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International Finance Conference, IIM-Calcutta: Asset Pricing
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Kushankur Dey and Debasish Maitra, Fellow Participant, IRMA (Oct-2009)
Multifactor Analysis of Capital Asset Pricing Model in Indian Capital
Market
(Kushankur Dey & Debasish Maitra, Doctoral Participant1, IRMA)
Abstract
Investment theory in securities market pre-empts the study of the relationship between risk and returns. A review of studies conducted for various markets in the world that researchers have used a number of methodologies to test the validity of CAPM. While some studies have supported and agreed with the validity of CAPM, some others have reported that beta alone is not a suitable predictor of asset pricing and that a number of other factors could explain the cross-section of returns. The paper reiterates the importance of a multifactor model in the explanation of investor‟s required rate of return of the portfolio in the Indian capital market.
The results show that intercept is significantly different from zero and the combination of sizei, ln(ME/BE)i, (P/Ei –P/Em) do not explain the variation in security returns under both percentage and log return series while (di-Rf) shows very dismal result. The combination of βi, ln(ME/BE)i, (P/Ei –P/Em), sizei, and (di-Rf) do not explain the variation in security returns when log return series is used and the combination of βi, ln(ME/BE)i, sizei
also do not explain any variation in security returns when percentage return series is used. However, beta alone, when considered individually in two parameter regressions and also multi-factor model, does not explain the variation in security/portfolio returns. This casts doubt on the validity of extended and standard CAPM.
The empirical findings of this paper would be useful to financial analysts in the Indian capital market. From the researcher‟s prerogative multifactor analysis would be more indicative one to include some macroeconomic factors, firm-specific factors and market factors to enlarge the understanding of modern finance and to unfold the dilemma of using CAPM model in asset-pricing.
Key words: multifactor model, CAPM, security returns, portfolio returns
1 First author is a third year doctoral participant of the Institute of Rural Management Anand, can be reached at [email protected] . Second author is pursuing his course work of the second year of Fellow Programme (FPRM). He can be contacted at [email protected].
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Kushankur Dey and Debasish Maitra, Fellow Participant, IRMA (Oct-2009)
1. INTRODUCTION
Relationship between return and risk has been received a significant importance in
realizing the optimal allocation of stocks or optimal investment strategy. More
implicitly, this makes a choice to the investor to take a wise action or prudent inaction
which, in turn, compels the investor to cogitate upon the risk-return embedded
relationship on the asset. In real world, we try to measure the standard deviation as a
proxy or surrogate to risk and investor attitudes toward portfolios depend exclusively
upon expected return and risk (Markowitz, 1959). Since diversified portfolios reduce
the occurrence of unsystematic risk, avoidance of systematic one is of huge challenge to
the investor. As noted that the variance of returns on an asset is a measure of its total
risk and variance can be halved into systematic and unsystematic risk, that is, 2i = β22m
+ 2εi, where β is systematic factor, 2m denotes the systematic risk and 2ε is
unsystematic risk contained portfolio. Thus, it would be relevant to measure the
correlation (rxy) of the two or more stocks to the ratio of their individual standard
deviation (σx, σy and σi). This raises serious concerns to the investor that how much
investment is required in each stock to form an optimal portfolio.
2. RATIONALE BEHIND THE PAPER
On the backdrop of this, simplified logical and elegant or a single-index model helps to
measure the capital asset pricing. Theoretically we can say that capital market theory is
a major extension of the portfolio theory of Markowitz (Sharpe, 1964). Portfolio theory is
really a connotation of how rational investors should build efficient portfolios or
frontiers. On the other hand, capital market theory pre-empts us how assets should be
priced in the capital markets if, indeed, everyone behaved in the way portfolio theory
suggests. So the capital asset pricing model (CAPM) is a relationship amplifying how
assets should be priced in the capital market. The model simplifies the complexity of
real world, tells us that a linear relationship exists between a security‟s (stock) required
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Kushankur Dey and Debasish Maitra, Fellow Participant, IRMA (Oct-2009)
rate of return and its beta as investment theory suggests that beta is an approximate
measure of risk for portfolios of securities that have been sufficiently diversified (Singh,
2008). Historically calculated beta and risk premium (Rm-Rf) used to determine the
required rate of return (Ri, or expressed as Ri=Rf +β(Rm-Rf) or Ri=α+bβ +εi) on the
investor‟s portfolio. The question is on whether we adopt the ex-ante or ex-post
measures of beta to arrive at realistic return of the investor.
3. OBJECTIVES AND SCOPE OF THE PAPER
The two-factor or standard CAPM model has several limitations with respect to time
dimension (two-period model), incorporation of less factors and lower explanatory
power of regression coefficient (R2) or lower magnitude of variance explained by the
factors. Multifactor models are of great significance in explaining the variance of the
investor‟s required rate of return or we can posit that more dynamic, realistic nature of
model is employed. This model reiterates the importance of multi-period investing or
financing and operating horizon (independent of each other) as mentioned by Fama
and Miller (1972) with respect to beta (β), size of the firm, price-earning ratio of
individual security to market portfolio or index as a surrogate with respect to inflated
covariance (ρ [P/Ei –P/Em]), risk premium (Rm- Rf), market value of equity to book value
of equity (ME/BE) and dividend yield in excess of risk-free return with respect to tax
imposition or impact [t(di-Rf)]. The model would have an empirical generalization in
the way of replication of Fama and French‟s original work (1992). The index or SNP
CNX NIFTY is considered in our study as market portfolio as it largely covers almost all
the sectors (21) with about 35-36 percent capitalization (NSE, 2009). Our result is
compared with bivariate analysis of βi and size of the firm, βi and (Rm- Rf), βi and (P/E)i,
βi and (BE/ME)i etc.
The first section deals with an extant literature review on the standard CAPM and inter-
temporal CAPM (ICAPM) and then looks at Multifactor models of CAPM. The second
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section focuses on methodology and the third section examines results and analysis.
The conclusion part focuses on further scope and improvement of the cross-section of
expected stock returns of CAPM or multifactor models.
4. EXTANT LITERATURE REVIEW
Investment in securities market requires the study of the relationship between risk and
returns (Manjunatha and Mallikarjunappa, 2009). According to Bodie, Kane and Marcus
(2004), “The CAPM presupposes that the only relevant source of risk arises from
variations in stock returns, and therefore a representative (market) portfolio can capture
the entire risk. As a result, individual-stock risk can be defined by the contribution to
overall portfolio risk…” (p. 312). Fama and French (1993, 1996) have shown that beta is
not only explanatory variable in capturing the variance of individual‟s portfolio return,
others are size of the firm, (ME/BE) ratios, or ME and (P/E) ratios. The argument is put
forward by them that multifactor model can improve on the descriptive power of the
index model is that betas seem to vary over the business cycle. One of the multifactor
examples is the seminal work of Chen, Roll and Ross (1986) which shows the
consistency with the empirical study of Merton (1973) and Fama and French (1993).
Inclusion of five-factor in the model of Chen, Roll and Ross (1986), namely, IP or
percentage change in industrial production, EI or percentage change in expected
inflation, UI or percent change in unanticipated inflation, CG or excess return of long-
term corporate bonds over long-term government bonds and GB or excess return o
long-term government bonds over T-bills, estimates the excess returns (Rit, t is the
holding period of portfolio of securities) of the stock in each period on the mentioned
macroeconomic factors by employing multiple regression and the residual variance
captures the firm-specific risk. An alternative approach proposed by Fama and French
(1996) in resuscitating asset pricing anomalies shows that market index (Rm) does play a
role and is expected to capture systematic risk stemming from macroeconomic factors.
The study also elucidates that two firm-characteristic variables chosen, viz., SMB or
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Kushankur Dey and Debasish Maitra, Fellow Participant, IRMA (Oct-2009)
small minus big2 and HML or high minus low3 because of corporate capitalization (firm
size) and (BE/ME) ratios seem to be predictors on average stock returns, and therefore
risk premiums. Fama and French (1996) propose this model on empirical ground by
arguing that while SMB and HML are not obvious predictors for relevant risk factors,
these may acts as surrogate to more fundamental variables, yet to be identified. For
instance, small sized firms have high returns for low (BE/ME) ratios and conversely,
large sized firms have low returns for high (BE/ME) ratios. This indicates clearly that
with high (BE/ME) ratios, firms are more likely to be in “financial distress” and that
small firms may be sensitive to changes in business conditions, hence, these variables
may capture sensitivity to risk factors in real world.
Sharpe (1964), Linter (1965), and Mossin (1968) have independently developed form of
CAPM. The studies conducted by Black, Jensen, and Scholes (1972), Black (1972, 1993),
Fama and MacBeth (1973), and Terregrossa (2001) have largely been supportive of the
standard form of CAPM or two-factor model. After 1970s, CAPM came under attack as
striking anomalies were reported by Reinganum (1981), Elton and Gruber (1984), Bark
(1981), and Harris et al. (2003). Further studies on the fundamental factors of securities
such as size effect of Banz (1981), book to market equity (BE/ME), earnings-price (E/P)
ratio of Ball (1978) and Basu (1983), and studies of CAPM models by Fama and French
(1992; 1993; 1996; 1998; 2002; 2004 and 2006), Davis, Fama and French (2000) show that
CAPM‟s beta is not a good determinant of the expected return of securities/portfolios.
As their argument is substantiated and put forward by earlier work of Rosenberg and
Guy (1976) in predicting betas as a function of past beta, firm size, debt to asset ratio etc.
They also identify some other variables to help predict betas, namely, variance of
earnings, growth in earnings per share (EPS), dividend yield and variance of cash flow.
2 The return of a portfolio of small stocks in excess of the return on a portfolio of large stocks
3 The return of a portfolio of stocks with high ratios of book value to market value in excess of the return on a portfolio of stocks with low book-to-market ratios
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Kushankur Dey and Debasish Maitra, Fellow Participant, IRMA (Oct-2009)
Afterwards, studies by Kothari and Shanken (1995), and Kothari, Shanken, and Sloan
(1995) argue in defense of inter-temporal CAPM. Guo and Withtelaw (2006) develop
and estimate an empirical model based on the inter-temporal capital asset pricing
model (ICAPM) that separately identifies the two components of expected returns,
namely, the risk component and the component due to the desire to hedge changes in
investment opportunities. The estimated coefficient of relative risk aversion is positive,
statistically significant, and reasonable in magnitude. They show that expected returns
are driven primarily by the hedge component arguing that omission of this component
is partly responsible for the existing contradiction in results. Theoret and Racicot (2007)
use a new set of instruments based on higher statistical moments to discard the
specification errors that might be present in the Fama and French (1992, 1993, and 1997)
model. They show that the usual instruments perform quite poorly in comparison to
higher moments. They estimate the Fama and French (1992, 1993, and 1997) model on a
sample and show that specification error exists for the loadings of the market premium
and the factor SMB (small minus big) which seem understated. Daniel and Titman
(1997) argue that it is the characteristics rather than the covariance structure of returns
that appear to explain the cross-sectional variation in stock returns. According to study
by Cooper et al. (2008), a firm‟s annual asset growth rate emerges as an economically
and statistically significant predictor of the US stock returns. Liu and Zhang (2008)
show that the growth rate of industrial production is priced risk factor in standard asset
pricing tests. In many specifications, this macroeconomic risk factor explains more than
half of the momentum profits. Their evidence also suggests that the expected growth
risk is priced and that the expected growth risk plays an important role in driving
momentum profits. Studies by Kothari, Shanken and Sloan (1995) show that excess
market returns (Rm-Rf) explains the variation of security or portfolio returns.
While many studies have been conducted on CAPM in the Western countries, there are
a few studies in the Indian context reported by the researchers. Still, there are some
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empirical studies are conducted to put forward the argument of CAPM as a robust
technique in risk-based asset pricing theory. In case of equity and risk premium
measures, India has earlier followed the U.S. based models. After 1996-97, the exact
measures of risk premium incorporated in standard CAPM is a scholastic contribution
to the financial economics. Studies by Varma (1988), Yalwar (1988), and Srinivasan
(1988) have generally supported the CAPM theory in India. Gupta and Sehgal (1993),
Vaidyanathan (1995), Madhusoodanan (1997), Sehgal (1997), Ansari (2000), Rao (2004)
and Manjunatha et al. (2006; 2007) have questioned validity of CAPM in Indian markets.
Ansari (2000) has opined that the studies of CAPM on the Indian markets are scanty
and no robust conclusions exist on this model. Mohanty (1998; 2002), Sehgal (2003),
Connon and Sehgal (2003) have supported the Factors model. Connon and Sehgal
(2003) have shown that the Factors model better than the single factor CAPM in the
context of Indian capital market. Manjunatha and Mallikarjunappa (2006) have used
five univariate variables (beta, size of the firm, BE/ME ratio, EPS/Price (E/P) ratio, and
Rm-Rf) to test the extent of the influence of these variables on the security/portfolio
returns and have found that none of the univariate variables significantly explained the
variance of security/portfolio returns with the exception of beta and excess market
returns (Rm-Rf) in certain cases. Manjunatha and Mallikarjunappa (2009) has tried to
capture the variation of returns using bivariate or two parameters test including beta
and size, beta and BE/ME, beta and EPS/Price, beta and Rm-Rf etc.
5. METHODOLOGY
Unlikely the effect of single-factor or two-factor model on asset pricing, that is, βi and
(Rm-Rf) in explaining the variance of the investor‟s expected rate of return on the said
portfolio of securities, some additional variables are used to approximate or correctly
measure the expected return from a security, what is known as the extended CAPM. Of
the variables incorporated to extend the CAPM, size and (P/E) ratios or (ME/BE) ratios,
(one or the other) have been found to be most consistent and significant in their effect.
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The dividend yield is the most controversial as reported by Horne (2002). Hence, for
multiple variables, the illustrated model is represented below:
Rj = Rf + bβjt + c (variable 2)t +d (variable 3)t + e (variable 4)t + f (variable 5)t + εit
(1)
Where, again, Rf is the risk-free rate, b, c, d, e and f are coefficients reflecting the relative
importance of the variables involved and t is the holding period of securities as a
function of explanatory variables. When variables other than beta are added, a better
data fit would have obtained. We define the mentioned variables in the specified model
as below:
(a) c (variable 2) t : t (dj –Rf) (2)
Where, t = coefficient indicating the relative importance of the tax effect,
dj = dividend yield on security j
Therefore, incorporating the above in eqn. (1) we get
Rj = Rf + bβjt + t (dj –Rf) (3)
This equation tells us that the higher the dividend yield, dj, the higher the expected
before-tax return that investors require. If t was 0.1 and the dividend yield was to rise
by 1.0 percent, the expected return would have to increase by .1 percent to make the
stock attractive to investors. In another way we can say that the market trade off would
be Rs.1.00 of dividends for Rs.0.90 of capital gains (Rs. 1-0.1). Considering the
systematic bias in favour of capital gains, the expected return on a stock would depend
on its β and its dividend yield. On the corollary, we can say that the use of trade-off
between tax effect and capital gains to investors.
(b) d (variable 3)t : market capitalization as size (4)
Our equation is therefore,
Rj = Rf + bβjt + t (dj –Rf) + d (size) (5)
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Kushankur Dey and Debasish Maitra, Fellow Participant, IRMA (Oct-2009)
The extension of the equation tells us that size as measured by the market capitalization
of a company relative to that for other companies, for instance, equal weightage given
to NIFTY indexed-50 companies. Market capitalization is simply the number of shares
outstanding multiplied by the share price. From time to time, a “small stock effect”
appears, where small capitalization stocks give a higher return than large ones, holding
other variables constant. It is presumed that small stocks provide less utility to the
investor and require a higher return. Often the size variable is treated as the decile or
out of total hundred percentage in which the company‟s market capitalization falls
relative to the market capitalizations of other companies in total, for instance, ACC has
„x‟ crore market capitalization on NIFTY index of total „y‟ crore, then the size for ACC is
expressed as „x‟/‟y‟ X100 or as equal weightage given to all indexed companies.
(c) e (variable 4)t : ρ (P/Ej –P/Em) (6)
At certain times, a price-earnings ratio effect has been observed to a greater extent.
Holding constant beta and other incorporated variables, observed returns tend to be
higher for low P/E ratio stocks and lower for high P/E ratio stocks. Put in different way
we can say that, low P/E ratio stocks earn excess returns above what the CAPM would
predict and conversely, high P/E ratio stocks ear less than what the CAPM would
explain or predict. This is a form of mean reversion, and it adds explanatory power to
the CAPM. With only this variable added to the illustrated model, it becomes
Rj = Rf + bβjt + t (dj –Rf) + d (size) - ρ (P/Ej –P/Em) (7)
Where, ρ is a coefficient akin to e mentioned in the first equation, reflecting the relative
importance of a security‟s price-earnings ratio, (P/E)j and weighted average of market
portfolio‟s price-earnings ratio, (P/E)m. Similar to the use of the price-earnings ratio, the
ratio of market-to-book value (ME/BE) has been used to explain security returns. We
propose that either one ratio or the other is employed in our model, not both, unlikely
to Fama and French (1993) model. The (ME/BE) ratio is the market value of all claims on
a company, including those of stockholders, divided by the book value of its assets.
Holding beta and other variables constant, observed returns would tend to be higher
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for low (ME/BE) or low (P/E) ratio stocks than for high (ME/BE) or high (P/E) ratio
stocks. Hence, in the model we use P/E as surrogate or which is proxied for M/B ratio.
(d) f (variable 5)t: i (inflation covariance/σi2) or i {Cov (Ri, i)/ σi2} (8)
Incorporating unanticipated changes in inflation, this implies that the market does not
anticipate changes that occur in the rate of inflation. Whether uncertain inflation is good
or bad for a stock depends on the covariance of this uncertainty with that of return on
stock, that is, Rjr = Rj – p (9)
Where, Rjr is the return for security j in real terms, Rj is the return for security j in
nominal terms and p is the inflation during the period, say, 2000 to 2008. If inflation is
highly predictable, investors simply would add an inflation premium on to the real
return they would require and markets would equilibrate. In the other case where
inflation causes unanticipated changes in expected rate of return, which implies that if
the return on a stock increases with unanticipated increases in inflation, this desirable
property reduces the systematic bias of the stock in real terms and provides a hedge
and conversely opposite to the other situation.
Hence, we would expect that the greater the covariance of the return of a stock with
unanticipated changes in inflation, the lower the expected nominal return the market
would require. If this is so, one could express the expected nominal return of a stock as
a positive function of its beta and a negative function of its covariance with
unanticipated inflation. We can define the notation, as i is a coefficient indicating the
relative importance of a security‟s covariance with inflation, σi2 is the variance of
inflation and the other variables are the same as defined in equation (7). Therefore, the
new one we can get
Rj = Rf + bβjt + t (dj –Rf) + [d (size)] + [ρ (P/Ej –P/Em)] +εit (10)
and, the final model would be, E(Rj)r = Rj +bβjt - i {Cov (Ri, i)/ σi2} (11)
The above illustration shows the incorporation of four-factor would expect a better
explanation of variance in the investor‟s expected rate of return of the portfolio. We
formulate a hypothesis below which is tested employing multiple regressions technique
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Kushankur Dey and Debasish Maitra, Fellow Participant, IRMA (Oct-2009)
and a comparison is also drawn against the two-factor model in terms of the
explanatory power of the test, that is, R2.
H1: Multifactor models have a better explanatory power on the expected rate of return of
investor’s portfolio of securities in Indian capital market.
H2: Multifactor models are robust and parsimonious in showing consistency with other existing
model of extended CAPM and thus, superior over the two-factor model of standard CAPM.
Data and Sample: Phase-I
The study is based on 50 S&P CNX NIFTY companies that were part of the index from
1999 to March 31, 2009. However, for the purpose of study the data are used from 1999-
00 to 2008-09 and since then same 50 companies are the part of this index. NIFTY capital
market segment‟s market capitalization is around 37% (36.674), while SENSEX
excluding BSE-100, BSE-500, BSE-IPO, MIDCAP, SMLCAP and other sectoral indices is
63.326% as reported on October 30, 2009. In case of free-float market capitalization
index, NIFTY (54.17%) is ahead of SENSEX (45.82%) other than BSE-100. S&P CNX
NIFTY is taken as market proxy and the average yields of Government of India (GOI)
securities are used as risk-free rate of returns of the respective years. 365 days average
of closing price, yearly return on securities, market capitalization, price-to-earnings of
index and individual company, dividend yield of each company, Market value of
equity (Market price of security times number outstanding shares) and Book value of
equity (Book value of share times number of outstanding shares) from 1999-00 to 2008-
09 are used for the study. The data were collected from Centre of Monitoring Indian
Economy (CMIE-Prowess database), BSE, NSE, RBI, SEBI websites.
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6. RESULTS AND ANALYSIS
Cross-Sectional Analysis: Average Ten Years Regression (Phase-II)
In order to get ten years effects of independent variables on individual security return, observations of all the years
were averaged of each parameter.
TABLE-1: Average Ten Years Cross Sectional Regression Results of Percentage Returns-Case of Combination of β and Firm-specific Factors
Data in parenthesis shows individual p value at 5% level of significance.
The study has been conducted by using combination of β, size, ln (ME/BE), (P/Ej-P/Em), (d-Rj) and also all the
variables together to get the influence of these variables on security returns. The outputs of different risk factors
along with their co-efficient are shown in the Table-1. The intercept and slope co-efficient are tested using t-test and
the overall goodness-of-fit of the regression is tested using analysis of variance (ANOVA F-test). In this analysis
one intercept and 2 slopes co-efficient are obtained for each combination of β and other firm specific factors. But
when all the independent variables are taken together, then one intercept and 5 slopes co-efficient are obtained.
Table-1 shows that in every case α (intercept) values are significant at 5% level of significance. None of the
Year β &Size Co-eff β & ln(ME/BE) Co-eff β & (P/Ej-P/Em) Co-
eff
β & (d-Rj) Co-eff β , Size ln (ME/BE), (P/Ej-P/Em) & (d-Rf) Co-eff
Te
n Y
ea
rs A
ve
rag
e α β Size α β ln(ME/BE) α β (P/Ej-
P/Em)
α β (d-
Rj)
α β Size ln
(ME/BE),
(P/Ej-
P/Em)
(d-
Rf)
0.31
(0.00)
0.06
(0.33)
-1.63
(0.10)
0.22
(0.03)
0.085
(0.25)
0.018
(0.63)
0.27
(0.00)
0.068
(0.32)
0.00
(0.41)
0.27
(0.00)
0.06
(0.39)
-0.51
(0.21)
0.19
(0.08)
0.08
(0.26)
-1.74
(0.33)
0.05
(0.18)
0.00
(0.39)
-0.73
(0.09)
R2-0.077, F Sig.-0.15 R2-0.029, F Sig.-0.51 R2-0.038, F Sig.-0.40 R2-0.056, F Sig.-0.26 R2-0.16, F Sig.-0.17
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combination of β and other factors shows significant results as their significance value of F-statistics is more than
0.05. Goodness-of-fit (R2) is very low. When β and firm size are taken together, R2 value is not able to explain 93%
of the variation. This it rejects the chances of the fact that β and size are significant determinant of security returns
(percentage). The p-values of slope of β and ln (ME/BE) are more than 0.05 and F-test indicates that the regression
is not fit. R2 value is not able to explain 97.1% of the variation. Therefore it also rejects the chances that the
combination of β and ln (ME/BE) do explain the variation in security returns. The similar result is also found in the
combination of β and (P/Ej-P/Em). The individual p-value of the coefficient is also more than 0.05 with goodness-
of-fit only 3.8%. Same result is also obtained in the combination of β and (d-Rj). This is also unfit for explaining the
variation upto 94.4% which is enough to reject the chances of determining the variation of security returns. To
overcome this limitation all the factors are taken together along with β to get the extent of effects caused by these
variables on security returns. But similar result is observed. The F-significance is much more than 0.05. Though
values of is found to be higher than other cases, but it is due to increased number of independent variables. None
of the slopes is having with P-value lower than 0.05. So, this is also unfit to explain the variation on security
returns.
CHART-1: Comparison of Actual Return, Predicted Return and Residual.
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Chart 1 shows that both the predicted and actual values are following each other but in some cases it is deviating from
actual value to a great extent. Residuals or unexplained variations are also very high. Predicted line is not capable enough
to capture the variations which are left as residuals without being explained.
TABLE-2: Combined Years Cross Sectional Regression Results of Log Returns-Case of Combination of β and Firm-specific
Factors
Data is parenthesis shows individual p-value at 5% level of significance.
The study has also been conducted by using combination of β, size, ln (ME/BE), (P/Ej-P/Em), (d-Rj) and also all the
variables together to get the influence of these variables on logarithmic security returns. The outputs of different risk
factors along with their co-efficient are shown in the Table-2. The intercept and slope co-efficient are tested using t-test
and the overall goodness-of-fit of the regression is tested using analysis of variance (ANOVA F-test). In this analysis one
intercept and 2 slopes co-efficient are obtained for each combination of β and other firm specific factors. But when all the
independent variables are tested together, then one intercept and 5 slopes co-efficient are obtained. Table-2 shows that in
every case α (intercept) values are significant at 5% level of significance. None of the combination of β and other factors
Year β &Size Co-eff β & ln(ME/BE) Co-eff β & (P/Ej-P/Em) Co-eff β & (d-Rj) Co-eff β , Size ln (ME/BE), (P/Ej-P/Em) & (d-Rf) Co-eff
Co
mb
ine
d
α β Size α β ln(ME/BE) α β (P/Ej-
P/Em)
α β (d-
Rj)
α β Size ln
(ME/BE),
(P/Ej-
P/Em)
(d-
Rf)
-1.26
(0.00)
0.17
(0.46)
-5.29
(0.13)
-1.38
(0.00)
0.19
(0.45)
0.003
(0.98)
-1.39
(0.00)
0.17
(0.45)
0.001
(0.27)
-1.39
(0.00)
0.14
(0.55)
-2.07
(0.13)
-1.51
(0.00)
0.17
(0.48)
-5.50
(0.11)
0.12
(0.38)
0.00
(0.28)
R2-0.063, F Sig.-0.22 R
2-0.015, F Sig.-0.71 R
2-0.04, F Sig.-0.39 R
2-0.061, F Sig.-0.23 R
2-0.15, F Sig.-0.21
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Kushankur Dey and Debasish Maitra, Fellow Participant, IRMA (Oct-2009)
shows significant results as their significance value of F-statistics is more than 0.05. Goodness-of-fit (R2) is very low. When
β and firm size are taken together, R2 value is not able to explain 93.7% of the variation. This it rejects the chances of the
fact that β and size are significant determinant of security returns (percentage). The p-values of slope of β and ln (ME/BE)
are more than 0.05 and F-test indicates that the regression is not fit. R2 value is not able to explain 97.1% of the variation.
Therefore it also rejects the chances that the combination of β and ln (ME/BE) do explain the variation in security returns.
The similar result is also found in the combination of β and (P/Ej-P/Em). The individual p-value of the coefficient is also
more than 0.05 with goodness-of-fit only 3.8%. Same result is also obtained in the combination of β and (d-Rj). This is also
unfit for explaining the variation upto 94.4% which is enough to reject the chances of determining the variation of security
returns. To overcome this limitation all the factors are taken together along with β to get the extent of effects caused by
these variables on security returns. But similar result is observed. The F-significance is much more than 0.05. Though
values of is found to be higher than other cases, but it is due to increased number of independent variables. None of the
slopes is having with P-value lower than 0.05. So, this is also unfit to explain the variation on security returns.
Cross-Sectional Analysis: Year wise Cross Sectional Regression Results of Percentage Returns-Case of
Combination of β and Firm-specific Factors
Capturing the explained variation on individual securities‟ rate of rerun on the basis of averaging of 10 years does not
prove significant. In order to see the trends of significance over the years, year wise regression is run to test the influence
of independent variables on security‟s return. But not impressive result is observed. Similar technique using combination
of β, size, ln (ME/BE), (P/Ej-P/Em), (d-Rj) and also all the variables together are used to get the influence of these
variables on logarithmic security returns. The slopes of every independent variable come with p-value more than 0.05.
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Kushankur Dey and Debasish Maitra, Fellow Participant, IRMA (Oct-2009)
But, it is also evident from the Table-2 (Appendix-I) that size is trying to capture the variation. The R2 is ranging from 2%
to 12% which does not suffice to explain the variation. In all the cases the F-significance is much more than 0.05.
Cross-Sectional Analysis: Year wise Cross Sectional Regression Results of Log Returns-Case of Combination
of β and Firm-specific Factors
The study has also been conducted by using combination of β, size, ln (ME/BE), (P/Ej-P/Em), (d-Rj) and also all the
variables together to get the influence of these variables on logarithmic security returns. But again similar output is
obtained. The slopes of every independent variable come with p-value more than 0.05. But, it is also evident from the
Table-3 (Appendix-II) that size is not able to capture the variation as opposed to regression results of percentage returns
on security. The R2 is ranging from 1.9% to 23% which does not suffice to explain the variation. In all the cases the F-
significance is much more than 0.05.
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Kushankur Dey and Debasish Maitra, Fellow Participant, IRMA (Oct-2009)
7. SUMMARY AND CONCLUSION
The present study has not only entailed different combination of two factors but also
included multi -factors together to test the CAPM. β and size , β and ln (ME/BE), β
and (P/Ej-P/Em), β and (d-Rj) and β, size, ln (ME/BE), (P/Ej-P/Em), (d-Rj) together are
used on Indian stock market (S&P CNX NIFTY). The overall summary of the findings
are as follows:
The intercept is coming significantly different from zero as its p-value is more
than 0.05. But over all F-significance is also higher than 0.05 which rejects the
validity of the model. The result shows that β and size β and ln (ME/BE), β and
(P/Ej-P/Em), β and (d-Rj) and β, size, ln (ME/BE), (P/Ej-P/Em), (d-Rj) together
are not capable enough to explain the variation in both the cases of percentage
security return and log return when average of every parameters are used.
Again the result also shows that β and size β and ln (ME/BE), β and (P/Ej-P/Em),
βi and (dj-Rj) and βi, size, ln(ME/BE), (P/Ej-P/Em), (dj-Rj) together are not
significantly capturing the variation both in the cases of percentage of returns
and log returns when individual year (1999-00 to 2008-09) is considered.
Hence, it is ostensible from the study that both the model rejects the alternative
hypothesis saying that Multifactor CAPM is better to capture variation of the investors
the required rate of return and is more robust than the two- factor CAPM. Results of
our study partially corroborate to the study of Fama and French (1992,
1993,1996,1998,2003 and 2004) and Manjunatha and Malikajunappa (2009).
On the posterity of financial maelstrom in continued globalised economy, serious
concern raises on the utility of the extended CAPM to unfold the asset-pricing
anomalies. “Data snooping” which is noted by Merton and put forward the argument
that researchers many a times try to identify the best explanatory variable to predict
and explain maximum variance of the investor‟s portfolio return or individual
security‟s required rate of return.
Few caveats revealed in this paper could be that beta, which we have taken directly
from the market or historical beta instead of doing estimation and avoidance of
employing time-series regression and daily return (instead of 365 days average return)
or to capture the lag effect on the combination of parameters on the dependent variable
or individual securities and portfolio return. Another would be incorporation of equity
risk premium, which often is employed in bivariate analysis (Manjunatha and
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Kushankur Dey and Debasish Maitra, Fellow Participant, IRMA (Oct-2009)
Mallikarjunappa, 2009). In effect, investor‟s required rate of return would pose a threat
on whether the model would have a better fit in explanation or two-factor model would
have a better explanatory power. Result shows that multi-factor model has relatively a
better fit over the two-factor model, but in sense we cannot say that both the model
would predicate the subject, that is, investor‟s return in a better and elegant way.
Hence, should we continue with the insignificant test-result to unravel the riddle and
ramifications of CAPM puzzle in a significant way?
****
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Websites
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Appendix-I
Table-3: Cross-sectional Regression Result of Percentage Returns-Case of Combination of β & Firm-specific Factors
Year β &Size Co-eff β & ln(ME/BE) Co-eff β & (P/Ej-P/Em) Co-
eff
β & (d-Rj) Co-eff β , Size ln (ME/BE), (P/Ej-P/Em) & (d-Rf) Co-eff
α β Size α β ln(ME/BE) α β (P/Ej-
P/Em)
α β (d-Rj) α β Size ln
(ME/BE),
(P/Ej-
P/Em)
(d-Rf)
1999-
00
0.29
(0.00)
0.039
(0.54)
-
1.566
(0.12)
0.15
(0.14)
0.083
(0.25)
0.047
(0.215)
0.25
(0.00)
0.04
(0.51)
0.000
(0.50)
0.25
(0.00)
0.03
(0.57)
-0.04
(0.28)
0.14
(0.16)
0.084
(0.232)
-1.77
(0.071)
0.085
(0.037)
0.0003
(0.405)
-0.084
(0.063)
R2-0.0599, F Sig.-
0.237
R2-0.042, F Sig-0.361 R
2-0.019, F Sig-0.62 R
2-0.03, F Sig-0.43 R
2-0.179, F-Sig-0.109
2000-
01
0.29
(0.00)
0.04
(0.50)
-
1.455
(0.15)
0.18
(0.07)
0.075
(0.30)
0.032
(0.39)
0.25
(0.00)
0.04
(0.49)
0.00
(0.37)
0.27
(0.00)
0.05
(0.45)
0.76
(0.52)
0.22
(0.04)
0.07
(0.33)
-1.44
(0.16)
0.041
(0.27)
0.00
(0.30)
0.68
(0.57)
R2-0.054, F Sig.-0.26 R
2-0.02, F Sig.-0.52 R
2-0.028, F Sig.-0.50 R
2-0.02, F Sig.-0.61 R
2-0.10, F Sig.-0.432
2001-
02
0.29
(0.00)
0.06
(0.36)
-1.40
(0.16)
0.19
(0.06)
0.09
(0.21)
0.031
(0.40)
0.26
(0.00)
0.06
(0.34)
0.00
(0.39)
0.27
(0.00)
0.06
(0.30)
0.45
(0.70)
0.23
(0.03)
0.088
(0.32)
-1.50
(0.14)
0.039
(0.30)
0.00
(0.34)
0.57
(0.63)
R2-0.06, F Sig.-0.23 R
2-0.035, F Sig.-0.43 R
2-0.03, F Sig.-0.42 R
2-0.02, F Sig.-0.56 R
2-0.10, F Sig.-0.43
2002-
03
0.28
(0.00)
0.071
(0.29)
-1.52
(0.14)
0.17
(0.10)
0.10
(0.16)
0.035
(0.92)
0.24
(0.13)
0.07
(0.28)
0.00
(0.46)
0.24
(0.00)
0.07
(0.27)
-0.12
(0.92)
0.20
(0.07)
0.09
(0.18)
-1.63
(0.12)
0.04
(0.27)
0.00
(0.42)
0.11
(0.93)
R2-0.07, F Sig.-0.17 R
2-0.04, F Sig.-0.34 R
2-0.037, F Sig.-0.40 R
2-0.02, F Sig.-0.52 R
2-0.10, F Sig.-0.39
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Kushankur Dey and Debasish Maitra, Fellow Participant, IRMA (Oct-2009)
2003-
04
0.27
(0.00)
0.06
(0.32)
-1.50
(0.12)
0.24
(0.00)
0.06
(0.35
)
-0.001
(0.80)
0.23
(0.0
0)
0.06
(0.30
)
0.00
(0.5
4)
0.23
(0.00)
0.06
(0.3
0)
-0.03
(0.97
)
0.28
(0.00
)
0.05
(0.41)
-1.50
(0.13)
0.00
(0.86
)
0.00
(0.55)
0.24
(0.87)
R2-0.07, F Sig.-0.17 R
2-0.02, F Sig.-0.54 R
2-0.03, F Sig.-0.47 R
2-0.02, F Sig.-0.56 R
2-0.08, F Sig.-0.57
2004-
05
0.29
(0.00)
0.05
(0.36)
-1.55
(0.11)
0.23
(0.026
)
0.07
(0.30)
0.011
(0.76)
0.25
(0.0
6)
0.06
(0.35)
0.00
(0.44
)
0.24
(0.01)
0.06
(0.3
4)
-0.23
(0.90)
0.28
(0.04)
0.07
(0.32)
-1.64
(0.11)
0.019
(0.60)
0.00
(0.41)
0.53
(0.80)
R2-0.07, F Sig.-0.17 R
2-0.02, F Sig.-0.58 R
2-0.03, F Sig.-0.45 R
2-0.02, F Sig.-0.60 R
2-0.09, F Sig.-0.56
2005-
06
0.30
(0.00)
0.07
(0.25)
-1.81
(0.08)
0.25
(0.025
)
0.13
(0.095)
0.012
(0.755
)
0.27
(0.0
0)
0.11
(0.12)
0.00
(0.37
)
0.28
(0.00)
0.12
(0.1
2)
0.05
(0.98)
0.29
(0.02
7)
0.12
(0.17)
-1.87
(0.08)
0.02
(0.60)
0.00
(0.36)
0.25
(0.89)
R2-0.092, F Sig.-0.10 R
2-0.034, F Sig.-0.439 R
2-0.042, F Sig.-0.37 R
2-0.0042, F Sig.-0.37 R
2-0.12, F Sig.-0.31
2006-
07
0.32
(0.00)
0.00
(0.11)
-1.84
(0.079)
0.25
(0.025
)
0.13
(0.095)
0.012
(0.755
)
0.27
(0.0
0)
0.11
(0.11)
0.00
(0.37
)
0.28
(0.00)
0.12
(0.1
2)
0.05
(0.98)
0.29
(0.02
7)
0.12
(0.12)
-1.87
(0.08)
0.02
(0.60)
0.00
(0.36)
0.25
(0.89)
R2-0.12, F Sig-0.052 R
2-0.059, F Sig.-0.233 R
2-0.074, F Sig.-0.16 R
2-0.058, F Sig.-0.26 R
2-0.14 , F Sig.-0.235
2007-
08
0.37
(0.00)
0.06
(0.35)
-1.88
(0.08)
0.28
(0.012)
0.09
(0.26)
0.019
(0.60)
0.32
(0.0
0)
0.069
(0.34)
0.00
(0.30)
0.27
(0.02)
0.06
(0.4
22)
-1.05
(0.56)
0.028
(0.05)
0.07
(0.36)
-1.89
(0.09)
0.029
(0.45)
0.00
(0.31)
0.73
(0.69)
R2-0.085, F Sig-0.13 R
2-0.03, F Sig-0.52 R
2-0.044, F Sig-0.35 R
2-0.029, F Sig-0.50 R
2-0.12, F Sig-0..33
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Kushankur Dey and Debasish Maitra, Fellow Participant, IRMA (Oct-2009)
Data in parenthesis shows p-value at 5% level of significance
Appendix-II
Table-4: Cross-sectional Regression Result of Log Returns-Case of Combination of β & Firm-specific Factors
2008-
09
0.34
(0.00)
0.05
(0.42)
-1.73
(0.09)
0.25
(0.02)
0.08
(0.28)
0.027
(0.48)
0.30
(0.0
0)
0.06
(0.41
0.00
(0.32)
0.46
(0.00)
0.07
8
(0.27
)
3.09
(0.17)
0.46
(0.00)
0.09
(0.18)
-1.73
(0.09)
0.04
(0.20)
0.00
(0.15)
4.17
(0.07)
R2-0.085, F Sig-0.13 R
2-0.085, F Sig-0.13 R
2-0.085, F Sig-0.13 R
2-0.085, F Sig-0.13 R
2-0.085, F Sig-0.13
Year β &Size Co-eff β & ln(ME/BE) Co-eff β & (P/Ej-P/Em) Co-eff β & (d-Rj) Co-eff β , Size ln (ME/BE), (P/Ej-P/Em) & (d-Rf) Co-
eff
α β Size α β ln(ME/
BE)
α β (P/Ej-
P/Em)
α β (d-Rj) α β Size ln
(ME/
BE),
(P/Ej-
P/Em)
(d-Rf)
1999
-00
-1.31
(0.00
)
0.05
(0.87)
-5.80
(0.21)
-1.76
(0.00)
0.20
(0.55)
0.16
(0.37)
-1.45
(0.00
)
0.06
(0.85)
0.001
(0.34)
-1.40
(0.00)
0.043
(0.88
)
-0.17
(0.38
)
-1.81
(0.00
)
0.19
(0.55
)
-6.51
(0.16
)
0.30
(0.12
)
0.00
(0.29
)
-0.31
(0.15
)
R2-0.035, F Sig.-0.44 R
2-0.181, F Sig.-0.65 R
2-0.021, F Sig.-0.611 R
2-0.018, F Sig.-0.66 R
2-0.12, F Sig.-0.32
2000
-01
-1.31
(0.00
)
0.14
(0.62
1)
-6.51
(0.13
8)
-1.67
(0.00)
0.22
(0.50)
0.05
(0.35)
-1.51
(0.00
)
0.15
(0.61)
0.00
(0.28)
-1.36
(0.00)
0.17
(0.56
)
6.31
(0.22
)
-1.42
(0.00
)
0.19
(0.56
)
-5.80
(0.19
)
0.09
(0.54
)
0.00
(0.20
)
6.16
(0.24
)
R2-0.053, F Sig.-0.28 R
2-0.009, F Sig.-0.79 R
2-0.03, F Sig.-0.46 R
2-0.039, F Sig.-0.39 R
2-0.11, F Sig.-0.36
International Finance Conference, IIM-Calcutta: Asset Pricing
Page 25 of 26
Kushankur Dey and Debasish Maitra, Fellow Participant, IRMA (Oct-2009)
2001
-02
-1.31
(0.00
)
0.17
(0.45)
-4.61
(0.20)
-1.49
(0.00)
0.22
(0.39)
0.038
(0.77)
-1.41
(0.00
)
0.18
(0.46)
0.00
(0.27)
-1.34
(0.00)
0.22
(0.37
)
4.25
(0.31
)
-1.34
(0.00
)
0.22
(0.39
)
-4.80
(0.18
)
0.06
(0.63
)
0.00
(0.23
)
4.78
(0.25
)
R2-0.048, F Sig.-0.311 R
2-0.016, F Sig.-0.69 R
2-0.039, F Sig.-0.39 R
2-0.036, F Sig.-0.43 R
2-0.11, F Sig.-0.41
2002
-03
-1.33
(0.00
)
0.17
(0.53)
-5.86
(0.16)
-1.58
(0.00)
0.24
(0.42)
0.06
(0.72)
-1.46
(0.00
)
0.18
(0.51)
0.00
(0.31)
-1.34
(0.00)
0.23
(0.40
)
5.02
(0.35
)
-1.36
(0.00
)
0.26
(0.39
)
-6.23
(0.14
)
0.09
(0.53
)
0.00
(0.24
)
6.13
(0.25
)
R2-0.053, F Sig.-0.28 R
2-0.014, F Sig.-0.72 R
2-0.033, F Sig.-0.45 R
2-0.029, F Sig.-0.49 R
2-0.11, F Sig.-0.39
2003
-04
-1.42
(0.00
)
0.21
(0.44)
-6.23
(0.12)
-1.36
(0.00)
0.14
(0.62)
-0.026
(0.33)
-1.56
(0.00
)
0.22
(0.42)
0.001
(0.40)
-1.44
(0.00)
0.27
(0.32
)
4.39
(0.49
)
-1.06
(0.01
)
0.16
(0.58
)
-6.28
(0.12
)
-0.02
(0.37
)
0.00
(0.34
)
5.86
(0.36
)
R2-0.065, F Sig.-0.21 R
2-0.036, F Sig.-0.42 R
2-0.032, F Sig.-0.48 R
2-0.026, F Sig.-0.54 R
2-0.11, F Sig.-0.36
2004
-05
-1.26
(0.00
)
0.19
(0.40)
-5.44
(0.11)
-1.35
(0.00)
0.20
(0.42)
-0.02
(0.87)
-1.38
(0.00
)
0.20
(0.88)
0.00
(0.31)
-1.19
(0.00)
0.29
(0.23
)
6.35
(0.30
)
-1.03
(0.04
)
0.16
(0.55
)
-5.40
(0.15
)
-0.03
(0.83
)
0.00
(0.27
)
5.64
(0.46
)
R2-0.054, F Sig.-0.27 R
2-0.016, F Sig.-0.69 R
2-0.034, F Sig.-0.44 R
2-0.014, F Sig.-0.71 R
2-0.088, F Sig.-0.53
2005
-06
-1.26
(0.00
)
0.19
(0.40)
-5.44
(0.11)
-1.35
(0.00)
0.20
(0.42)
-0.02
(0.87)
-1.38
(0.00
)
0.20
(0.88)
0.00
(0.31)
-1.19
(0.00)
0.29
(0.23
)
6.35
(0.30
)
-1.02
(0.01
)
0.25
(0.32
)
-5.20
(0.13
)
0.00
(0.98
)
0.00
(24)
7.19
(0.25
)
International Finance Conference, IIM-Calcutta: Asset Pricing
Page 26 of 26
Kushankur Dey and Debasish Maitra, Fellow Participant, IRMA (Oct-2009)
Data in parenthesis shows p-value at 5% level of significance
R2-0.071, F Sig.-0.18 R
2-0.019, F Sig.-0.64 R
2-0.04, F Sig.-0.39 R
2-0.041, F Sig.-0.37 R
2-0.121, F Sig.-0.33
2006
-07
-1.16
(0.00
)
0.23
(0.24)
-4.52
(0.13)
-1.24
(0.00)
0.24
(0.27)
-0.19
(0.86)
-1.27
(0.00
)
0.23
(0.23)
0.00
(0.24)
-1.26
(0.00)
0.26
(0.23
)
0.47
(0.93
)
-1.11
(0.00
)
0.24
(0.30
)
-4.49
(0.14
)
0.00
(0.99
)
0.00
(0.24
)
1.43
(0.79
)
R2-0.080, F Sig.-0.14 R
2-0.034, F Sig.-0.44 R
2-0.061, F Sig.-0.23 R
2-0.034, F Sig.-0.45 R
2-0.11, F Sig.-0.39
2007
-08
-1.09
(0.00
)
0.17
(0.40)
-5.15
(0.08
9)
-1.32
(0.00)
0.23
(0.30)
0.049
(0.65)
-1.22
(0.00
)
0.17
(0.39)
0.00
(0.22)
-1.22
(0.00)
0.19
(0.37
)
0.04
(0.99
)
-1.16
(0.00
)
0.21
(0.34
)
-5.33
(0.08
5)
0.068
(0.52
)
0.00
(0.21
)
1.15
(0.82
)
R2-0.068, F Sig.-0.19 R
2-0.023, F Sig.-0.58 R
2-0.05, F Sig.-0.30 R
2-0.019, F Sig.-0.64 R
2-0.12, F Sig.-0.34
2008
-09
-1.81
(0.00
)
0.16
(0.45)
-5.27
(0.11)
-1.48
(0.00)
0.25
(0.30)
0.09
(0.46)
-1.31
(0.00
)
0.17
(0.44)
0.00
(0.23)
-0.64
(0.13)
0.244
(0.26
)
13.08
(0.06
)
-0.62
(0.16
)
0.33
(0.14
)
-5.17
(0.09
)
17.00
(0.14
)
0.00
(0.07
)
17.1
6
(0.01
)
R2-0.068, F Sig.-0.19 R
2-0.026, F Sig.-0.53 R
2-0.045, F Sig.-0.34 R
2-0.086, F Sig.-0.12 R
2-0.23, F Sig.-0.04