title: portfolio selection revisited: evidence from … · title: portfolio selection revisited:...

Kushankur Dey & Debasish Maitra, Fellow Participant, IRMA

Draft Paper/IFID Conference/May-2010

TITLE: PORTFOLIO SELECTION REVISITED: EVIDENCE FROM THE

INDIAN STOCK MARKET

Authors’ Affiliation

First Author: Shri Kushankur Dey

Doctoral Student, 3rd Year

Fellow Programme in Rural Management

Institute of Rural Management, Anand (IRMA)

Gujarat-388001

Email: [email protected] / [email protected]

Second Author: Shri Debasish Maitra

Doctoral Student, 2nd Year

Fellow Programme in Rural Management

Institute of Rural Management, Anand (IRMA)

Gujarat-388001

Email: [email protected] / [email protected]

mailto:[email protected]






ABSTRACT

Investment theory in securities markets pre-empts the study of the relationship between risk and

returns. In this parlance, the behavior of stock-price (movement) has been a recurrent topic in

financial jargon. A large number of studies have reported the risk-return equation of the group of

assets or the portfolios. A couple of literature have been carrying the magnitude of the results with

respect to the portfolio selection, evaluation and optimisation since a long time-period. Several

models are also being proposed and reviewed in view of their utilities and validities with renewed

interests of the diverse participants. Hence, this paper is an attempt to examine the reliability and

usefulness of the ex-ante measures for formulating the portfolio in a congruent manner.

Prima facie the Sharpe single-index model is incorporated in the study, besides, the Treynor-index, the

Jensen-index, and the Sortino-index, which of course, have yielded relatively a superior and legitimate

result as compared to a single-index model or measure. The study is conducted in Indian context

with special reference to S&P CNX NIFTY index. NIFTY is considered as a proxy of the market,

that comprises of 50 individual stocks and incorporation of these stocks are subject to three criteria;

liquidity, market capitalisation, and floating stocks. Using the Sharpe postulated “algorithm”, cut-off

is calculated to select and formulate the portfolio. 26 stocks have qualified to form the portfolio. A

comprehensive analysis of each individual stock, portfolio, and the index is carried out with respect

to their annualised returns, annualised standard deviations, betas, residual variances or deviations

using the mentioned ratios. Mean-variance efficient portfolio is graphically presented in the paper

adopting the Markowitz’ risk-return measures approach.

Therefore, this paper is an amalgamation of both the modern- and post-modern portfolio theory

with a logical and an elegant approach. Moreover, this study, evidently, provides a basis to a large

section of investors, especially retail investors for analysing, selecting, and evaluating the portfolio as

a mirror image of the index on a specific reference point of his/her portfolios in order to achieve

the optimisation of assets allocation and risk-restructuring in the Indian context.

Keywords: Portfolio theory, post-modern portfolio theory, Sharpe-ratio or index, Treynor-ratio,

Jensen-ratio, Sortino-ratio, Coherent measures of risk



1. MOTIVATION

With the advent of information technology, there have been significant changes

observed in the landscape of stock markets worldwide. Obviously, Indian stock market

is not an exception to the effect of globalization. Besides the relay-race of a band of

qualified institutional buyers (QIBs) and non-institutional buyers (NIBs) in the market,

evidently, small or retail investors are also taking interest to invest now-a-days.

Moreover, they understand and play the game by virtue of the “buy-low and sell-high”

strategy. Often this type of investor falls into a trap by showing “herd” behaviour or

sometimes reaps a quantum of “momentum-profit” by adopting “contrarian” strategy.

A good mix of fundamental and technical analysis helps the investor to formulate the

strategy either for buying or for selling the stocks or securities. This is, in a true sense,

called portfolio selection and evaluation. On apriori basis, if investor seems to have a set

of full-information about the market, he/she can invest proportionately to make a

relative gain. Once the investor experiences his/her gain (loss) without knowing or

predicting the market, he or she further does investment while taking the lessons from

the past. We try to make it clear that individual or personal finance influenced by

individual’s mental accounting, representativeness in the market (law of small

numbers), disposition effect, conservatism, overconfidence, etc.;-which have

undoubtedly taken a distinct place in the realms of “behavioural finance”. We depart

from this, rather we take our position to explore and explain adopting the philosophy of

positive economics behind the occurrence of gain or loss of the investor. It is of course, a

branch of financial economics, called security analysis and portfolio management (part

of modern portfolio theory). There were many contributions already made enrichment

of this field till late eighties. Hence, an attempt has been made to analyse the use of

security to improve the portfolio selection adopting the single-index (algorithmic)

model of William Sharpe (1964) in this paper along with a tinge of other approaches of

post-modern portfolio theory, say, Sortino ratio or index.

In first section, introduction is narrated succinctly; section-two looks at literature review

followed by objectives, hypotheses, and methodology in section-three. Section-four

discusses the results and findings. Section-five summarises the whole paper and comes

out with implication or leaves few signposts for the future research.



SECTION-I

2. INTRODUCTION

Relationship between return and risk has been receiving significant importance in

realising the optimal allocation of stocks or optimal investment strategy or even for

testing the market anomalies for abnormal stock returns in a horizon of time-period

(Nath and Dalvi 2004). Hence, portfolio analysis has remained one of the highly

pursued areas of research in financial economics for more than three decades. 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 of 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 split into systematic and unsystematic risk, that is, 2i = β22m + 2εi,

where β is systematic factor, 2m denotes the systematic risk and 2εi is unsystematic

risk contained portfolio. Thus, it would be relevant to measure the correlation or

covariances (rx,y or Covx,y) 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 formulate an optimal portfolio.

At this juncture, we try to bring some classics in the context of modern portfolio theory,

which is obviously recounted with few barons of financial economics, namely, Roy,

Markowitz, William Sharpe, Treynor, Black, Jensen, and Sortino. Markowitz in his

noble winning paper arguably stated that the process of selecting a portfolio may be

divided into two stages. The first stage starts with observation, experience, and ends up

with beliefs about the future performances of available securities. The second stage

starts with the relevant beliefs about future performances and ends with the choice and

selection of portfolio (Markowitz 1952). This actually gave a birth to the modern

portfolio theory in positive economics. Markowitz is also clear that historical data does

not matter rather beliefs about the future as intuitively he posited that historical data is

of interest only in so far as it helps form those beliefs about the future. Since different

people have different beliefs, Markowitz’s pathbreaking research gives a motivation to

investors to formulate a portfolio that can serve a proxy for the market in true sense.

More so, he is not bothered about how those choices affect equilibrium process in the

market. Sharpe (1964) assumed that investors are homogeneous in nature and are

expected to agree on the expected returns, standard deviations and correlations of the



securities or stocks in chosen portfolio. Following the legendary works of others, two

questions are relevant to pose at this juncture; (i) what would be the security return as a

result of the event occurred in the economy or stock market in some point in time,

which might be unexpected, or (ii) what would be the market return as a result of that

particular event?

SECTION-II

3. LITERATURE REVIEW

Going by the definition of market efficiency which denotes that a market is efficient

with respect to make abnormal returns or profits (other than by an incidence or by

chance) by using this set of information to formulate buying and selling decisions

(Bharadwaj 2009). We look at two types of popular analyses; one is “fundamental” and

the other “technical”. These two have their own significant impact on investor’s

decision making (DM) with respect to self-financing portfolio or zero-investment

(arbitrage) portfolio. Precisely, fundamental analysis takes into accounts of

macroeconomic indicators, industry benchmark ratio and company whereas technical is

based on charting and trend analysis, say, breadth analysis (dispersion of price-volume

ratio), relative-strength-indicator, moving average convergence-divergence (MACD)

and Elliot’s wave study and band (Bollinger) analysis, etc. There are many tools and

techniques already evolved to make the payoff or loss more certain without a mere and

naïve investment strategy. On the corollary, it is obvious that market follows its own

pattern satisfying the random walk hypothesis (RWH) or Chartists’ theory. Hence, we can

say that “the behaviour of stock price has been a recurrent topic in financial jargon.

Stock price is time varying and depends upon its past information, market news, and

various macroeconomic factors*” (Pradhan 2009: 1). French and Roll (1986) empirically

showed that flow of information affects the magnitude of trading time following the

observations and impacts on volatility, which follows trading time hypothesis (French and

Rogalski 1980) rather than calendar time hypothesis. Hence, there is a trend-reversal

observed following the “formation” (say 6 months) and “test” (say, rest 6 months)

period in post-event phenomena. This seems to have a formation of “conformity bias”

as a difference between winner’ and looser’ portfolio (W-L) as pointed out by Jagdish

and Titman (1986). On the other side, there is an impact of value of assets and growth *Adapted from the paper, “Stock Price and Macroeconomic Indicators in India: Evidence from

Causality and Cointegration Analysis” by Rudra P. Pradhan, Vinod Gupta School of Management, Indian Institute of Technology Kharagpur. This paper was presented at the conference, “Advanced Data Analysis, Business Analytics and Intelligence”, Indian Institute of Management-Ahmedabad, 2009.



on stock return. Cooper (2009) suggested that stocks with higher assets growth usually

underperform relative to those with lower assets growth. Hence, it is advisable to take a

long (buy or bid) position of stocks with higher return on assets (ROA) and a short (sell

or ask) position of stocks with relatively lower ROA or assets growth. Hvidkjaer (2005)

discussed the role of (extrapolation bias) small traders in the market showing the trade-

based analysis of momentum through the cross-sectional analysis of stock returns.

Factors determining this momentum profit or variances in the stock returns with a

sentiment period in trading are namely, one month across return (negative), trading

volume/market capitalisation (negative), earnings-to-price (positive), return on equity

(positive), book-to-price (positive),etc. Here, momentum is the effect that reasons out

that winner tends to “win” and losers tend to “loose” for three to six-months horizon or

reference frame of wealth allocation. This explanation draws argument from the realms

of behavioural finance. Now-a-days, algorithmic studies are conducting in this branch

which is akin to positive financial economics.

Against this backdrop, 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 (Fama and French 2004). The model

simplifies the complexity of real world, tells us that a linear relationship exists between

a security’s (stock) required 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=+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. This holds

true for a hemophilic group of people containing same belief.

Treynor and Black (1973) showed empirically that adequate usage of security analysis

can help to improve portfolio selection and they interpreted CAPM as putting forward

that the investor should hold a model or replica of the market portfolio as investors

have different expectations from the market consensus because of the absence of insight

generating information. This implicitly tells about that the market is “noisy” and the

assumption of Efficient Market Hypothesis (EMH) does not hold true in all cases



(Grossman and Stiglitz 1980; Fama 1991; Nelson and Schertz 1996; Campbell, Lo and

MacKinlay 1997). Very often, semi-strong (containing historical and public information)

form of the market seems to persist. Following the elegant model of Treynor and Black

on “portfolio choice” while investors had out of consensus beliefs, assumptions

underlying EMH connotes that individual investor who is attempting to trade

profitably on the difference between her expectations and those of a monolithic or

gigantic market so large in relation to her own trading activities or strategies that

market prices are unaffected by it (Varma 2010). Similar ideas can be traced in the

popular Black-Litterman model of “Global Portfolio Optimisation” (1992) which started

with some postulations, namely, we ready to accept that there are two distinct sources

of information about future excess returns;- investor views and market equilibrium; we

assume that both sources of information are uncertain and are best expressed as

occurrence of probability or distributions; lastly, we choose expected excess returns that

are as consistent as possibly with both sources of information.

Even we stick to the market consensus, the CAPM beta itself has to be interpreted with care. The deviation of the CAPM makes it clear that the beta is actually the ratio of covariance of security’s return and market return to a variance of the market return and both of these are parameters of the subjective probability distribution that defines the market consensus…this may be formally correct, but it is misleading because it suggests that the beta is defined in terms of a regression on past data (Varma2010: retrieved from www.iimahd.ernet.in/~jrvarma/blog/index.cg on May 5, 2010).

Beta is considered as regressor (excess return of market portfolio on excess return of

individual stock). But the conceptual meaning of beta is somehow different as empirical

work of Guy and Rosenberg (1976) established in their paper, “prediction of beta from

investment fundamentals” by incorporating few industry estimates, viz., variance in

earnings, variance in cash flows, debt-to-equity ratio (levered or unlevered firm), debt-

to-asset ratio, etc. Hence, there should be subjective beliefs about possible yet uncertain

future changes in the beta because of changing business strategy or financial strategy

must also be considered. The underpinning of this can serve purposes of an investor,

assuming a rational one in positive economics, seems to be agreeable at several

occasions that market is random and it has long-indefinite memory to reach equilibrium

or may show a mean-reverting process or simply white noise after removing trend or

drift. Therefore, it is quite intuitive that the data generating process does not remain

same for too long being coupled with a proper method or fundamental judgment to

reduce the sampling error. Being a rational investor wants to optimise the return and

risk theoretically that gives a “mean-variance efficient portfolio frontier” underlying

some feasible regions.

http://www.iimahd.ernet.in/~jrvarma/blog/index.cg%20on%20May%205



Fortunately, Markowitz’s propositions about the efficient frontier that postulates two

relevant parameters of the frequency distributions or two moments which are, namely,

mean (first moment) and variance (second). He further stated that formulation of

portfolio does not require any further higher-order parameters (Markowitz 1952; Ghosh

2009). Added that the covariance feature is most important that promotes the advantage

through diversification of assets in the portfolio. This actually minimises the probability

of occurrence of unsystematic risk to a certain limit. This criterion is applicable for more

than 2-security’s (NC2) portfolio. If securities are two, there is no advantage from

diversification if rates of return from those securities are positively and perfectly

correlated (rx,y =+1) which is unlikely happened with perfectly, negatively correlated

security’s portfolio (rx,y =-1). In this case, portfolio return would be achieved with

certainty. On the other side, the lower the magnitude of correlation, the better it is for

diversification, and the negative value, if it is to be ascertained for correlation, is most

desirable. Hence, there is a relation of inequality between the correlation coefficient and

the ratio of 2-security’s standard deviations would score good to delineate cases of

advantage from diversification to those which are not. Markowitz’ work was precisely a

post-hoc work that was mostly concentrated on a small set of securities. Sharpe’s

algorithm (1963 and 1964) tried to overcome the actual problem of formulating efficient

portfolio in reality (stock market) and he had come out with a predictive, ex-ante model

to establish the generalisation of modern portfolio theory covering a large set of

securities or the universe in the gamut of financial economics. His single-index model

brought an approach to the covariance of the stock prices that has been to identify the

underlying economic forces simultaneously affecting all the stocks in the market.

Hence, a shift from microeconomic bias to macroeconomic one was taken place

gradually. This single-index model is nothing but a forecast of the market rate of return

and also of its variance during the holding period, in addition the expected rate of

return and the variance for each security or stock in the starting selection vector of those

stocks.

The distinction between Markowitz’ model and Sharpe’s model was that the former

model was based on historical data that underscored the merit to attempt to foresee or

forecast a relevant parameters or value in the future, involving the holding period for

the fund relation or investment. The latter model specifically brought in the expected

future values of the market return and in variance and these are essential elements

determining the various parts of the optimisation or optimally calculations. Sharpe ratio

or index (excess return from risk-free rate of return to standard deviation of return of

portfolio) helps to identify the “reward-to-variability” of the investor’s portfolio.

Treynor ratio or index (excess return from risk-free rate of return to beta of portfolio)



and Jensen performance-measures (difference between investor’s excess return and

market return as a proxy for alpha coefficient) contributed substantially to the modern

portfolio theory.

After 1990s, few observations were noticed and documented by financial experts, viz.,

Sortino (1991) in view of asymmetric distributions of stock values and random

cashflow. This situation compelled to incorporate several model-building approaches,

namely, mean-risk model, expected utility maximisation, and stochastic dominance to

capture the randomness of the stock-return precisely. These phenomena gave a rebirth

or transformation of modern portfolio theory to post-modern portfolio theory (PMPT). Sortino

index (excess return from risk-free rate of return to down-side risk) came into being for

allocating assets or securities to capture the asymmetric distribution of stock return.

Sortino and Price (1994), and Pederson and Satchell (2002) proved that the risk-return

frontier while risk is defined by stochastic second-order dominance (SSD-II), exhibits

the same expected convexity properties of the traditional mean-variance frontier, thus,

is desirable for portfolio analytics. Sortino index is defined as:

As an alternative, the Sortino ratio has been advocated in order to capture the asymmetry of the return distribution. It replaces the standard deviation in the Sharpe ratio by the downside deviation which captures only the downside risk. However, higher moments are incorporated only implicitly (Bacmann and Scholz, see also, Sortino 1998; http://www.sortino.com/htm/Sortino%20Ratio.htm.)

Therefore, the Sortino ratio is akin to the Sharpe ratio except that the square root of the

semi-variance replaces the volatility or it connotes that the risk is only measured with

down-moves that is, relative to some target value or minimum acceptable returns

(MAR). Lien (2002) argued that excessive kurtosis (fourth moment) has hardly any

impact on the monotonic relation between Sortino and Sharpe ratios. Considering

portfolio returns are normally distributed (log-normal), it is obvious that both Sortino

ratio (SR) and upside potential ratio (UPR) are monotonically increasing functions of

the Sharpe ratio. Hence, these three risk-measures provide an extent for identical

ranking of portfolio alternatives. Plantinga and de Groot (2001) stated that for higher

levels of loss or risk-aversion, the Sortino ratio succumbs to the best results with a

correlation of approximately 60% with the preference function. Still, Sortino ratio has

attracted few critics from the point of coherent risk measures as this ratio or “value at

risk” (VaR) are ad-hoc attempts to measure the downside risk whereas there is potential

ignorance of incorporating upside risk-measures (Leland 1998). Hence, both are

“generally inaccurate as an appropriate risk and/or performance measures” (Leland

1998).

http://www.sortino.com/htm/Sortino%20Ratio.htm



SECTION-III

4. OBJECTIVES

Based on the literature review, we try to formulate a portfolio using the database of

Indian capital market, which is the constituent of stock and bond market precisely.

i. Use of Sharpe-single index model and ratio-analysis (Treynor, Jensen and

Sortino) to formulate and improve the portfolio selection are to be ascertained

through adequate employment of stocks returns- and market returns-series of

the S&P CNX NIFTY index.

ii. Performance of portfolio is to be evaluated with respect to index by setting few

relevant parameters, namely, beta, market return, stock return, systematic risk,

unsystematic risk, and downside risk.

Cross-sectional analysis is incorporated to administer the revenant tests in order to

arrive at the stated objectives.

5. HYPOTHESES

H1: Mean-variance efficient portfolio is likely to be achieved by incorporating Sharpe

single-index model approach as an ex-ante measure of the modern portfolio theory in

Indian context.

H2: Portfolio risk-return optimisation scores relatively higher than the index or market

risk and return equation.

H3: Optimal portfolio selection is possible using the Sharpe single-index model if and

only market is considered a proper vector space.

H4: A good combination of all ratios would define the portfolio relatively superior to a

single-ratio based approach as a contingency approach and corroborate to the

principles-based coherent risk measures and post-modern portfolio theory.

Negations of the above mentioned alternate hypotheses are nothing but the null ones

(hypotheses).

6. METHODOLOGY

Methodological purposiveness and congruence are two most critical issues in financial

economics. Concordance about the model selection should be achieved to empirically

test the chosen statistical model in order to arrive at precision and to approximate the



reality (ontology). Model is a representative of the theory which tries to explain any

phenomena comprehensively and consistently. In this section, we try to define the

model and to delineate the set of procedures for the measurement.

6.1. Model Specifications and Notations

We consider that let there be N risky assets with mean vector μ and covariance matrix Ω

assuming that expected return from at least two assets differ and their covariance

matrix is of full rank (linearly independent or orthogonal in nature). Define ωa as the (N

X 1) vector of portfolio weights for an arbitrary portfolio “a” with weights summing to

unity (1). Portfolio “a” has mean return μa = ωa’ μ and variance, σ2a = ωa’ Ω ωa. The

covariance between any two portfolios “a” and “b” is ωa’ Ω ωb. Given the population of

assets, minimum-variance portfolios are constructed in the absence and presence of

risk-free asset (Merton 1972; Roll 1977; Campbell, Lo, and Mackinlay 2007).

Stylized Fact: Portfolio p is the minimum-variance portfolio of all portfolios with mean return

μp if its portfolio weight vector is the solution to the following constrained optimisation:

min ω’ Ω ω (i)

ω

subject to

ω’ μ = μp (ii)

ω’τ = 1 (iii)

To solve the optimisation problem, we formulate the Lagrangian function L,

differentiate with respect to ω, set the resulting equation to zero, and then solve for ω.

To arrive at stable solution, the Lagrangian function we have

L = ω’ Ω ω + δ1 (μp- ω’ μ) + δ2 (1- ω’τ) (iv)

Where τ is a conforming vector of ones and δ1 and δ2 are Lagrangian multipliers.

Differentiating L with respect to ω and setting the result equal to zero, we get

2 Ω ω - δ1 μ - δ2 τ = 0 (v)

Combining (v), (ii), and (iii) equations, we find the solution

ωp = g + hμp (vi)

Where g and h are (N X 1) vectors, g = 1/D [B (Ω-1 τ) – A (Ω-1 μ)] (vii)



h = 1/D [C (Ω-1 μ) – A (Ω-1 τ)] (viii)

and A = τ’ Ω-1 μ, B = μ’Ω-1 μ, C = τ’ Ω-1 τ, D = BC- A2

For example, p and r are two minimum-variance portfolios. The covariance of the return

of p with the return of r is

Cov (Rp, Rr) = C/D (μp –A/C) (μr –A/C) +1/C (ix)

And portfolio g as the global minimum-variance portfolio and for each minimum-

variance portfolio, say p, except the global one, there exists a unique minimum-variance

portfolio that has zero covariance with p. This portfolio is said to be the zero-beta

portfolio with respect to p. Hence, we have

ωg= 1/C Ω-1 τ, μg= A/C, σ2g = 1/C (x)

Cov (Rg, Rp) = 1/C (xi)

We now introduce a risk-free asset into the analysis and consider portfolios composed

of a combination of the N risky assets and the risk-free asset. With a risk-free asset the

portfolio weights of the risky assets are not constrained to sum to unity, since (1- ω’τ)

can be invested in the risk-free asset. Therefore, given a risk-free asset with return Rf the

minimum-variance portfolio with expected return μp will be the solution to the

constrained optimisation.

min ω’ Ω ω (xi)

ω

subject to ω’ μ+ (1- ω’τ) = μp (xii)

Taking the Lagrangian function L, differentiate it with respect to ω, set the resulting

equation to zero, and then solve for ω. Hence, we have

L = ω’ Ω ω+ δ μp- ω’ μ-(1- ω’τ) Rf (xiii)

Differentiating L with respect to ω and setting the result equal to zero, we get

2 Ω ω+ δ (μ-Rf τ) = 0 (xiv)

Combining (xiv) and (xii) equations, we get the solution,

ωp = (μp - Rf) / (μ-Rf τ)’ Ω-1(μ-Rf τ)* Ω-1(μ-Rf τ) (xv)

We can express ωp as a scalar which depends on the mean of p times a portfolio weight

vector which does not depend on p in the given vector space.



ωp = cpŵ where cp = (μp - Rf) / (μ-Rf τ)’ Ω-1(μ-Rf τ) and ŵ = Ω-1(μ-Rf τ) (xvi)

Thus with a risk-free asset all minimum-variance portfolios are a combination of a given

risky asset portfolio with weights proportional to ŵ and the risk-free asset. This

portfolio of risky assets is said to be the tangency portfolio and has a weight vector.

Therefore, with the help of portfolio weight vector, tangency portfolio is construed and

with a risk-free asset all efficient portfolios lie along the line from the risk free asset

through portfolio q. Hence, we get

ωq =1/ τ’Ω-1(μ-Rf τ)* Ω-1(μ-Rf τ) (xvii)

The expected excess return per unit risk is useful to provide a basis for economic

interpretation of tests of the CAPM. This can be achieved using the Sharpe ratio. For any

asset or portfolio “a”, the ratio is defined as the mean excess return (Ri–Rf or μa –Rf)

divided by the standard deviation of return of assets or portfolio.

Sra = (μa –Rf )/σa (xviii)

Treynor index is slightly different from the Sharpe ratio. It is defined as the mean excess

return (Ri–Rf or μa –Rf) divided by the beta of assets or portfolio.

Tra = (μa –Rf )/βa (xix)

Jensen performance-measures approach provides a basis for calculating alpha ()

coefficient or intercept of the portfolio. Hence, we can get from the CAPM (two-factor)

model

(μa –Rf) = +βa (μm - Rf), or Jensen measures, = [(μa –Rf) - βa (μm - Rf)] (xx)

Sortino index is defined as the mean excess return (Ri–Rf or μa –Rf) divided by the

downside risk or asymmetric distribution of stock or portfolio return.

Sora = (μa –Rf )/da (xxi)

In analysis, we have used the mentioned ratios. Sharpe-Linter version of the CAPM is

drawn from market-model building approaches which we have used for calculating

beta as regressor and residual variance or unsystematic risk on daily-count basis of the

index. Define Zt as an (N X 1) vector of excess returns for N assets or portfolios of assets,

for these N assets; the excess returns can be described using the excess-return market

model:

Zt = +βZmt +Єt, where E[Єt] = 0, E [Єt, Єt’] = ∑, E [Zmt] = μm, E [(Zmt - μm) 2] = σ2m,



Cov [Zmt, Єt] = 0 (xxii)

β is the (N X 1) vector of betas, Zmt is the time period t market portfolio excess return,

and and Єt are (N X 1) vectors of asset return intercepts and disturbance or noise,

respectively. In case of Sharpe single-index model, the algorithm involves the following

equations presented in the table below:

Table 1: William Sharpe Single-index model-notation

Rank-

order

(1)

Security

No.

(2)

Excess

mean

return

(3)

Excess

mean

return

to beta

(4)

Excess

return

times beta

to residual

variance

(5)

Beta to

Residual

variance

(6)

Cum.

(5)

Cum.

(6)

Cut-off

or C*

(7)

Z-value

or

Optimal

portfolio

selection

(8)

1, 2,

3…

a1, a2, a3… (μa –Rf ) (μa –Rf

)/βa

(μa –Rf )

βa/σa2

βa/σa2 ∑(μa

–Rf )

βa/σa2

∑

βa/σa2

[σ2m∑(μa

–Rf )

βa/σa2]/

[1+

σ2m(∑

βa/σa2]

βa/σa2((μa

–Rf )/βa -

C*)

Note: Security’s selection to formulate portfolio is based on benchmark ratio or cut-off score. Securities which have

higher excess mean return to beta to calculated cut-off score, those would be eligible to enter into the portfolio. Z-

value would decide the proportion or weights of stocks or securities in the portfolio and based on this, ranking of

security is done or optimisation is achieved (Fischer and Jordan 2008: 610-614).

6.2. Sampling Frame and Data

The study is based on 50 S&P CNX NIFTY companies that were part of the index since

November 3, 1995 to till date. S&P CNX NIFTY is recognised as a benchmark stock

index based on the selected stocks traded at the National Stock Exchange (NSE). It is

primarily owned and overseen by India Index Services and Products Ltd. (IISL), which

is joint venture (JV) between the NSE (1992), India’s most advanced and leading Stock

Exchange (3rd ranked world-wide) and Credit Rating and Information Services of India

Limited (CRISIL, 1987), India’s leading Credit Rating Company (1988-89) promoted by

the S&P. IISL is the first specialised company in the country focused upon developing

the stock indices as a core product by encompassing more than 20 sectors (24) in the



designed index, that is, NIFTY. In fact, this index was developed by Shah and Thomas

during nineties. It has a consulting and licensing agreement with the Standard & Poor’s

(S&P), who are world leaders in these services. It is noteworthy to mention that the

average traded value of all NIFTY stocks is more than 80% of the traded value of all

stocks available for trading on the NSE. The stocks are subject to inclusion in NIFTY

based on their (listed companies) average market capitalization, that is, more than or

equal to 500 crores; liquidity which is calculated on impact cost (ratio of actual buy/sell

size to ideal buy/sell size) which should be 0.75% or even less than that either for

buying or for selling the stocks and trade-frequencies of those stocks should be more

than 90% of total trades over six months period; lastly, floating stocks should be at least

of 12% which should not be held by promoters and associates or it is possible that 88%

of the total stocks can be held by them (for more details, see, Patwari and Bhargava

2009).

However, for the purpose of study the data are used from April, 2009 to March, 2010

(244-days closed-trade-price and since then, same 50 companies are the parts 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 reporting 63.326% as reported on December, 2009. In case of free-float

market capitalistion index, NIFTY (54.17%) is ahead of SENSEX (45.82%) other than or

excluding 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. The data are collected from Centre of Monitoring Indian Economy (CMIE-

Prowess database), BSE, NSE, RBI, SEBI websites.

SECTION-IV

7. RESULTS AND DISCUSSIONS

Index data with respect to index return and stock return are retrieved from CMIE for

244-trading days-counts. Regressing index or market return on individual stock return

(taking natural-log of both return-series), beta is calculated for each 50-stock. Calculated

betas have achieved the precision of about 95% with the beta of the NSE-provided

database. 50 independent regressions are run to estimate the predictor or regressor, that

is, beta and unsystematic risk or residual variance (error component). Besides,

descriptive statistics are also ascertained for both the index- and stock-return series of

all 50-stocks cumulatively. The positive skewness coefficients indicate that frequency

distribution of index- and stock-returns series are positively skewed or have longer

thinner tail to the right. The unconditional distribution of both index and stock returns



0

10

20

30

40

50

60

70

80

-0.05 0.00 0.05 0.10 0.15

Series: INDEX_RETURN

Sample 1 243

Observations 243

Mean 0.002220

Median 0.001662

Maximum 0.163343

Minimum -0.060216

Std. Dev. 0.018848

Skewness 2.450687

Kurtosis 24.19185

Jarque-Bera 4790.317

Probability 0.000000

Descriptive Statistics_Index Retrun

exhibit thin tails (leptokurtic) and excessive peak at the mean than the corresponding

normal distributions. Both series follow an empirical distribution, say, log-normal,

normality is not achieved as reported by J-B (Jarque-Bera) statistic (4790.317 with

significant p-value for index return and 3838.90 with significant p-value for stock-return

series on daily-counts) besides the unit-root check, which is shown in the following

histogram and graph (Fig-1, Fig-2, and Fig-3). Here the J-B statistic is highly statistically

significant for both index and stock-returns series, and hence we fail to accept the null

hypothesis of normality.

Table-2 represents the results of Augmented Dickey-Fuller (ADF) (Dickey and Fuller

1979) unit-root tests applied on the log-first differences of daily stock- and index-

returns series to test the existence of unit roots and identify the order of integration

[I(1), in this case] of each variable. Phillips-Perron (PP) (Phillips and Perron, 1988) unit-

root test was not conducted to test the same as the sample-size is relatively large

enough to follow the asymptoticy. Results show that the first differences of logarithm of

the both index and stock-prices yielded larger ADF statistics that rejected the null

hypothesis with three critical values at three levels of significance, 1%, 5%, and 10%.

Hence, we can safely infer that both series are stationary at their first differences but

non-stationary processes are observed at their individual log-series. Therefore,

evidently, movements of stock-return series follow a mean-reverting process, which is

known as white noise (mean zero, variance, and covariance constant) conforming non-

linearity returns-series. Beta, F-statistic, Rj2, residual variance (σε2) of each stock are

presented in Exhibit-1.

FIG-1: Descriptive statistics of Index return (S&P CNX NIFTY)



-.10

-.05

.00

.05

.10

.15

.20

25 50 75 100 125 150 175 200 225

Stock Return

0

10

20

30

40

50

60

70

-0.05 0.00 0.05 0.10 0.15 0.20

Series: STOCK_RETURN

Sample 1 243

Observations 243

Mean 0.001987

Median 3.26e-05

Maximum 0.195857

Minimum -0.059181

Std. Dev. 0.023446

Skewness 2.519550

Kurtosis 21.80846

Jarque-Bera 3838.899

Probability 0.000000

FIG-2: Descriptive statistics of Stock return (50 stocks)

FIG-3: Pictorial presentation of NIFTY-stock return

Table 2: Results of Unit Root Tests

Variables ADF (t-statistic)

Levels

First Differences

dln Index_return (Rm) -10.15786*

dln Stock_return (Ri) -11.73572*

Note: The Mackinnon (1996) critical values for ADF test is -3.457, -2.873, -2.573 for both stock-returns series and index-returns series with one-sided p-values and lag-length is 5 (maximum 14) and lag-length 8 (maximum is 14) at 1%, 5%, and 10% significance levels, respectively. Information criterion chosen is SIC. * -indicates the significant-p-value rejecting the null-hypothesis.



We have taken (regressed) predictor or beta to estimate the Sharpe-single index model

for the portfolio optimisation. Individual stock return (Ri), risk-free return (Rf) or T-bills

rate, that is, 4.7% annualised yield (0.035525% on daily count), beta (βj), market risk (σm2,

calculated from the daily-variance of the index-return), residual variance (σε2);-these

indicators are taken into consideration to calculate cut-off (C*) score to choose and select

the stock from the given index, NIFTY to formulate the portfolio. In fact, systematic risk

or βj-multiple of index-return-variance (β2σm2) to total risk (β2σm2 + σε2) is called “Sharpe-

appraisal ratio” (Bodie et al., 2002). Finally, Z-value for qualified individual stock is

calculated which is nothing but to assign certain weights to the selected stocks in the

portfolio or to arrive at the proportion of the stocks in the formulated portfolio or

“Sharpe-style analysis”, say, “N” stocks comprise of single-index portfolio following the

covariance terms, [(N2- N)/2]. In this case, 26 stocks are finally scored above C* or 0.253

to form a portfolio. Hence, total covariance-terms are 325 or NC26 out of 1225 (for the

index). Following the Markowitz’ approaches, number of covariance-terms are 377 out

of 1325. Enumeration satisfies the equation, that is, [N× (N+3)/2].

We have considered the market model approach other than constant return approach

(μi) to calculate the beta which is not exactly similar with CAPM. In market model, we

have incorporated market return (Rm) and individual stock return (Ri) where as i and βj

are chosen as coefficients of the OLS-regression model. CAPM takes into account of Rf

as replacement of and Rm as (Rm-Rf) the difference as excess market return or equity-

risk premium. Error component is considered as unsystematic risk that corroborates

residual variance or noise in the return-series of individual stock. This represents the

unexplained variance or residual sum square (RSS) in the stock’s or security’s return.

The following table provides an outlook of portfolio that is constructed after selecting

26-individual security from the given index, with respect to portfolio beta, R2, F-

statistic, and t-statistics with p-values at 5% level of significance, respectively. We try to

estimate the predictive ability of NIFTY as explanatory or exogenous variable on the

chosen portfolio as dependent or endogenous variable. β of the portfolio is 0.951

(standardized) and intercept is not significantly different from zero, that is, 0.168.

Explained variance of the model is almost 90% with moderate to good Durbin-Watson

statistic (2.009). Hence, we can say that the first differences of logarithm of the both

index and portfolio are free from serial correlation or auto-correlation problem and fail

to reject the robustness of the model as the model is devoid of “spurious regression

trap”. Residuals statistics are also mentioned in the table.



Table 3: Results of Regression

Dependent

Variable

Portfolio

Independent

Variable

Index (NIFTY)

R2 0.904 (0.573**) D-W 2.009

F-stat

(Goodness of fit

index)

2261.296**

Coefficients

Intercept (α) t-statistic 4.542 (0.037**)

Beta (β) t-statistic 47.553 (0.020**)

Residuals

statistics (N

=243)

Minimum Maximum Mean Std. deviation

Predicted value -5.43 15.35 0.37 1.752

Residual -2.118 2.633 0.000 0.572

Std. Predicted

value

-0.312 8.546 0.000 1.000

Std. Residual -3.696 4.593 0.000 0.998

Note: **-indicates significant p-values of the mentioned tests’ statistics at 5% level of significance,

respectively. In parentheses standard errors of the respective tests-statistics are mentioned.

Fig-4, 5, and 6 imply the pictorial presentation of portfolio’s actual, predicted and

residuals movement, frequency distributions or histogram (descriptive statistic), and

stationarity of regression standardised residuals, respectively.



FIG-4: Actual-Predicted-Residual movement of the Portfolios

-8

-4

0

4

8

12

16

25 50 75 100 125 150 175 200 225

ACTUAL PREDICTED RESIDUAL

FIG- 5 &6: Histogram of the Portfolio and Normal P-P plot of Regression Resiudals



Based on the C* and ratio analysis (Sharpe, Treynor, Jensen, and Sortino) we have

calculated the security’s rank in the chosen portfolio and down-side risk considering

calculation parameter, that is, minimum acceptable return (MAR) 0.05%. The following

tables 4 & 5 in view of post-modern portfolio theory provide the details of portfolio’s

average rank, security’s beta, annualised return, annualised standard deviation, etc.

Mean-variance efficient frontier using Markowitz’ two parameters approach is shown

in the following Fig-7.

FIG-7: Mean-Variance-Efficient Return of the Portfolio

Table-4: Post-Modern Portfolio Theory S&P CNX NIFTY Portfolio

Risk-Return Analysis

Sharpe Ratio 1.88 4.64

Downside Deviation (MAR) % 1.060 1.017

Downside Deviation (RFR) % 4.827 4.694

Downside Deviation (0%) 1.035 0.993

Sortino Ratio (MAR) 0.135 0.301

Sortino Ratio (RFR) -0.942 -0.934

Sortino Ratio (0%) 0.186 0.359

Mean Day Return (%) 0.22 0.37

Standard Deviation (%) 1.88 1.84

Compounding Daily Return (%) 0.19 0.36

Annualized Return (%) 60.04 138.24

Annualised SD (%) 29.44 28.79



Sr No. Portfolio

Rank Order

Z -Value

Proportion/Weightage(%)

Annualised Ri

Annualised SD Beta

Sharpe Ratio Rank

Treynor Index

Rank

Jensen Index

Rank

Average Rank

1 A B B Ltd. 14 1.426 2.716 81.791 39.298 0.82 1.961 18 93.965 17 3.171 19 12.654

2

Ambuja Cements Ltd. 25 0.348 0.663 54.790 38.873 0.72 1.288 24 69.514 25 1.024 25 17.096

3 Axis Bank Ltd. 11 2.419 4.609 149.533 48.139 1.23 3.008 7 117.718 10 7.679 8 7.003

4

Bharat Petroleum Corpn. Ltd. 23 0.464 0.883 32.112 37.571 0.42 0.729 26 65.172 26 0.415 26 17.576

5 Cipla Ltd. 20 0.947 1.805 45.382 34.051 0.51 1.194 25 79.691 21 1.244 24 15.398

6 G A I L (India) Ltd. 21 0.606 1.155 55.041 35.452 0.68 1.419 23 73.972 24 1.270 23 16.140

7

H C L Technologies Ltd. 5 3.277 6.244 209.214 52.571 1.04 3.889 3 196.610 1

14.697 2 2.296

8 H D F C Bank Ltd. 3 3.714 7.076 85.028 30.712 0.76 2.614 10 105.642 12 3.827 15 9.871

9

Hero Honda Motors Ltd. 9 2.683 5.112 76.293 33.869 0.61 2.113 17 117.300 11 3.783 16 9.704

10

Hindalco Industries Ltd. 12 2.378 4.531 194.353 56.453 1.33 3.359 6 142.566 7

11.608 3 4.453

11 I C I C I Bank Ltd. 18 1.240 2.363 139.935 51.022 1.4 2.650 9 96.568 16 5.779 11 9.883



Sr No. Portfolio

Rank Order

Z -Value


Annualised Ri

Annualised SD Beta

Sharpe Ratio Rank

Treynor Index

Rank

Jensen Index

Rank

Average Rank

13

Infrastructure Development Finance Co. Ltd. 15 1.363 2.598 141.309 55.135 1.35 2.477 14 101.162 15 6.193 10 9.159

14

Kotak Mahindra Bank Ltd. 24 0.360 0.687 117.347 53.243 1.37 2.115 16 82.195 20 3.686 17 13.038

15 Larsen & Toubro Ltd. 16 1.255 2.392 119.481 44.643 1.26 2.570 12 91.064 18 4.508 13 11.190

16

Maruti Suzuki India Ltd. 17 1.244 2.370 66.667 37.007 0.7 1.673 21 88.467 19 2.322 21 13.891

17

Punjab National Bank 2 5.088 9.695 133.840 36.591 0.83 3.528 4 155.542 5 8.321 7 5.176

18

Ranbaxy Laboratories Ltd. 7 2.788 5.312 138.664 47.057 0.79 2.846 8 169.524 4 9.024 5 3.949

19 Siemens Ltd. 4 3.499 6.668 158.183 45.384 1.18 3.381 5 130.036 8 8.820 6 5.794

20

Steel Authority Of India Ltd. 13 1.577 3.005 130.244 48.391 1.24 2.594 11 101.213 14 5.694 12 9.531



Sr No. Portfolio

Rank Order

Z -Value


Annualised Ri

Annualised SD Beta

Sharpe Ratio Rank

Treynor Index

Rank

Jensen Index

Rank

Average Rank

22

Sun Pharmaceutical Inds. Ltd. 10 2.602 4.958 58.605 33.690 0.36 1.599 22 149.624 6 3.396 18 8.533

23 Tata Motors Ltd. 8 2.778 5.293 250.168 60.566 1.26 4.052 1 194.784 2

17.576 1 2.351

24 Tata Power Co. Ltd. 22 0.543 1.035 62.875 34.594 0.78 1.680 20 74.532 23 1.501 22 15.560

25 Tata Steel Ltd. 19 1.181 2.250 153.758 58.757 1.42 2.536 13 104.942 13 7.051 9 8.179

26 Wipro Ltd. 1 5.278 10.057 160.261 39.008 0.8 3.987 2 194.401 3 11.12

9 4 3.662

Portfolio 138.240 28.790 0.93 4.637 143.548 8.208

S&P CNX NIFTY 60.030 29.440 1 1.878 55.290

From the above Fig-7, it can be inferred that feasible region would be any point on the mean-variance efficient frontier

where tangency of potential portfolio would be a particular point intersecting the concave shaped curve. Sharpe-Linter

version postulates that with a decrease in tangency of potential portfolio or assets, grouping of assets are likely to be

increased. From the index, we have drawn 26 stocks that can form NC26 portfolios subject to the efficient frontier of the

minimum variance. Portfolio performs relatively better than index with respect to its annualised return (138.240% vs.

60.030%), annualised standard deviation (28.790% vs. 29.440%), the Sharpe-index (4.637 vs. 1.878), the Treynor-index

(143.548 vs. 55.290), and the Sortino-index (0.301 vs. 0.135), respectively. Jensen index of the portfolio is 8.208. Hence, all

four formulated hypotheses cannot be rejected or we fail to accept the null hypotheses. Coherent measures of risk (positive

homogeneity, sub-additivity, translation invariance, monotonicity) are considered while accomplishing the selection, evaluation

of the portfolio (for more details, see, Acerbi and Scandolo 2007; Hull 2007).



SECTION-V

8. SUMMARY AND CONCLUSION

The present study has touched upon the area of portfolio selection and evaluation in the

lights of both modern- and post-modern portfolio theories. Ratio-analysis is succinctly

interpreted and presented in order to improve the portfolio selection. Minimum-

variance portfolio is desired outcome if and only certain assumptions, namely, market

as proper vector space, no randomness or stochastic nature of the measured variables,

expected mean-shortfall or tail conditional expectancy (TCE) or conditional value-at-

risk (VaR), etc. are not violated while formulating hypotheses and methodology.

Sharpe’s single-index approach has taken care of portfolio selection and optimisation

well in this context. Although Sharpe’s postulations have possessed distinctiveness and

parsimony, that is, containment of minimum assumptions and minimum complexity,

incorporation of other ratios or indices have helped to improve or modify the portfolio

selection. Markowitz’s mean-variance efficient frontier is considered during the

determination of the portfolio’s risk- and return-equations.

We have chosen the NIFTY index as it serves a better proxy of the market than any

other indices, viz., BSE-SENSEX, BSE-midcap, BSE-100 etc., in Indian context. 50-stocks

are considered and Sharpe-algorithm is incorporated for calculating the cut-off score,

which comes about 0.253% on average-daily count basis. We have calculated beta,

residual variance by regressing index return on individual stock return considering

average yield of both index and stock on daily basis. Excess mean return and

cumulative beta to residual variance are calculated using the Sharpe single-index model

and then, other ratios are also determined to look at the top-26 stocks in regards to their

annualised returns, annualised standard deviations, betas, Sharpe-index scores,

Treynor-index scores, Jensen-index scores, and finally, we have arrived at average rank

of individual stock, the portfolio, and the index. Evidently, portfolio’s performance is

relatively superior to the index with respect to the Sharpe-ratio or index, Treynor-ratio,

Sortino-ratio, annualised return. Coefficient of determination (CD) shows that the

portfolio is a good mirror of the index and the standard deviation of the portfolio or the

systematic risk component is on lower side compared to the index. Hence, we conclude

that mean-variance efficient portfolio can be achieved by incorporating the Sharpe

single-index measure as an ex-ante approach, which would take care of portfolio risk-

return optimisation (with the given constraints). Therefore, a good combination of all

ratios incorporated in the paper provides a better ground to achieve the conformity of

both the modern- and post-modern portfolio theory.



EXHIBIT-1

Table-6: Results of regression (on average daily counts basis using high-frequency data)

Dependent

variable

Individual security (50 stocks)

Independent

variable

Index or NIFTY

Security’s name Model-R2 (%) Beta (t-Stat) F-Stat (GFI) Residual

variance (%)

ABB 38.078 0.823 (12.173**) 148.20** 0.000391

ACC 34.472 0.767 (12.259**) 126.78** 0.000397

Ambuja 29.814 0.720 (10.118**) 102.374** 0.000435

Axis Bank 56.775 1.232 (17.791**) 316.554** 0.000411

Bharat Heavy

Electricals

59.966 0.963 (18.999**) 360.991** 0.00022

Bharat

Petroleum

10.835 0.420 (5.411**) 29.286** 0.000516

Bharti 7.000 0.720 (4.260**) 18.151** 0.002451

Cairn Energy 47.415 0.946 (14.741**) 217.306** 0.000353

Cipla 19.639 0.512 (7.674**) 58.898** 0.000382

DLF 56.003 1.639 (17.514**) 306.764** 0.00075

GAIL 31.997 0.681 (10.648**) 113.399** 0.00035

HCL 33.390 1.039 (11.119**) 123.651** 0.000749

HDFC 53.310 0.761 (16.588**) 275.176** 0.00018

Hero Honda 28.706 0.616 (9.850**) 97.038** 0.000335

Hindalco 48.145 1.330 (14.958**) 223.760** 0.000677

Hindustan

Unilever

13.739 0.369 (6.195**) 38.387** 0.000305




variance (%)

HDFC Ltd. 58.357 1.102 (18.377**) 337.737** 0.000308

ICICI Bank 64.951 1.396 (21.133**) 446.621** 0.000374

ITC 24.560 0.561 (8.857**) 78.459** 0.000345

Idea 45.122 1.097 (14.076**) 198.161** 0.000521

Infosys 33.494 0.645 (11.017**) 121.375** 0.000293

IDFC 52.260 1.353 (16.242**) 263.825** 0.000595

JAIPRAKASH 45.688 1.623 (14.239**) 202.74** 0.001113

JINDAL Steel 3.533 1.172 (2.970**) 8.826** 0.013343

Kotak Mahindra 57.159 1.367 (17.931**) 321.549** 0.000498

L&T 69.053 1.260 (23.189**) 537.772** 0.000253

M&M 13.684 1.038 (6.181**) 38.207** 0.002418

Maruti Suzuki 30.971 0.699 (10.398**) 108.130** 0.000387

NTPC 45.948 0.659 (14.313**) 204.870** 0.000182

ONGC 42.853 0.803 (13.443**) 180.723** 0.000306

Power Grid 55.804 0.859 (17.444**) 304.300** 0.000208

PNB 44.717 0.831 (13.962**) 194.941** 0.000303

RANBAXY 24.723 0.794 (8.896**) 79.153** 0.000683

Reliance Capital 61.682 1.577 (19.696**) 387.951** 0.000549

Reliance Comm 52.388 1.344 (16.284**) 265.18** 0.000548

RIL 20.634 1.271 (7.915**) 62.658** 0.00221

Reliance Infra 59.460 1.405 (18.801**) 353.487** 0.000478

Reliance Power 52.365 1.057 (16.276**) 264.931** 0.000361

Siemens 59.058 1.184 (18.645**) 347.640** 0.000346




variance (%)

SBI 62.835 1.153 (20.185**) 407.471** 0.00028

SAIL 57.198 1.243 (17.946**) 322.062** 0.000411

Sterlite 49.915 1.311 (15.497**) 240.184** 0.000613

Sun Pharma 9.897 0.359 (5.145**) 26.473** 0.000419

Suzlon 41.804 1.544 (13.157**) 173.12** 0.001179

TCS 7.432 0.735 (4.398**) 19.349** 0.002393

Tata Motors 37.803 1.264 (12.102**) 146.480** 0.000935

Tata Power 43.813 0.777 (13.708**) 187.926** 0.000276

Tata Steel 50.733 1.421 (15.753**) 248.178** 0.000697

Unitech 48.929 1.684 (15.195**) 230.893** 0.001053

Wipro 36.219 0.797 (11.698**) 136.86** 0.000398

Note: t-statistics are given in the parentheses; p-values of t-stat and F-stat are significant at 95%

level of confidence or at 5% level of significance (**). GFI implies for Goodness of Fit Index



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