Multifactor Analysis of Capital Asset Pricing Model in Indian … · International Finance Conference, IIM-Calcutta: Asset Pricing Page 1 of 26 Kushankur Dey and Debasish Maitra,

International Finance Conference, IIM-Calcutta: Asset Pricing

Page 1 of 26

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].

mailto:[email protected]

mailto:[email protected]


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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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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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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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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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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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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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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.


Page 16 of 26


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.


Page 17 of 26


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


Page 18 of 26


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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Page 22 of 26


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


Page 23 of 26


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


Page 24 of 26


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


Page 25 of 26


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

)


Page 26 of 26


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

Multifactor Analysis of Capital Asset Pricing Model in Indian … · International Finance Conference, IIM-Calcutta: Asset Pricing Page 1 of 26 Kushankur Dey and Debasish Maitra,

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