Tests of the Fama and French model in India

Abstract

This study empirically examines the Fama-French three-factor model of stock returns
for India. We find evidence for pervasive market, size, and book-to-market factors in
Indian stock returns. We find that cross-sectional mean returns are explained by
exposures to these three factors, and not by the market factor alone. We find mixed
evidence for parallel market, size and book-to-market factors in earnings; we do not
find any reliable link between the common risk factors in earnings and those in stock
returns. The empirical results, as a whole, are reasonably consistent with the Fama-French three-factor model.

Full text

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Tests of the Fama and French Model in India*
Gregory Connor and Sanjay Sehgal*
May 2001
Gregory Connor (corresponding author)
Department of Accounting and Finance
London School of Economics
Houghton Street
London, WC2A 2AE United Kingdom
g.connor@lse.ac.uk
(44) (020) 7955-6407
Sanjay Sehgal
Department of Financial Studies
University of Dehli, South Campus
India
alkas@vsnl.com
(0091) (11) 713-0579
*We would like to thank Laura Stafford for research assistance.

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Tests of the Fama and French Model in India
Abstract
This study empirically examines the Fama-French three-factor model of stock returns
for India. We find evidence for pervasive market, size, and book-to-market factors in
Indian stock returns. We find that cross-sectional mean returns are explained by
exposures to these three factors, and not by the market factor alone. We find mixed
evidence for parallel market, size and book-to-market factors in earnings; we do not
find any reliable link between the common risk factors in earnings and those in stock
returns. The empirical results, as a whole, are reasonably consistent with the Fama-
French three-factor model.

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1. Introduction
Fama and French (1992) find that the main prediction of the CAPM, a linear
cross-sectional relationship between mean excess returns and exposures to the market
factor, is violated for the US stock market. Exposures to two other factors, a size-
based factor and a book-to-market-based factor, often called a “value” factor, explain
a significant part of the cross-sectional dispersion in mean returns. If stocks are
priced rationally, then systematic differences in average returns should be due to
differences in risk. Thus, given rational pricing, the market, size and value exposures
must proxy for sensitivity to pervasive risk factors in returns. Fama and French
(1993) confirm that portfolios constructed to mimic risk factors related to market,
size, and value all help to explain the random returns to well-diversified stock
portfolios. Fama and French (1995) attempt to provide a deeper economic foundation
for their three-factor pricing model by relating the random return factors to earnings
shocks. They claim that the behaviour of stock returns in relation to market, size and
value factors is consistent with the behaviour of earnings. They admit that their
findings are weak, especially relating to the value factor, but attribute this to the
measurement error problems in earnings data. There is a burgeoning research
literature contradicting, confirming, criticizing, and extending the Fama-French
model, see for example the discussion and references in Davis, Fama and French
(2000).
This paper empirically examines the Fama-French three-factor model for the
Indian stock market. We test the one- factor linear pricing relationship implied by the
CAPM and the three-factor linear pricing model of Fama and French. We analyze
whether the market, size and value factors are pervasive in the cross-section of
random stock returns. We investigate whether there are market, size and value factors
in corporate earnings similar to those in returns, and whether the common risk factors
in earnings translate into common risk factors in returns.
The empirical evidence is generally supportive of the Fama and French model.
All three Fama-French factors, market, size, and value, have a pervasive influence on
random returns in the Indian stock market. The one-factor CAPM relationship for
mean returns can be rejected, but the three-factor model cannot. There is some weak
evidence for market, value and size factors in earnings shocks, although our sample is
too small to make confident statements. We can find no evidence that the common
risk factors in one-year-ahead earnings growth rates are related to the common factors
in current portfolio returns.
In section 2 we describe our data and its sources. In Section 3 we analyze and
test the pricing models using returns data. In section 4 we examine whether market,
value and size factors can be found in corporate earnings, and if there is a discernible
relationship between the factors in earnings and in returns. Summary and concluding
remarks are provided in section 5.
2. Data
2.1 The Sample Securities
India is a very large emerging market, with about 8000 listed companies. The
top ten percent of listed companies account for a major portion of market

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capitalisation and trading activity; the remainder of the market is thinly traded. Our
share price data consists of month-end adjusted share prices of 364 companies from
June 1989 to March 1999. A maximum of 117 observations is available for each
monthly return series based on these prices. There are some missing observations for
some of the individual share series, since some of the companies came onto the
exchange on a date later than the initial date of the study period. The sample
companies form part of the CRISIL-500 list. CRISIL-500 is a broad-based and value-
weighed stock market index in India constructed along the lines of the S&P index in
the US. It covers 97 industry groups and gives a representation to companies of
varying levels of size and trading activity. The sample companies account for a major
portion of market capitalisation as well as average trading volume for the Indian
equity market. The bulk of the Indian shares not included in the sample are either
thinly traded or do not have accounting and financial information on a continuous
basis.
The share data has been obtained from Capital Market Line, a financial
database widely used in India by practitioners and researchers. The price data has
been adjusted for capitalisation changes such as bonus rights and stock splits. The
adjusted share price series has been converted into return series using arithmetic
returns. The return calculations have been done using the capital gain component
only, since we do not have data on dividends. However, over our sample period,
dividend yields on Indian stocks were very small. Equity capital was released to
shareholders mostly through cash-based acquisitions, or reinvested. As we will
discuss in Section 3, we do not believe that the exclusion of dividends from the return
calculations has a marked effect on our results or conclusions therefrom.
2.2 Risk-free Proxy
The implied yield on the month-end auction of 91-day Treasury bills has been
used as a risk-free proxy. The data source for 91-day T-bills is the Report of Currency
and Finance, an annual publication of the Reserve Bank of India. It should be noted
that prior to 1993, 91-day T-bills were regulated in India to have a constant yield of
4.6% per annum, and banks were forced to hold them through government-regulated
reserve requirements. This fixed yield was an underestimation of the nominal yields
required by investors in this era of high inflation. Since 1993, the 91-day T-bill yield
has been exogenously determined on an auction basis. In Section 3, we analyze the
effect of this regulated T-bill rate, by using zero-beta variants of the standard model,
and differentiating between the regulated and unregulated subperiods.
2.3 Company Attributes
The accounting information has been obtained for the sample companies for
the financial years 1989 to 1998. The financial year in India is from April of year t to
March of calendar year t+1. The book value per share and number of shares
outstanding for the sample companies are recorded in March-end of each year. The
data source is CMIE Provis, a provider of financial statement related information for
Indian companies. The accounting information combined with share price data has
been used to construct measures of size and value employed in the study, as discussed
in the next section.

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Additionally annual profit information measured as Profit Before Depreciation
and Taxes (PBDT) has been collected for the sample companies from 1988 to 1998.
The choice of profit figure has been guided by the fact that PBDT figures are seldom
negative, making them amenable for growth rate calculations. The earnings
information is used in a latter section to explore the economic foundation for common
risk factors in stock returns.
3. Tests of the CAPM, Fama -French Model, and Variants
3.1 The Size and Value Sorted Portfolios
In June of each year t from 1989 to 1998, all the sample stocks are ranked on
the basis of size (price times shares). The median sample size is then used to split the
sample companies into two groups: small (S) and big (B). Book equity to market
equity (BE/ME) for year t is calculated by dividing book equity at the end of financial
year t by market equity at the end of financial year t. It may be noted that the
financial year closing in India is March for all companies every year. The sample
stocks are broken into three BE/ME groups based on the breakpoints for the bottom
30% (low), middle 40% (medium) and top 30% (high) of the ranked values of BE/ME
for the sample stocks.
We construct six portfolios (S/L, S/M, S/M, B/L, B/M, B/H) from the
intersection of the two size and three BE/ME groups. For example S/L portfolio
contains stocks that are in the small size group and also in the low BE/ME group
while B/H consists of big size stocks that also have high BE/ME ratios. Monthly
equally-weighted returns on the six portfolios are calculated from the July of year t to
June of year t+1, and the portfolios are re-formed in June of year t+1. The returns are
calculated from July of year t to ensure that book equity for year t-1, i.e., March, is
known to investors by the time of portfolio formation.
The six size-BE/ME portfolios are constructed to be equally-weighted, as
suggested by Lakonishok, Shliefer and Vishny (1994). Fama and French (1996)
document that the three factor model does a better job in explaining LSV equally-
weighted portfolios as compared with value-weighted portfolios. A recent study by
Muneesh and Sehgal (2001) also examines the relationship between these factors and
stock returns for the Indian market using equally-weighted portfolios.
3.2 The Factor Portfolios
The Fama-French model involves the use of three factors for explaining
common stock returns: the market factor (market index return minus risk-free return)
proposed by the CAPM, and factors relating to size and value. For the market index
we use the International Finance Corporate Investable India index, a value-weighted
index of the returns to Indian stocks. Note that this market index return includes
dividend yield.
SMB (Small Minus Big) is meant to mimic the risk factor in returns related to
size. SMB is the difference each month between the simple average of the returns of
the three small stock portfolios (S/L, S/M and S/H) and the average of the returns on

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the three big portfolios (B/L, B/M, B/H). It is the difference between the returns on
small and big stock portfolios with about the same weighted-average BE/ME. Hence
SMB is largely clear of BE/ME effects, focussed on the different behaviour of small
and big stocks.
HML (High Minus Low) is meant to mimic the risk factor in returns related to
value (that is book-to-market ratios). HML is the difference each month between the
simple average of the returns on two high BE/ME portfolios (S/H and B/H) and the
average returns on two low BE/ME portfolios (S/L and B/L); it is constructed to be
relatively free of the size effect.
3.3 Descriptive Statistics on the Return Series
Table 1 shows the first four moments and the first three autocorrelations of the
six size and value sorted portfolio returns and the three factor portfolio returns. The
results confirm the worldwide evidence for a negative relation between size and
average return. More interestingly, the relation between value and average return is
positive for small stocks, but negative for big stocks. This is different from US
findings (Fama and French (1992, 1993)) of a strong positive relation between value
and average returns irrespective of size. It seems that the Indian market exhibits a
strong size effect and a conditional value effect, the latter being present only for small
stocks. Fama and French (1995) on the contrary cite a strong value effect and a
conditional size effect for the US market. The portfolio returns have fairly high
volatility, e.g., the market factor has monthly volatility of 10.26%, which corresponds
to an annual volatility of 35.54%. All the portfolios have some positive skewness and
positive excess kurtosis. There is some evidence for positive autocorrelations of
measured returns, which may reflect stale price effects. Table 2 shows the correlation
coefficients between the MKT, SMB and HML factors, which serve as the
independent variables in our main regression model.
3.4 Seasonality in the Returns.
Before beginning our pricing tests we digress to examine seasonality, since in
the US seasonality in returns has been shown to be related to the Fama-French factor
risk premia, e.g., Fama and French (1993). Testing for seasonality in monthly returns
is problematic in India since several different seasonal effects can be justified. The
financial closing in India is at the end of March. Thus, according to the tax-loss
selling hypothesis (Keim (1983)) investors would be inclined to sell loss-making
stocks in March and earlier months, and reposition their portfolios in April. An April
effect in India is analogous to a January effect for the USA, based on this tax-loss
explanation of the January effect in the USA.
The government financial budget in India is presented on the last day of
February each year, which could lead to portfolio rebalancing in response to
government spending patterns. The conjecture of a March effect is inspired by a
recent survey by Sehgal (2001) in which a majority of Indian investors mention such a
seasonal pattern in investment behaviour. A January effect might be attributed to a
general globalisation of the Indian economy in recent years, including the listing on

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NASDAQ of some Indian high-tech companies. Further, foreign institutional
investors in the Indian market mostly use a December financial closing in their
investment reporting, which could lead to rebalancing and a subsequent January
effect.
Lastly, the festival of Divali, which falls in October-November of every year,
is very important in its effect on Indian consumption spending. This may push down
stock prices in the two festival months, with recovery in the succeeding month. We
test for January, March, April and October-November seasonality in mean returns.
Table 3 shows simple mean differences and t-statistics testing whether mean returns
differ in a given month (or months, for the October-November test). There is no
January, March or April effect, but there is evidence for an October-November
(Divali) negative return difference. This Divali effect seems to be spread evenly
across the size and value spectrum: it appears in the market portfolio excess return
and in most of the size and value sorted portfolios but not in the size (small-minus-
big) and value (high-minus-low) portfolio return differences.
3.5 Explaining Common Variation in Returns with the Factor Portfolios
Our tests of the Fama-French model use the standard multivariate regression
framework (see Campbell, Lo and MacKinlay (1997) for an excellent review) . Let
Rjt denote the excess return to portfolio j in month t, MKTt the excess return to the
market portfolio, SMBt the return to the size factor portfolio, and HMLt the return to
the value factor portfolio. We estimate the multivariate regression system:
Rjt = aj + bjMKTt+sjSMBt+hjHMLt+εt, j=1,...,N ; t=1,…,T (1)
where bj, sj, and hj are the market, size and value factor exposures of portfolio j, aj is
the abnormal mean return of portfolio j, which equals zero under the hypothesized
pricing model, and εt is the mean-zero asset-specific return of portfolio j. We also
estimate and test variants of the Fama-French model by forcing some of the
coefficients to be zero, that is, excluding the variables from the regression. Note in
particular that (1) can be used to estimate and test the Sharpe-Lintner CAPM by
imposing the restriction sj=hj=0 for all j.
Suppose that (1) is the true model and that εt has a multivariate normal
distribution and is independently and identically distributed through time. Maximum
likelihood estimation of the system (1) is straightforward and decomposes into
equation-by-equation time-series ordinary least squares. The estimates are shown in
Table 3, both for the full model and for variants that exclude one or more of the
factors.
Given rational pricing, in order to justify their use in the asset pricing model
the factors must contribute substantially to the risk of well-diversified portfolios.
Table 4 shows that the market factor explains by far the largest fraction of common
variation in stock returns for the six size and value sorted portfolios. Used alone, the
market factor produces an adjusted R2 of 70-80%; the adjusted R2 declines to below
25% when the other two factors are used without the market factor. However the
other two factors each contributes to explaining these portfolio returns. Except for the

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portfolio B/L (big, low value stocks) the adjusted R2 in the three-factor regression is
higher than in the one-factor market model regression. For some portfolios, adding
HML to the market model regression increases R2 more than adding SMB; and for
other portfolios the reverse holds. In the three-factor regression, the SMB factor has
three significant exposures and the HML has four. In summary, the market factor
clearly ranks first in explanatory power, but there is no clear ranking of the other two
factors.
Note the factor exposure estimates in the three-factor model, at the bottom of
Table 4, panel A. As expected, the estimated size exposures increase monotonically
with size ranking, and analogously for the estimated value exposures and value
ranking. The market exposures of the portfolios are all slightly below one, mostly in
the range .8 to .9. Recall that the sorted portfolios are equally weighted and so have a
low-capitalization bias relative to the value-weighted market index. In India, as in
many emerging markets, low-capitalization stocks tend to have market factor
exposures somewhat below one.
Table 4 indicates that, of the variants considered here, the three-factor model
provides the most suitable description of pervasive risk in these size and value-sorted
portfolios. Our results are limited however by the relatively small number of sorted
portfolios we use, and the fact that the only sorting variables available to us rely on
the same characteristics of size and value used to create the risk factors. Alternative
sorts (such as sorts based on industry categories) and a wider range of sorted
portfolios would be valuable to more reliably identify the pervasive risk factors in
Indian equities, and confirm or contradict our findings. Next we turn to the tests of
mean return predictions.
3.6 Tests of the Cross-sectional Restriction on Mean Returns
We examine whether the risk factors explain the cross-section of mean returns
on stocks by focussing on the intercept estimates of the multivariate regression system
(1). If the pricing theory holds, the true intercepts equal zero. We test the restriction
aj = 0 in two ways. We examine the t-statistics for each individual intercept, and use
the adjusted Wald statistic proposed by Gibbons Ross and Shanken (1989) (GRS) to
test all the intercepts jointly.
In the model with a market factor alone (the CAPM) the intercepts of the three
small stock portfolios are positive and all are significant at the 95% confidence level.
Note that the market index return includes dividend yield but the explained portfolio
returns do not; this tends to bias the intercept estimates negatively. Yet, the CAPM
rejection is due to positive intercepts for the small size portfolios, supporting our
contention that the missing dividend yields are not consequential to the empirical
analysis. The GRS statistic is significant with high confidence.
Using the three-factor model, intercept values for all sample portfolios are
indistinguishable from zero at the 95% level. The results show the ability of the
three-factor model to capture the cross-section of average returns missed by the
standard CAPM. Note however that evidence for a value factor premium is mixed;
the two-factor model with size and market factors (excluding the value factor) does
not produce significantly nonzero intercepts, although adding the value factor lowers

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the magnitude of the point estimates. There is definitely a (negative) size premium,
and there may be a value premium, in Indian equity returns.
3.7 Tests of Zero-beta Variants of the Fama-French Model
Standard multifactor pricing theories, such as the APT, ICAPM and Sharpe-Lintner
CAPM, rely on observation of a risk-free rate at which all investors can borrow and
lend freely. As mentioned, we have used the Indian government T-bill rate as our
observable risk-free return. There are two problems with this assumed rate. First, as
discussed above, the observed rate was regulated and fixed at an artificially low level
during the first 30 months of our sample period. Second, even in the deregulated
period, many Indian equity market investors faced a borrowing rate, and possibly
lending rate, much higher than the rate on Indian government T-bills.
We address both of these potential problems by estimating a zero-beta version
of (1) in which the appropriate zero-beta rate is estimated rather than observed.
Suppose that the true model of expected returns has a zero-beta expected return
different from the observed risk-free return. Imposing the condition aj=0 for all j, and
replacing the risk-free return, Rf, with the zero-beta expected return, Rz, in (1) gives:
Rjt +Rf-Rz = bj(MKTt+ Rf-Rz )+sjSMBt+hjHMLt+εt, (2)
(Note that SMB and HML are unaffected by the use of zero-beta versus risk free
return since they are portfolio return differences). Rearranging (2) gives:
Rjt = (1-bj )γ + bj(MKTt)+sjSMBt+hjHMLt+εt, (3)
where γ= Rz-Rf.
We also estimate a zero-beta version of the model that allows the zero-beta
correction (the difference between the true zero-beta and the observed risk-free rate)
to differ during the regulated period and unregulated periods. This has the form:
Rjt = δ1t(1-bj )γ1 + δ2t(1-bj )γ2+ bj(MKTt)+sjSMBt+hjHMLt+εt, (4)
where δ1t, δ2t are dummy variable for the pre and post periods, and γ1, γ2 are the
seperate zero-beta return premia in the two periods.
Due to the cross-equation restriction, the multivariate regression system (3)
does not decompose into equation-by-equation ordinary least squares, and must be
estimated as a multivariate system subject to a nonlinear cross-equation constraint (the
same applies to (4)). However it is quite straightforward to estimate this nonlinear
system. We proceed as follows. First, we estimate the linear system (1) to get initial
estimates of the parameters. We use the cross-sectional average of the implied values
of γ from the estimated intercepts as an initial estimate for γ. Then we estimate the
nonlinear system by maximum likelihood using the Bernt-Hausman-Hall-Hall
algorithm with numerical derivatives. The estimates and approximate z-statistics of
the coefficients are shown in Table 5. Although the point estimate for the zero-beta
premium is substantially higher in the regulated period than in the unregulated period,

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none of the values is significantly different from zero. The only reliable conclusion is
that, given the high volatility of Indian equity returns, the sample size is insufficient to
estimate a zero-beta return accurately. We show the time-series mean residual
returns, which correspond to the intercept estimates in the unconstrained model (1).
The other parameter estimates are very similar to those in the linear model and are not
shown; they are available from the authors.
4. Common Risk Factors in Earnings
The evidence that market, size and value equity factors are pervasive risk
factors in portfolio returns is consistent with the rational asset pricing explanation for
the role of their factor exposures in the cross-section of mean returns. However it
does not provide an economic explanation for why these characteristics are sources of
pervasive risk in the first place. Fama and French (1995) argue that the pervasive
market, size and value factors in returns can be associated with common factors in
earnings shocks. We examine the evidence in this regard for India.
We first test for common factors in the year-to-year growth in earnings,
measured using PBDT (Profit Before Depreciation and Taxes). PBDT has been
employed as a measure of profitability as it is unlikely to be negative thereby posing
no problems for growth rate calculations. The common factors in earnings growth are
constructed like those in stock returns. EGSMB, the size factor in earnings growth is
the simple average of the percentage change in earnings for the three small stock
portfolios (S/L, S/M and S/H) minus the average for the three big stock portfolios
(B/L, B/M, and B/H). The value factor in earnings growth, EGHML, is the simple
average of the percentage change in earnings for the two high BE/ME portfolios (S/H
and B/H) minus the average for the two low BE/ME portfolios (S/L and B/L). The
market factor in earnings growth, EGMKT, is the average of percentage change in
earnings for all stocks.
The time-series regressions of earnings growth for the six portfolios on
common factors in earnings growth are shown in Table 6. The results are broadly in
line with intuition, with the exception of the SMB factor exposure of the B/M
portfolio. (The B/M portfolio is a high cap portfolio and we would expect its
exposure to the small-minus-big factor to be negative rather than positive.) The
adjusted R2s of these regressions are reasonably high, reflecting the fact that we are
regressing earnings growth rates of portfolios on contemporaneous earnings growth
rates of other portfolios. The next two tables attempt to replicate Fama and French’s
(1995) findings on the links between current portfolio returns and future earnings
growth. Table 7 relates current portfolio returns to own-portfolio earnings growth
next year; Table 8 relates current portfolio returns to factor-portfolio earnings growth
next year. It seems our sample size is too small to support any reliable conclusions,
since there are virtually no statistically significant findings1 and the adjusted R2s are
close to zero. Recall that Fama and French (1995) even with their much longer
sample period and larger cross-section of earnings data found statistically weak
relationships.
Although Table 6 seems to indicate a discernible factor structure in Indian
earnings growth rates, the links between these factors and equity return factors are left

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unresolved by our research. Exploring the relationships between earnings growth and
equity returns in India is an important area for future research.
5. Summary and Concluding Remarks
Fama and French offer three central findings in support of their three-factor
asset-pricing model. One, there are pervasive market, size and value factors in US
equity returns. Two, the linear exposures of US equities to these factors explains the
cross-sectional dispersion of their mean returns. Three, the same types of market, size
and value factors are pervasive in US earnings growth rates, and these earnings
factors can be tied to the equity return factors. This paper examines these three
central findings on the Indian equity market. We confirm the first two of them, but
cannot draw a reliable conclusion on the third. We view our findings as generally
supportive of the Fama-French model applied to Indian equities.
There are numerous questions left unanswered by our study. Are the size and
value factors pervasive in explaining the risk of a wider range of portfolios (such as
industry-sorted portfolios)? Is there evidence for any other pervasive factors in
returns? Can the random returns on these equity return factors be related to corporate
earnings shocks or other business cycle variables? Are our findings on a significant
(negative) size premium and insignificant (positive) value premium robust to
alternative samples and different estimation methods? India is a very large emerging
market with a growing and fast maturing equity market. A better understanding of the
risk and return characteristics of this market is an important research problem.

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Notes
1. With 7 degrees of freedom (as in Table 7), the 95% confidence level for a t-statistic
is 2.37; with 5 degrees of freedom (as in Table 8), it is 2.57. This assumes normality
and no time-series autocorrelation of residuals.

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Table 1
Summary statistics on the portfolio returns
(July 1989 – March 1999, 117 observations)
Portfolio Mean Standard
deviation skewness Excess
kurtosis ρ1 ρ2 ρ3
S/L .0158 .1037 .5812 .9304 .114 .019 -.054
S/M .0215 .0975 .5822 1.087 .215 .073 -.038
S/H .0211 .1093 1.300 5.515 .206 .028 -.028
B/L .0095 .0961 .9661 4.706 .161 -.032 -.089
B/M .0081 .0976 .9000 5.280 .272 .018 -.143
B/H .0034 .1131 1.691 7.853 .266 .039 -.073
MKT .0107 .1026 .9714 2.718 .147 .045 -.140
SMB .0120 .0329 .2580 1.494 -.046 -.100 .117
HML .0003 .0450 .3474 1.494 .107 .131 .024

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Table 2
Correlations between the factor portfolios
MKT SMB HML
MKT - -.1132 .1325
SMB - - -.2682
HML - - -

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Table 3
Monthly seasonals in portfolio returns
Panel a: Estimated differences in mean returns
Portfolio µJanuary-µother µMarch-µother µApril-µother µFestival-µother
S/L -.0162 .0319 -.0244 -.0661
S/M -.0159 .0300 -.0173 -.0543
S/H -.0067 .0250 -.0229 -.0574
B/L -.0005 .0279 -.0175 -.0506
B/M -.0100 .0272 -.0244 -.0580
B/H .0006 .0323 -.0133 -.0457
MKT -.0013 .0247 .0002 -.0636
SMB -.0087 .0011 -.0021 -.0066
HML .0063 .0008 .0045 .0057
Panel b: t-statistics for differences in mean returns
Portfolio t(µJanuary-µother) t(µMarch-µother) t(µApril-µother) µFestival-µother
S/L -.471 .930 -.675 -2.664
S/M -.491 .931 -.510 -2.310
S/H -.184 .691 -.602 -2.174
B/L -.017 .877 -.523 -2.181
B/M -.308 .842 -.720 -2.474
B/H .017 .864 -.339 -1.660
MKT -.037 .727 .004 -2.585
SMB -.800 .103 -.186 -.815
HML .420 .054 .289 .516

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Table 4
Regressions of size and book-to-market sorted portfolio excess returns
(Rt) on combinations of the market (MKT), size (SMB) and value (HML)
factor portfolios
Rt = a + bMKTt + sSMBt + hHMLt + εt
Panel a: Coefficients estimates and R-squared statistics
Explanatory Variables Dependent
Variable a b s h R2
Market S/L 0.007 0.865 - - 0.731
S/M 0.013 0.803 - - 0.712
S/H 0.012 0.884 - - 0.686
B/L 0.000 0.845 - - 0.813
B/M -0.001 0.871 - - 0.837
B/H -0.007 0.937 - - 0.720
SMB and HML S/L 0.006 - 0.781 0.156 0.040
S/M 0.012 - 0.808 0.562 0.088
S/H 0.011 - 0.833 1.096 0.192
B/L 0.011 - -0.103 0.131 -0.011
B/M 0.011 - -0.246 0.541 0.064
B/H 0.005 - -0.156 1.193 0.226
Mkt and SMB S/L -0.006 0.903 1.043 - 0.839
S/M 0.002 0.836 0.897 - 0.802
S/H 0.002 0.911 0.753 - 0.735
B/L -0.001 0.850 0.149 - 0.814
B/M 0.001 0.866 -0.139 - 0.838
B/H -0.003 0.927 -0.266 - 0.724
Mkt and HML S/L 0.006 0.881 - -0.263 0.742
S/M 0.013 0.794 - 0.164 0.715
S/H 0.012 0.844 - 0.678 0.761
B/L 0.000 0.851 - -0.105 0.814
B/M -0.001 0.852 - 0.332 0.859
B/H -0.006 0.881 - 0.957 0.863
Mkt, SMB and HML S/L -0.006 0.906 1.018 -0.071 0.838
S/M 0.000 0.820 1.022 0.357 0.825
S/H -0.001 0.871 1.061 0.878 0.856
B/L -0.001 0.854 0.120 -0.083 0.814
B/M -0.001 0.851 -0.023 0.328 0.858
B/H -0.007 0.883 0.075 0.971 0.862

17
Pane l b: t-statistics of the estimated coefficients and Gibbons -Ross-Shanken
statistics jointly testing the intercepts equal zero
Explanatory Variables Dependent
Variable t(a) t(b) t(s) t(h)
Market S/L 1.960 9.432 - -
S/M 2.915 9.224 - -
S/H 2.484 8.852 - -
B/L 1.224 10.24 - -
B/M 1.010 10.77 - -
B/H 0.207 9.371 - -
GRS statistic 3.8069 p-value 0.0017
SMB and HML S/L 0.640 - 2.623 0.718
S/M 1.273 - 2.960 2.820
S/H 1.117 - 2.895 5.214
B/L 1.118 - -0.364 0.635
B/M 1.169 - -0.888 2.677
B/H 0.506 - -0.534 5.601
GRS statistic 1.7999 p-value 0.1057
Mkt and SMB S/L 0.462 10.48 4.386 -
S/M 1.560 10.05 3.862 -
S/H 1.486 9.259 2.610 -
B/L 1.115 10.17 0.083 -
B/M 1.433 10.66 -1.392 -
B/H 0.784 9.274 -1.701 -
GRS statistic 1.5174 p-value 0.1791
Mkt and HML S/L 1.962 9.477 - -0.960
S/M 2.933 9.074 - 1.708
S/H 2.703 9.134 - 4.876
B/L 1.219 10.15 - -0.005
B/M 1.039 10.79 - 3.151
B/H 0.225 10.45 - 7.211
GRS statistic 4.1369 p-value 0.0009
Mkt, SMB and HML S/L 0.447 10.39 4.246 0.119
S/M 1.316 10.11 4.644 3.007
S/H 1.104 10.14 4.563 6.293
B/L 1.103 10.09 0.084 0.017
B/M 1.194 10.71 -0.635 2.867
B/H 0.261 10.38 -0.143 6.891
GRS statistic 1.7478 p-value 0.1168

18
Table 5
Constrained estimation of the three-factor model with an excess zero-beta
return
Rjt = γ0(1-bj) + bjMKTt + sjSMBt + hjHMLt + εjt
Panel A: Coefficient Estimates
Without an excess
zero-beta return (from
Table 3)
With a single-regime
excess zero-beta return With a two-regime excess zero-
beta return
a γ0 ε γ01 γ02 ε
S/L 0.003 -0.002 -0.003
S/M 0.009 0.002 0.002
S/H 0.008 0.002 0.001
B/L 0.008 0.002 0.001
B/M 0.008 0.002 0.001
B/H 0.002
0.012
-0.003
0.063 -0.005
-0.004
Panel B: t-statistics
Without an excess
zero-beta return (from
Table 3)
With a single-regime
excess zero-beta return With a two-regime excess zero-
beta return
t(a) t(γ0) t(ε) t(γ01) t(γ02) T(ε)
S/L 0.447 -0.299 -0.410
S/M 1.316 0.382 0.266
S/H 1.104 0.268 0.161
B/L 1.103 0.241 0.131
B/M 1.194 0.291 0.175
B/H 0.261
0.962
-0.508
2.681 -0.343
-0.624

19
Table 6
Growth in earnings for the six size and value sorted portfolios (GE) regressed on
contemporaneous market (GEMKT), size (GESMB) and value factors (GEHML) in
the growth in earnings.
GEt = a + bGEMKTt + sGESMBt + hGEHMLt + εt
Panel A: Coefficient Estimates and Adjusted R2s
Portfolio a b s h R2
S/L −.0520 1.72 .912 -.471 .967
S/M −.0103 .964 .145 .267 .945
S/H .0623 .316 .442 .204 .644
B/L .0414 .554 -1.563 −1.165 .993
B/M .0315 .490 1.156 1.005 .840
B/H -.0729 1.957 −1.093 .160 .680
Panel B: t-statistics
Portfolio t(a) t(b) t(s) t(h)
S/L −1.275 4.240 3.922 -3.971
S/M −.723 6.784 1.781 6.413
S/H 1.836 .937 2.284 2.070
B/L 3.268 4.393 −21.620 −31.601
B/M .535 .837 3.445 5.876
B/H −1.114 3.007 −2.927 .838

20
Table 7
Annual portfolio excess returns (R) regressed on portfolio specific growth in earnings
(GE) one year ahead.
Rt = a + bGEt+1 + εt
Portfolio a b R2 t(a) t(b)
S/L 1.227 .549 −.004 7.721 .985
S/M .995 2.043 −.060 3.228 .741
S/H .236 8.694 .484 .682 2.918
B/L 1.324 −.0812 −.142 7.384 −.087
B/M 1.099 .952 .008 5.813 1.031
B/H 1.208 −1.919 .245 6.486 −1.896

21
Table 8
Annual portfolio excess returns (R) regressed on market (GEMKT) , size (GESMB)
and value (GEHML) factors in the growth in earnings one year ahead.
Rt = a + bGEMKTt+1 + sGESMBt++ hGEHMLt++ εt
Panel A: Coefficient Estimates and Adjusted R2s
Portfolio a b s h R2
S/L 1.182 1.184 .771 -.321 -.241
S/M 1.190 .0691 2.349 -.169 -.014
S/H 1.029 .464 3.184 .247 -.173
B/L 1.356 .261 1.307 -.020 -.376
B/M 1.188 .248 1.224 -.107 -.340
B/H .962 .391 .940 -.158 -.398
Panel B: t-statistics
Portfolio t(a) t(b) t(s) t(h)
S/L 2.989 .301 .342 -.279
S/M 2.561 .015 .885 -.125
S/H 1.423 .065 .772 .118
B/L 3.159 .061 .534 -.016
B/M 2.665 .056 .481 -.082
B/H 2.136 .087 .366 -.121

22
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