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Investigating Stock Market Indices of India - Empirical Analysis
Dr.Jaspal Singh* and Sidharath Seth**
I. Introduction
Charles Dow is credited to have conceived the idea of the first stock index i.e. Dow Jones
Industrial Average in 1896. Since then, all stock exchanges across the globe have built their own
indexes. While they are widely used by the investors to know overall daily market performance,
fund managers use them as a benchmark in evaluating their periodical performance. Studies have
found that mutual fund managers fail to beat their respective benchmark index (Jensen, 1968;
Malkiel, 1995; Gruber, 1996; Carhart, 1997; Daniel et al., 1997 and Chevalier and Ellison,
1999). These findings encourage the passive mode of investment through index funds, where
money is invested in the same proportion among the securities representing the underlying index.
Bogle is credited to have founded the Vanguard 500 Index Fund as the first index fund in 1975.
He popularized the index funds as a better instrument for the long term investment over
traditional mutual funds owing to lower management costs and their perpetual growth with
economy (Bogle, 2000). Due to its attractiveness towards investment, the total worldwide assets
under internal indexed management has escalated to US$5.994 trillion as of June 30, 2011
(Olsen, 2011) while global ETF market stood at about US$1.4 trillion at the end of 2011
(BlackRock, 2011).
At the end of September 2014, there were 43 index funds and 38 exchange-traded funds (ETFs)
in India (listed on the National Stock Exchange and the Bombay Stock Exchange), of which 24
were index-based ETFs and 14 were gold-based ETFs (ISMR, 2014). Given the variety of
indexes and index funds in India, there are numerous queries in the mind of a passive investor
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like how the indexes have performed in the past and which index is the most profitable to invest
with.
The present study aims at examining the long run performance of all the broad market
stock indexes operational at NSE (National Stock Exchange, India) and evaluating the best
performing index amongst them which could be recommended to the passive investor to
invest with over a long term.
The paper is organized in the following manner: Section II briefly explains about various broad
market indexes at national stock exchange, India followed by the discussion on the previous
literature in Section III, then, Section IV explains the data analyzed and the methodology
adopted. Section V deals with the discussion of the observed results and finally, Section VI
concludes this paper.
II. About the indexes at NSE, India.
Among the recognized stock exchanges in India, NSE (National Stock Exchange) is the largest
stock exchange with maximum daily turnover in cash and derivatives segment followed by BSE
(Bombay Stock Exchange) (ISMR, 2014). As on 30 June 2014, there are 36 indexes at NSE,
maintained and managed by IISL (India Index Service Ltd, a subsidiary of NSE). They are
broadly classified by NSE into four categories, namely Broad market, Sectoral, Thematic and
Strategy indexes. This paper focuses solely on the Broad market indexes consisting of the large,
liquid stocks listed on the exchange. They serve as a benchmark for measuring the performance
of the stocks or portfolios such as mutual fund investments. Stocks are broadly classified into
large cap, mid cap and small cap categories based on their market capitalization. Based on this
classification, there are five large cap indexes (CNX Nifty, CNX Nifty Junior, CNX 100, CNX
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200 and CNX 500), two mid cap indexes (CNX Midcap 50 and CNX Midcap) and one small cap
index (CNX Small cap) as listed in appendix I.
III. Review of Literature
A limited amount of research has been done comparing various indexes across the globe. In the
context with American markets, Statman (2000) primarily compared the Domini social index
(DSI) with S&P 500 from May 1990 to September 1998 but failed to find any risk adjusted
superior returns by the former. Later, Hakim and Rashidian (2002) examined risk-return
characteristics of Dow Jones Islamic Stock Market Indexes (DJIM) with Wilshire 5000 stock
market index from 1999 to 2002 and found that they failed to generate any excess returns over
three month T-bill. Also, return and risk of Islamic index was found to be less than Wilshire
5000. Thereafter, Hussein (2005) found that Financial Time Stock Exchange (FTSE) Global
Islamic index and Dow Jones Islamic Market Index performed in similar manner but behaved
significantly different from their common index for the period January 1996 to December 2004.
Later in the same year, using Dow Jones index and its Islamic version, Hussein and Omran
(2005) concluded that the Islamic index outperformed the non-Islamic index both over the entire
period from 1995 to 2003 and the bull period, while the vice-versa was true for the bear period.
Further, Chan et. al. (2009) found negative and statistically significant alpha for Russell 2000
growth index while assessing merits of popular performance evaluation procedures adopted by
academicians to a sample of active money managers and passive indexes. Finally, in an extensive
work on indexes and pricing models, Cremers et. al. (2013) concluded that standard fama-french
and cahart models produce economically and statistically significant non-zero alpha for passive
benchmark indexes like S&P 500 and Russell 2000.
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In context to Malaysian stock market, we came across only two studies namely Ahmad and
Ibrahim (2002) and Albaity and Ahmad (2008) who compared performance of KLSI with KLCI
over different time periods and found no statistically significant difference in their mean returns.
In the global context, using the data from July 1996 till August 2003, Hussein (2004) tested the
performance of FTSE Global Islamic Index with their index counterpart (FTSE All- World
Index) and found that while Islamic index yielded statistically significant positive abnormal
returns in bull market period (July 1996 –March 2000), it underperformed in bear market period
(April 2000 - August 2003). On analyzing social responsible investing across the globe,
Schroeder (2007) compared performance characteristics of SRI equity indices with benchmark
indices and found no statistical difference between them.
In Indian context, the authors came across only two studies on indices, one by Narasimhan and
Balasubramanian (1999) and the other by Dharani and Natarajan (2011). While Narasimhan and
Balasubramanian (1999) compared risk-return characteristics of only three indexes namely
Sensex, Natex and BSE 200 using mean difference test and variance difference test and found
statistically insignificant difference in the risk-return characteristics of these indices, Dharani and
Natarajan (2011) compared risk and return of only two indexes i.e. Nifty Shariah index and Nifty
index for four years from 2nd January 2007 to 31st December 2010. They tested the difference in
the mean returns of both the indices using t- test and found that there was no statistical difference
between average daily returns of both the indexes. However, there existed significant difference
between average return of both the indexes in the month of July and September.
Thus, it can be seen that very limited research is done on performance of indexes in the Indian
context. At the international level, while, majority of the studies found that there is insignificant
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difference in the returns of indices, however, only two studies namely, Chan et. al. (2009) and
Cremers et. al. (2013) exclusively concluded that few indices show statistically significant
different performance from others. Compared to the above mentioned studies on Indices, our
study extends the research in two aspects. Firstly, we analyze performance characteristics of all
the broad market stock indexes operational at national stock exchange, India using total return
index values, and secondly, the study is done for a longer period i.e. from 1st January 2004 till
31st march 2014.
IV. Database and Methodology
Out of 36 indexes operational at NSE, 10 are broad market stock indexes that have been
considered for our analysis (the other two are India VIX, a volatility index, and Nifty Dividend, a
running total of dividend points of the securities forming part of CNX Nifty Index). However,
each index has a different base date (as shown in appendix I). As a result, distinct time period is
available for calculating performance evaluation parameters, thereby rendering them to be
exposed to dissimilar market conditions. To illustrate, CNX Nifty Junior will be evaluated for
17.5 years (4th November 1996 till 31st March 2014), witnessing two bull and two bear periods
but CNX Smallcap will be evaluated for only 10.25 years (1st January 2004 till 31st March 2014),
observing only one bull and one bear period . Considering this disparity in evaluation due to
varied time periods, a common period representing one complete business cycle of stock market
that includes a bear and a bull run, has been selected from 1st January 2004 till 31st March 2014
for making meaningful comparison of performance. Out of 10 broad based stock indexes, it was
found that 9 stock indexes have base date prior to 2nd January 2004. Hence, these are 9 stock
indexes are analyzed using total returns index values from a common date i.e. 1st January 2004
till 31st March 2014 (covering complete cycle comprising one bull and bear period), after being
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exposed to similar market conditions. The total return index values reflect the returns arising
from dividend receipts and price movement of the constituent stocks. The total return index
values of all indexes is taken from bloomberg database. The implicit yield of 91-day treasury
bills of Government of India is taken as a proxy of risk free rate (Connors and Sehgal, 2001).
The data of risk free rates is taken from the website of Reserve Bank of India (www.rbi.gov.in).
CNX Nifty is taken as market proxy. The daily data on factor portfolio excess returns for Indian
stock
market
was
obtained
from
the
website
of
IIM
Ahmedabad
(http://www.iimahd.ernet.in/~iffm/Indian-Fama-French-Momentum/ accessed on 30th January
2015) (Agarwalla et al., 2013). The performance of indexes is evaluated using annualized return,
annualized standard deviation, Sharpe ratio, Jensen alpha and Cahart four factor alpha.
The annualized return is the annual compounded return earned by an investor over a period by
investing in an asset. It is useful in a way that for comparing returns over different lengths of
time, the returns are rescaled to one year. It is calculated as follows:
R=
(I)
X
Where: R= Annualized Return (expressed as percentage), Xt =Terminal Value, Xo =Initial Value,
t= Number of years.
Annualized Standard Deviation is a measure of volatility. An index with high annualized
standard deviation is considered more volatile and hence, more risky. It is calculated as follows:
(II)
X
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Where: σA = Annualized Standard Deviation, σd = Standard Deviation computed using daily
returns, T= Number of trading days in a year
The Sharpe Ratio measures the risk premium return earned per unit of total risk. It is calculated
by dividing the excess of average daily portfolio rate of return over average daily risk free rate
with the standard deviation of excess average daily portfolio returns. It is stated as follows:
(III)
Where: Si=Sharpe ratio for a portfolio,
= Mean return on the portfolio,
91-day RBI Treasury bills (proxy for risk-free rate of interest),
= Mean return on
= Standard
deviation of the excess average daily portfolio returns.
The Sharpe ratio shows the excess return earned by an investor for per unit of variability, they
are exposed to by holding a riskier asset. A portfolio with highest positive Sharpe ratio is
considered best for investment while the one having negative Sharpe ratio indicates that it failed
to generate any superior return over risk free rate.
Jensen alpha is a risk-adjusted measure of fund managers’ performance that measures the
excess return on a portfolio over the expected returns as predicted by the capital asset pricing
model (CAPM). Jensen alpha is stated as follows:
(V)
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Where:
= Jensen Alpha,
(proxy for market),
interest),
ISBN : 9780974211428
= Mean return on the portfolio,
= Mean Return of CNX Nifty
= Mean return on 91-day RBI Treasury bills (proxy for risk-free rate of
= Beta of the portfolio.
The null hypotheses tested are as follows:
H0 = An index does not generate significant excess return than CNX Nifty i.e.
α=0
H0= There is no significant difference in the relative risk of the particular index and CNX
NIFTY i.e.
β =1
H0= The particular index can be replicated by CNX Nifty, using joint hypothesis i.e.
α = 0 and β = 1
If a stock/portfolio/fund generates a better return than its beta would predict, it has a positive
Jensen Alpha, and if it returns less than the amount predicted by beta, it has a negative Jensen
Alpha. An investment manager yields a statistically significant positive Jensen alpha, if he has a
superior stock picking or market timing ability in excess of the benchmark. Similarly, a portfolio
whose beta is more than 1 is considered more volatile and hence, more risky than the market. On
the contrary, a portfolio with beta less than 1 is considered less risky than the market. Also, the
joint hypothesis H0: (α = 0 and β = 1) is tested to check if a portfolio can be replicated by the
benchmark index. If the null hypothesis is not rejected, then investing in the benchmark index,
on average, is equivalent to investing in the portfolio, without any significant difference in return
or risk.
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Cahart Four Factor Alpha measures the excess return on a portfolio over the expected returns
as predicted by Cahart four factor model. It is an improvement over CAPM model as it includes
more explanatory variables. According to this model, the excess portfolio returns are explained
by controlling market-wide four risk factors i.e. market, size, value and momentum. The alpha
obtained using Cahart four factor model is stated as follows:
Where:
= Four factor Alpha,
Nifty (proxy for market),
rate of interest),
= Mean Return of CNX
= Mean return on 91-day RBI Treasury bills (proxy for risk-free
= excess daily market premium,
stocks over large cap stocks,
book-to-market stocks,
= Mean return on the portfolio,
= daily premium of smallcap
= daily premium of high book-to-market stocks over low
= daily premium of one year winners vs losers.
The Cahart four factor alpha is excess return over what was predicted in the Cahart four factor
model. The Carhart model shows that alpha is attributed to investing in small and value
companies with price momentum. The positive Jensen alpha may turn into reduced Carhart
alpha, when exposed to these additional variables (i.e. size, value and momentum), showing that
the excess returns evidenced by positive Jensen alpha were attributed to these factors, not due to
the manager’s skill, whereas, the fund managers are paid for generating excess alpha.
V. Data Analysis
Table I reports the annualized return, annualized standard deviation and Sharpe ratio of each
index, calculated from 1st January 2004 till 31st march 2014. Among all the indexes, CNX
NIFTY Junior was most profitable by yielding highest annualized return (15.146), followed by
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CNX Nifty (14.702). CNX Midcap was found to be least risky due to its lowest annualized
standard deviation (24.60) followed by CNX 500 (24.61). All the stock indexes were found to
generate positive Sharpe ratio, showing that they were successful in generating excess returns
over risk free rate.
Insert Table I
The table II compares the performance of each broad market index with CNX NIFTY using
capital asset pricing model (CAPM). The results are estimated using ordinary least squares
method. The variance-covariance matrix of residuals is corrected for autocorrelation and
heteroscedasticity using the Newey and West (1987) approach. It was found that none of broad
market indexes generated statistically superior risk adjusted excess return over CNX Nifty. On
considering economic significance, only three indexes yielded positive Jensen Alpha. Among
them, CNX Midcap (0.00442) outperformed, followed by CNX Smallcap (0.00305) and CNX
Nifty Junior (0.00249).
Insert Table II
The null hypothesis,
β = 1, used to test that there is no statistically significant difference in the
relative risk of each broad market index and CNX NIFTY is rejected for all indexes except CNX
Midcap 50, as the significance value of Beta for this index is more than 0.05. It shows that these
indexes are significantly lesser risky than CNX Nifty.
The sixth column of table II shows results of the test of joint hypothesis H0: (α = 0 and
β =1).
The null hypothesis is rejected at 5 per cent level in case of five indexes namely CNX 200, CNX
500, CNX Midcap, CNX Small cap and CNX 100 Equal Weight. However, in the context of
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CNX 100, the null hypothesis is rejected at 10 per cent level. It means that CNX Nifty cannot be
used to replicate these indexes since, on average they do not have similar risk and return
characteristics as of CNX nifty.
After evaluating the performance of broad market indexes using CAPM, it was intended to check
whether the factors like size, value and momentum create any difference among the performance
of these indexes because they have been built using different sample sizes and type of stocks.
For this purpose, Cahart four factor model was used. The results of which are captured in Table
III. It shows that the alpha (captured through Cahart model) of all the indexes is negative,
meaning that superior return, if any, was due to value, size and momentum factors. While size
and value factors were found to play significant positive role in their performance, momentum
impacted negatively. The numerical value of the value factor is found highest for CNX Midcap,
CNX Midcap 50 and CNX Small cap indexes, showing that midcap and small cap stocks tend to
rise with the increase in the return of value stocks in the market. Also, the numerical value of
size factor is found highest for CNX Small cap index. However, the null hypothesis,
β
= 1,
remains rejected for only two indexes i.e. CNX Midcap and CNX 100 equal weight, at 5 per
cent level, meaning thereby that only these two indexes remain significantly lesser risky than
CNX NIFTY.
Insert Table III
VI. Findings and Conclusion
The study examines the long run performance of all the broad market stock indexes, currently
operational at NSE (National Stock Exchange, India) from 1st January 2004 till 31st March 2014.
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It is found that CNX Nifty, the flagship index of NSE, along with all other broad market indexes,
is successful in generating superior return over risk free rate proving that Indian equity markets
tend to generate better returns as compared to 91-day treasury bills of Government of India. On
using CAPM, none of them were able to generate statistically superior risk adjusted excess return
over CNX Nifty. However, on considering economic significance, only three indexes yielded
positive Jensen Alpha, namely CNX Midcap, CNX Smallcap and CNX Nifty Junior. Thus, CNX
Midcap proves to be the best performer among all broad stock indexes after adjusting for risk.
So, a passive investor, planning to invest in broad based indexes, should consider CNX Midcap
index for investment. But the alpha (Jensen alpha) of these broad market indexes turns negative
(Cahart alpha) on being exposed to additional factors i.e. size, value and momentum in Cahart
four factor model. This shows that the excess returns evidenced by positive Jensen alpha were
attributed to these factors and not due to superior index composition criteria. Moreover, the
results of the test of joint hypothesis using CAPM revealed that CNX Nifty cannot be used to
replicate most of the other broad market indexes namely CNX 200, CNX 500, CNX Midcap,
CNX Small cap and CNX 100 Equal Weight.
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Insert Appendix I
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