 14 have insignificant value of WML indicating that the overreaction is not
justified in majority of portfolios.
stock market. The sign of coefficients has a significant role in these equations.
As in the equations coefficient of SMB and HML are positive (Table 2) in majority
of the portfolios thus showing that these have a direct effect on the portfolio’s
returns. But however coefficient of WML has a negative (Table 2) sign in majority
of the equations showing inverse relationship but insignificant in majority of
the cases.
5.
CONCLUSIONS
From the above analysis the work concludes that size factor, book to market
ratio and return of market play a significant role in determining portfolio’s
returns; however it was seen that momentum effect is not evident for the Indian
stock market. Further it is also observed that the past losers were seen to perform
248
Santosh Kumar & Tavishi
well in future by giving higher returns while the past winners were
underperforming and were giving very low rate of returns. Therefore contrarian
profits do seem to exist in the Indian Stock market and therefore contrarian
investments strategy would be the most suitable investment strategy.
References
Aiyagari, S. Rao, and Gertler, Mark (1997), Overreaction of Asset Prices in General
Equilibrium, Journal of Economic Literature, Classification Numbers: G1, E0,
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Ali, Norli, Annuar, Md. Nassir, Hassan, Taufiq and Abidin, Sazali Zainal (2009), Does
Bursa Malaysia Overreact?, International Research Journal of Finance and
Economics, ISSN 1450-2887 Issue 34 (2009)© Euro Journals Publishing, Inc. 2009
http://www.eurojournals.com/finance.htm.
Antoniou, Antonios and Galariotis, Emilios C. and Spyrou, Spyros I. (2005), Contrarian
Profits and the Overreaction Hypothesis: The Case of the Athens Stock Exchange,
European Financial Management, Vol. 11, No. 1, 71-98.
Bondt Werner F.M. De and Thaler Richard H. (1985), Does Stock Markets Overreact?
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Bondt, Werner F. M. De and Thaler, Richard H., Further Evidence on Investor
Overreaction and Stock Market Seasonality, The Journal of Finance, Vol. 42, No.
3, Papers and Proceedings of the Forty-Fifth Annual Meeting of the American
Finance Association, New Orleans, Louisiana, December 28-30, 1986. (Jul., 1987),
pp. 557-581.
Bondt, Werner F. M. De and Thaler, Richard H. (1990), Do Security Analysis Overreact?
The American Economic Review, Vol. 80, No. 2, May.
Du, Ding and Denning, Karen C. (2009), US and International Stock Reaction to Common
Information”, International Research Journal of Finance and Economics,
ISSN 1450-2887 Issue 24 (2009) © Euro Journals Publishing, Inc.
Karan, Mehmet Baha , Tarim, S. Armagan, Muradoglu, Gülnur (2003), Overreaction to
Daily Price Limits in the Istanbul Stock Exchange, January.
Lawrence, Kryzanowski and Hao, Zhang (1992), “The Contrarian Investment Strategy
Does Not Work in Canadian Markets”, Journal of Financial and Quantitative
Analysis, Vol. 27. No. 3, September 1992, http://www.tandf.co.uk/journals.
Page, M. J. and Way, C. V. (1992), Stock Market Overreaction: The South African
Evidence, Investment Analysis Journal.
Rastogi, Nikhil, Chaturvedula, Chakrapani, Bang, Nupur Pavan (2009), Momentum
and Overreaction in Indian Capital Markets, International Research Journal of
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Paul, Zarowin (1990), Size, Seasonality and Stock Market Overreaction, Journal of
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249
An Empirical of Carhart Model in Indian Stock Market
APPENDIX
Table A1
Detailed Description of 27 Portfolios (SAS Output)
(1) The SAS System
The REG Procedure
Model: MODEL1
Dependent Variable: _41
Number of Observations Read
250
Number of Observations Used
250
Analysis of Variance
DF
Sum of
Squares
Mean
Square
F Value
Pr > F
Model
4
Error
245
0.06418
0.01604
250.96
<.0001
0.01566
0.00006393
249
0.07984
Root MSE
0.00800
R-Square
0.8038
Dependent Mean
0.00155
Adj R-Sq
0.8006
Source
Corrected Total
Coeff Var
514.34163
Parameter Estimates
Variable
DF
Parameter
Estimate
Standard
Error t
Intercept
1
0.00138
0.00054522
2.54
0.0117
mktreturns
1
0.90270
0.05470
16.50
<.0001
hml
1
1.03303
0.10510
9.83
<.0001
smb
1
1.16574
0.06719
17.35
<.0001
wml
1
-0.73442
0.14466
-5.08
<.0001
Value
Pr > |t|
250
Santosh Kumar & Tavishi
(2) The SAS System
The REG Procedure
Model: MODEL2
Dependent Variable: _42
Number of Observations Read
250
Number of Observations Used
250
Analysis of Variance
DF
Sum of
Squares
Model
4
Error
245
Corrected Total
249
0.04786
Source
Root MSE
Mean
Square
F Value
Pr > F
0.03744
0.00936
219.96
<.0001
0.01043
0.00004255
0.00652
R-Square
0.7822
Dependent Mean
0.00043894
Adj R-Sq
0.7786
Coeff Var
1486.14409
Parameter Estimates
Parameter
Estimate
Standard
Error t
Variable
DF
Value
Pr > |t|
Intercept
1
0.00047311
0.00044482
1.06
0.2886
mktreturns
1
0.83203
0.04463
18.64
<.0001
hml
1
0.85369
0.08574
9.96
<.0001
smb
1
0.47527
0.05482
8.67
<.0001
wml
1
-0.22211
0.11802
-1.88
0.0610
251
An Empirical of Carhart Model in Indian Stock Market
(3) The SAS System
The REG Procedure
Model: MODEL3
Dependent Variable: _43
Number of Observations Read
250
Number of Observations Used
250
Analysis of Variance
Source
Sum of
Squares
DF
Mean
Square
Model
4
0.04062
0.01015
Error
245
0.01166
0.00004758
249
0.05228
Corrected Total
Root MSE
F Value
Pr > F
213.42
<.0001
0.00690
R-Square
0.7770
Dependent Mean
0.00039462
Adj R-Sq
0.7734
Coeff Var
1747.99316
Parameter Estimates
Parameter
Estimate
Standard
Error t
Variable
DF
Value
Pr > |t|
Intercept
1
0.00017084
0.00047037
0.36
0.7168
mktreturns
1
0.96467
0.04719
20.44
<.0001
hml
1
0.77128
0.09067
8.51
<.0001
smb
1
-0.01134
0.05796
-0.20
0.8451
wml
1
-0.34916
0.12480
-2.80
0.0056
252
Santosh Kumar & Tavishi
(4) The SAS System
The REG Procedure
Model: MODEL4
Dependent Variable: _46
Number of Observations Read
250
Number of Observations Used
250
Analysis of Variance
Source
DF
Sum of
Squares
Mean
Square
F Value
Pr > F
Model
4
0.04069
0.01017
218.75
<.0001
Error
245
0.01139
0.00004651
Corrected Total
249
0.05209
Root MSE
0.00682
R-Square
0.7813
Dependent Mean
0.00206
Adj R-Sq
0.7777
Coeff Var
330.85490
Parameter Estimates
Variable
DF
Parameter
Estimate
Standard
Error t
Intercept
1
0.00131
0.00046504
2.82
0.0052
mktreturns
1
0.83929
0.04665
17.99
<.0001
hml
1
0.41665
0.08964
4.65
<.0001
smb
1
0.96970
0.05731
16.92
<.0001
wml
1
-0.30609
0.12338
-2.48
0.0138
Value
Pr > |t|
253
An Empirical of Carhart Model in Indian Stock Market
(5) The SAS System
The REG Procedure
Model: MODEL5
Dependent Variable: _47
Number of Observations Read
250
Number of Observations Used
250
Analysis of Variance
Source
DF
Sum of
Squares
Mean
Square
F Value
Pr > F
Model
4
0.03394
0.00848
219.59
<.0001
Error
245
0.00947
0.00003864
Corrected Total
249
0.04340
Root MSE
0.00622
R-Square
0.7819
Dependent Mean
0.00199
Adj R-Sq
0.7783
Coeff Var
312.29606
Parameter Estimates
Parameter
Estimate
Standard
Error t
Variable
DF
Value
Pr > |t|
Intercept
1
0.00120
0.00042386
2.83
0.0051
mktreturns
1
0.93210
0.04252
21.92
<.0001
hml
1
0.37490
0.08170
4.59
<.0001
smb
1
0.47702
0.05223
9.13
<.0001
wml
1
-0.22103
0.11246
-1.97
0.0505
254
Santosh Kumar & Tavishi
(6) The SAS System
The REG Procedure
Model: MODEL6
Dependent Variable: _48
Number of Observations Read
250
Number of Observations Used
250
Analysis of Variance
DF
Sum of
Squares
Model
4
Error
245
Corrected Total
249
0.03889
Source
Mean
Square
F Value
Pr > F
0.02478
0.00620
107.58
<.0001
0.01411
0.00005759
Root MSE
0.00759
R-Square
0.6372
Dependent Mean
0.00273
Adj R-Sq
0.6313
Coeff Var
278.27134
Parameter Estimates
Variable
DF
Parameter
Estimate
Standard
Error t
Intercept
1
0.00160
0.00051748
3.10
0.0022
mktreturns
1
0.86183
0.05192
16.60
<.0001
hml
1
0.18102
0.09975
1.81
0.0708
smb
1
0.16309
0.06377
2.56
0.0111
wml
1
-0.60796
0.13730
-4.43
<.0001
Value
Pr > |t|
255
An Empirical of Carhart Model in Indian Stock Market
(7) The SAS System
The REG Procedure
Model: MODEL7
Dependent Variable: _51
Number of Observations Read
250
Number of Observations Used
250
Analysis of Variance
DF
Sum of
Squares
Model
4
Error
245
Corrected Total
249
0.09385
Source
Mean
Square
F Value
Pr > F
0.06454
0.01613
134.87
<.0001
0.02931
0.00011963
Root MSE
0.01094
R-Square
0.6877
Dependent Mean
0.00276
Adj R-Sq
0.6826
Coeff Var
396.34670
Parameter Estimates
Parameter
Estimate
Standard
Error t
Variable
DF
Value
Pr > |t|
Intercept
1
-0.00042050
0.00074585
-0.56
0.5734
mktreturns
1
1.16225
0.07483
15.53
<.0001
hml
1
-0.41612
0.14377
-2.89
0.0041
smb
1
0.98812
0.09191
10.75
<.0001
wml
1
-1.93312
0.19789
-9.77
<.0001
256
Santosh Kumar & Tavishi
(8) The SAS System
The REG Procedure
Model: MODEL8
Dependent Variable: _52
Number of Observations Read
250
Number of Observations Used
250
Analysis of Variance
DF
Sum of
Squares
Model
4
Error
245
Corrected Total
249
0.04397
Source
Mean
Square
F Value
Pr > F
0.02543
0.00636
84.05
<.0001
0.01853
0.00007565
Root MSE
0.00870
R-Square
0.5785
Dependent Mean
0.00303
Adj R-Sq
0.5716
Coeff Var
286.89785
Parameter Estimates
Variable
DF
Parameter
Estimate
Standard
Error t
Intercept
1
0.00124
0.00059309
2.10
0.0369
mktreturns
1
0.83919
0.05950
14.10
<.0001
hml
1
-0.16330
0.11432
-1.43
0.1544
smb
1
0.48828
0.07309
6.68
<.0001
wml
1
-0.85962
0.15736
-5.46
<.0001
Value
Pr > |t|
257
An Empirical of Carhart Model in Indian Stock Market
(9) The SAS System
The REG Procedure
Model: MODEL9
Dependent Variable: _53
Number of Observations Read
250
Number of Observations Used
250
Analysis of Variance
DF
Sum of
Squares
Model
4
Error
245
Corrected Total
249
0.02803
Source
Mean
Square
F Value
Pr > F
0.02367
0.00592
332.73
<.0001
0.00436
0.00001779
Root MSE
0.00422
R-Square
0.8445
Dependent Mean
0.00273
Adj R-Sq
0.8420
Coeff Var
154.74690
Parameter Estimates
Variable
DF
Parameter
Estimate
Standard
Error t
Intercept
1
0.00125
mktreturns
1
0.94718
hml
1
smb
wml
Value
Pr > |t|
0.00028759
4.35
<.0001
0.02885
32.83
<.0001
-0.13674
0.05544
-2.47
0.0143
1
0.06606
0.03544
1.86
0.0635
1
-0.19695
0.07630
-2.58
0.0104
258
Santosh Kumar & Tavishi
(10) The SAS System
The REG Procedure
Model: MODEL10
Dependent Variable: _61
Number of Observations Read
250
Number of Observations Used
250
Analysis of Variance
DF
Sum of
Squares
Model
4
Error
245
249
0.06650
Source
Corrected Total
Mean
Square
F Value
Pr > F
0.05988
0.01497
554.43
<.0001
0.00662
0.00002700
Root MSE
0.00520
R-Square
0.9005
Dependent Mean
0.00101
Adj R-Sq
0.8989
Coeff Var
512.40033
Parameter Estimates
Parameter
Estimate
Standard
Error t
Variable
DF
Value
Pr > |t|
Intercept
1
0.00074807
0.00035435
2.11
0.0358
mktreturns
1
0.96878
0.03555
27.25
<.0001
hml
1
0.82086
0.06830
12.02
<.0001
smb
1
1.10809
0.04367
25.38
<.0001
wml
1
-0.15828
0.09402
-1.68
0.0935
259
An Empirical of Carhart Model in Indian Stock Market
(11) The SAS System
The REG Procedure
Model: MODEL11
Dependent Variable: _62
Number of Observations Read
250
Number of Observations Used
250
Analysis of Variance
Source
DF
Sum of
Squares
Mean
Square
F Value
Pr > F
Model
4
0.03537
0.00884
170.68
<.0001
Error
245
0.01269
0.00005181
Corrected Total
249
0.04806
Root MSE
0.00720
R-Square
0.7359
Dependent Mean
0.00184
Adj R-Sq
0.7316
Coeff Var
391.47079
Parameter Estimates
Variable
DF
Parameter
Estimate
Standard
Error t
Intercept
1
0.00153
0.00049083
3.11
0.0021
mktreturns
1
0.86897
0.04924
17.65
<.0001
hml
1
0.58626
0.09461
6.20
<.0001
smb
1
0.57322
0.06049
9.48
<.0001
wml
1
-0.00055406
0.13023
-0.00
0.9966
Value
Pr > |t|
260
Santosh Kumar & Tavishi
(12) The SAS System
The REG Procedure
Model: MODEL12
Dependent Variable: _63
Number of Observations Read
250
Number of Observations Used
250
Analysis of Variance
DF
Sum of
Squares
Model
4
Error
245
Corrected Total
249
0.07453
Source
Root MSE
Mean
Square
F Value
Pr > F
0.05534
0.01384
176.67
<.0001
0.01919
0.00007832
0.00885
R-Square
0.7426
Dependent Mean
0.00064888
Adj R-Sq
0.7384
Coeff Var
1363.81956
Parameter Estimates
Parameter
Estimate
Standard
Error t
Variable
DF
Value
Pr > |t|
Intercept
1
0.00087308
0.00060346
1.45
0.1492
mktreturns
1
1.05165
0.06054
17.37
<.0001
hml
1
1.09681
0.11632
9.43
<.0001
smb
1
0.03955
0.07437
0.53
0.5953
wml
1
-0.17580
0.16011
-1.10
0.2733
261
An Empirical of Carhart Model in Indian Stock Market
(13) The SAS System
The REG Procedure
Model: MODEL13
Dependent Variable: _66
Number of Observations Read
250
Number of Observations Used
250
Analysis of Variance
DF
Sum of
Squares
Model
4
Error
245
Corrected Total
249
0.06590
Root MSE
0.00926
R-Square
0.6811
Dependent Mean
0.00256
Adj R-Sq
0.6758
Source
Coeff Var
Mean
Square
F Value
Pr > F
0.04488
0.01122
130.79
<.0001
0.02102
0.00008579
361.97208
Parameter Estimates
Parameter
Estimate
Standard
Error t
1
0.00229
0.00063160
3.63
0.0003
1
0.80723
0.06336
12.74
<.0001
hml
1
0.69837
0.12175
5.74
<.0001
smb
1
1.02311
0.07783
13.14
<.0001
wml
1
-0.22935
0.16758
-1.37
0.1724
Variable
DF
Intercept
mktreturns
Value
Pr > |t|
262
Santosh Kumar & Tavishi
(14) The SAS System
The REG Procedure
Model: MODEL14
Dependent Variable: _67
Number of Observations Read
250
Number of Observations Used
250
Analysis of Variance
DF
Sum of
Squares
Model
4
Error
245
Corrected Total
249
0.04207
Root MSE
0.00561
R-Square
0.8166
Dependent Mean
0.00235
Adj R-Sq
0.8136
Source
Coeff Var
Mean
Square
F Value
Pr > F
0.03436
0.00859
272.75
<.0001
0.00772
0.00003149
238.78716
Parameter Estimates
Variable
DF
Parameter
Estimate
Standard
Error t
Intercept
1
0.00137
0.00038266
3.57
0.0004
mktreturns
1
0.95152
0.03839
24.79
<.0001
hml
1
0.25765
0.07376
3.49
0.0006
smb
1
0.54834
0.04716
11.63
<.0001
wml
1
-0.18577
0.10153
-1.83
0.0685
Value
Pr > |t|
263
An Empirical of Carhart Model in Indian Stock Market
(15) The SAS System
The REG Procedure
Model: MODEL15
Dependent Variable: _68
Number of Observations Read 250
Number of Observations Used 250
Analysis of Variance
DF
Sum of
Squares
Model
4
Error
245
Corrected Total
249
0.04876
Source
Root MSE
Dependent Mean
Mean
Square
F Value
Pr > F
0.04043
0.01011
297.39
<.0001
0.00833
0.00003399
0.00583
R-Square
0.8292
0.00084494
Adj R-Sq
0.8264
Coeff Var
690.01481
Parameter Estimates
Parameter
Estimate
Standard
Error t
1
-0.00003229
0.00039756
-0.08
0.9353
1
1.08840
0.03988
27.29
<.0001
hml
1
0.40804
0.07664
5.32
<.0001
smb
1
0.07729
0.04899
1.58
0.1160
wml
1
-0.25261
0.10548
-2.39
0.0174
Variable
DF
Intercept
mktreturns
Value
Pr > |t|
264
Santosh Kumar & Tavishi
(16) The SAS System
The REG Procedure
Model: MODEL16
Dependent Variable: _71
Number of Observations Read
250
Number of Observations Used
250
Analysis of Variance
DF
Sum of
Squares
Model
4
Error
245
Corrected Total
249
0.09744
Source
Mean
Square
F Value
Pr > F
0.05061
0.01265
66.18
<.0001
0.04684
0.00019117
Root MSE
0.01383
R-Square
0.5193
Dependent Mean
0.00170
Adj R-Sq
0.5115
Coeff Var
815.04650
Parameter Estimates
Variable
DF
Parameter
Estimate
Standard
Error t
Intercept
1
-0.00137
0.00094284
-1.46
0.1468
mktreturns
1
1.16780
0.09459
12.35
<.0001
hml
1
-0.86022
0.18174
-4.73
<.0001
smb
1
0.97052
0.11619
8.35
<.0001
wml
1
-0.39070
0.25015
-1.56
0.1196
Value
Pr > |t|
265
An Empirical of Carhart Model in Indian Stock Market
(17) The SAS System
The REG Procedure
Model: MODEL17
Dependent Variable: _72
Number of Observations Read
250
Number of Observations Used
250
Analysis of Variance
DF
Sum of
Squares
Model
4
Error
245
Corrected Total
249
0.03892
Source
Mean
Square
F Value
Pr > F
0.02952
0.00738
192.35
<.0001
0.00940
0.00003837
Root MSE
0.00619
R-Square
0.7585
Dependent Mean
0.00309
Adj R-Sq
0.7545
Coeff Var
200.68211
Parameter Estimates
Variable
DF
Parameter
Estimate
Standard
Error t
Intercept
1
0.00195
mktreturns
1
0.90055
hml
1
smb
wml
Value
Pr > |t|
0.00042239
4.61
<.0001
0.04238
21.25
<.0001
0.10532
0.08142
1.29
0.1971
1
0.54916
0.05205
10.55
<.0001
1
-0.17300
0.11207
-1.54
0.1240
266
Santosh Kumar & Tavishi
(18) The SAS System
The REG Procedure
Model: MODEL18
Dependent Variable: _73
Number of Observations Read
250
Number of Observations Used
250
Analysis of Variance
DF
Sum of
Squares
Model
4
Error
245
Corrected Total
249
0.03096
Source
Mean
Square
F Value
Pr > F
0.02443
0.00611
229.17
<.0001
0.00653
0.00002665
Root MSE
0.00516
R-Square
0.7891
Dependent Mean
0.00207
Adj R-Sq
0.7857
Coeff Var
249.11370
Parameter Estimates
Parameter
Estimate
Standard
Error t
1
0.00080794
0.00035201
2.30
0.0226
1
0.93440
0.03531
26.46
<.0001
hml
1
-0.07421
0.06785
-1.09
0.2752
smb
1
0.20210
0.04338
4.66
<.0001
wml
1
0.05858
0.09340
0.63
0.5311
Variable
DF
Intercept
mktreturns
Value
Pr > |t|
267
An Empirical of Carhart Model in Indian Stock Market
(19) The SAS System
The REG Procedure
Model: MODEL19
Dependent Variable: _81
Number of Observations Read
250
Number of Observations Used
250
Analysis of Variance
DF
Sum of
Squares
Model
4
Error
245
Corrected Total
249
0.07189
Source
Root MSE
Dependent Mean
Mean
Square
F Value
Pr > F
0.06232
0.01558
398.63
<.0001
0.00958
0.00003908
0.00625
R-Square
0.8668
0.00099021
Adj R-Sq
0.8646
Coeff Var
631.33969
Parameter Estimates
Parameter
Estimate
Standard
Error t
Variable
DF
Value
Pr > |t|
Intercept
1
0.00060957
0.00042630
1.43
0.1540
mktreturns
1
1.03041
0.04277
24.09
<.0001
hml
1
0.72398
0.08217
8.81
<.0001
smb
1
1.12354
0.05253
21.39
<.0001
wml
1
0.05523
0.11311
0.49
0.6258
268
Santosh Kumar & Tavishi
(20) The SAS System
The REG Procedure
Model: MODEL20
Dependent Variable: _82
Number of Observations Read
250
Number of Observations Used
250
Analysis of Variance
DF
Sum of
Squares
Model
4
Error
245
Corrected Total
249
0.05829
Root MSE
0.00713
R-Square
0.7863
Dependent Mean
0.00102
Adj
R-Sq
Source
Coeff Var
Mean
Square
F Value
Pr > F
0.04584
0.01146
225.42
<.0001
0.01245
0.00005083
0.7829
699.19716
Parameter Estimates
Variable
DF
Parameter
Estimate
Standard
Error t
Intercept
1
0.00108
0.00048619
2.22
0.0273
mktreturns
1
0.94160
0.04878
19.30
<.0001
hml
1
0.81524
0.09372
8.70
<.0001
smb
1
0.63582
0.05991
10.61
<.0001
wml
1
0.27306
0.12900
2.12
0.0353
Value
Pr > |t|
269
An Empirical of Carhart Model in Indian Stock Market
(21) The SAS System
The REG Procedure
Model: MODEL21
Dependent Variable: _83
Number of Observations Read
250
Number of Observations Used
250
Analysis of Variance
DF
Sum of
Squares
Model
4
Error
245
Corrected Total
249
0.04917
Source
Root MSE
Mean
Square
F Value
Pr > F
0.03773
0.00943
202.03
<.0001
0.01144
0.00004669
0.00683
R-Square
0.7674
Dependent Mean
0.00040224
Adj R-Sq
0.7636
Coeff Var
1698.82601
Parameter Estimates
Parameter
Estimate
Standard
Error t
Variable
DF
Value
Pr > |t|
Intercept
1
-0.00004046
0.00046597
-0.09
0.9309
mktreturns
1
1.01879
0.04675
21.79
<.0001
hml
1
0.49548
0.08982
5.52
<.0001
smb
1
-0.16796
0.05742
-2.93
0.0038
wml
1
0.10097
0.12363
0.82
0.4149
270
Santosh Kumar & Tavishi
(22) The SAS System
The REG Procedure
Model: MODEL22
Dependent Variable: _86
Number of Observations Read
250
Number of Observations Used
250
Analysis of Variance
DF
Sum of
Squares
Model
4
Error
245
Corrected Total
249
0.05766
Source
Mean
Square
F Value
Pr > F
0.04016
0.01004
140.53
<.0001
0.01750
0.00007144
Root MSE
0.00845
R-Square
0.6964
Dependent Mean
0.00122
Adj R-Sq
0.6915
Coeff Var
694.92978
Parameter Estimates
Variable
DF
Parameter
Estimate
Standard
Error t
Intercept
1
0.00126
0.00057636
2.18
0.0304
mktreturns
1
0.80234
0.05782
13.88
<.0001
hml
1
0.61022
0.11110
5.49
<.0001
smb
1
0.90682
0.07103
12.77
<.0001
wml
1
0.59184
0.15292
3.87
0.0001
Value
Pr > |t|
271
An Empirical of Carhart Model in Indian Stock Market
(23) The SAS System
The REG Procedure
Model: MODEL23
Dependent Variable: _87
Number of Observations Read
250
Number of Observations Used
250
Analysis of Variance
DF
Sum of
Squares
Model
4
Error
245
Corrected Total
249
0.03666
Source
Mean
Square
F Value
Pr > F
0.02843
0.00711
211.55
<.0001
0.00823
0.00003360
Root MSE
0.00580
R-Square
0.7755
Dependent Mean
0.00211
Adj R-Sq
0.7718
Coeff Var
274.88525
Parameter Estimates
Variable
DF
Parameter
Estimate
Standard
Error t
Intercept
1
0.00152
0.00039528
3.84
0.0002
mktreturns
1
0.81841
0.03966
20.64
<.0001
hml
1
0.35082
0.07619
4.60
<.0001
smb
1
0.55691
0.04871
11.43
<.0001
wml
1
0.00233
0.10488
0.02
0.9823
Value
Pr > |t|
272
Santosh Kumar & Tavishi
(24) The SAS System
The REG Procedure
Model: MODEL24
Dependent Variable: _88
Number of Observations Read
250
Number of Observations Used
250
Analysis of Variance
DF
Sum of
Squares
Model
4
Error
245
Corrected Total
249
0.03973
Source
Mean
Square
F Value
Pr > F
0.03309
0.00827
305.27
<.0001
0.00664
0.00002710
Root MSE
0.00521
R-Square
0.8329
Dependent Mean
0.00133
Adj R-Sq
0.8302
Coeff Var
391.87336
Parameter Estimates
Variable
DF
Parameter
Estimate
Standard
Error t
Intercept
1
0.00043038
0.00035496
1.21
0.2265
mktreturns
1
1.04147
0.03561
29.25
<.0001
hml
1
0.17677
0.06842
2.58
0.0104
smb
1
0.04909
0.04374
1.12
0.2628
wml
1
0.26235
0.09418
2.79
0.0058
Value
Pr > |t|
273
An Empirical of Carhart Model in Indian Stock Market
(25) The SAS System
The REG Procedure
Model: MODEL25
Dependent Variable: _91
Number of Observations Read
250
Number of Observations Used
250
Analysis of Variance
DF
Sum of
Squares
Model
4
Error
245
Corrected Total
249
0.10046
Root MSE
0.01188
R-Square
0.6558
Dependent Mean
0.00143
Adj R-Sq
0.6501
Source
Coeff Var
Mean
Square
F Value
Pr > F
0.06588
0.01647
116.68
<.0001
0.03458
0.00014114
830.48793
Parameter Estimates
Parameter
Estimate
Standard
Error t
Variable
DF
Value
Pr > |t|
Intercept
1
0.00066731
0.00081013
0.82
0.4109
mktreturns
1
1.06391
0.08127
13.09
<.0001
hml
1
-0.13836
0.15616
-0.89
0.3765
smb
1
1.24116
0.09983
12.43
<.0001
wml
1
1.95827
0.21495
9.11
<.0001
274
Santosh Kumar & Tavishi
(26) The SAS System
The REG Procedure
Model: MODEL26
Dependent Variable: _92
Number of Observations Read
250
Number of Observations Used
250
Analysis of Variance
DF
Sum of
Squares
Model
4
Error
245
Corrected Total
249
0.02566
Source
Mean
Square
F Value
Pr > F
0.01671
0.00418
114.39
<.0001
0.00895
0.00003652
Root MSE
0.00604
R-Square
0.6513
Dependent Mean
0.00222
Adj R-Sq
0.6456
Coeff Var
271.92912
Parameter Estimates
Variable
DF
Parameter
Estimate
Standard
Error t
Intercept
1
0.00129
0.00041207
3.12
0.0020
mktreturns
1
0.72797
0.04134
17.61
<.0001
hml
1
-0.08969
0.07943
-1.13
0.2599
smb
1
0.35762
0.05078
7.04
<.0001
wml
1
0.31153
0.10933
2.85
0.0048
Value
Pr > |t|
275
An Empirical of Carhart Model in Indian Stock Market
( 27) The SAS System
The REG Procedure
Model: MODEL27
Dependent Variable: _93
Number of Observations Read
250
Number of Observations Used
250
Analysis of Variance
DF
Sum of
Squares
Model
4
Error
245
Corrected Total
249
0.02498
Source
Mean
Square
F Value
Pr > F
0.01932
0.00483
208.90
<.0001
0.00566
0.00002312
Root MSE
0.00481
R-Square
0.7733
Dependent Mean
0.00249
Adj R-Sq
0.7696
Coeff Var
193.04513
Parameter Estimates
Variable
DF
Parameter
Estimate
Standard
Error t
Intercept
1
0.00141
mktreturns
1
0.83634
hml
1
smb
wml
Value
Pr > |t|
0.00032785
4.31
<.0001
0.03289
25.43
<.0001
-0.03004
0.06320
-0.48
0.6350
1
0.07893
0.04040
1.95
0.0519
1
0.01395
0.08699
0.16
0.8727
If we look at the equations of these portfolios, then portfolio 41’s equation is
r = Rf + beta (Km-Rf) + bs.SMB + bv.HML + bw.WML
Table A2
Detailed Representation of Carhart Model for 27 Portfolios
Portfolio no 41
r = 0.00138 + 0.90270 (Km-Rf) + 1.16574SMB + 1.03303HML -0.73442 WML
Portfolio no 42
r = 0.00047311 + 0.83203 (Km-Rf) + 0.47527 SMB + 0.85369 HML -0.22211 WML
Portfolio no 43
r = 0.00017084 + 0.96467 (Km-Rf) - 0.01134SMB + 0.77128HML - 0.34916 WML
Portfolio no 46
r = 0.00131 + 0.83929 (Km-Rf) + 0.96970 SMB + 0.41665 HML - 0.30609 WML
Portfolio no 47
r = 0.00120 + 0.93210 (Km-Rf) + 0.47702 SMB + 0.37490 HML-0.22103 WML
276
Santosh Kumar & Tavishi
Portfolio no 48
r = 0.00160 + 0.86183 (Km-Rf) + 0.16309SMB + 0.18102HML - 0.60796 WML
Potfolio no 51
r = -0.00042050 + 1.16225 (Km-Rf) + 0.98812SMB - 0.41612HML - 1.93312 WML
Portfolio no 52
r = 0.00124 + 0.83919 (Km-Rf) + 0.48828SMB - 0.16330HML - 0.85962 WML
Portfolio no 53
r = 0.00125 + 0.94718 (Km-Rf) + 0.06606SMB - 0.13674HML - 0.19695 WML
Portfolio no 61
r = 0.00074807 + 0.96878 (Km-Rf) + 1.10809SMB + 0.82086HML - 0.15828 WML
Portfolio no 62
r = 0.00153 + 0.86897 (Km-Rf) + 0.57322SMB + 0.58626HML - 0.00055406 WML
Portfolio no 63
r = 0.00087308 + 1.05165 (Km-Rf) + 0.03955SMB + 1.09681HML - 0.17580 WML
Portfolio no 66
r = 0.00229 + 0.80723 (Km-Rf) + 1.02311SMB + 0.69837HML - 0.22935 WML
Portfolio no 67
r = 0.00137 + 0.95152 (Km-Rf) + 0.54834SMB + 0.25765HML - 0.18577 WML
Portfolio no 68
r = -0.00003229 + 1.08840 (Km-Rf) + 0.07729SMB + 0.40804HML -0.25261 WML