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 DOI: 10.1177/0972150912466445

2013 14: 89Global Business ReviewSubhrangshu Sekhar Sarkar, Santanu Dutta and Pinky Dutta

A Review of Indian Index Funds  

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Military-Madrasa-Mullah Complex 89

India Quarterly, 66, 2 (2010): 133–149

A Global Threat 89Article

A Review of Indian Index Funds

Subhrangshu Sekhar SarkarSantanu DuttaPinky Dutta

AbstractAnindexfundisamutualfundthataimstoimitatesomebenchmarkindex.Thereareseveraladvan-tages of investing in an index fund, namely, exposure to a diversified portfolio, minimization ofcompany-specificrisks,highliquidity,etc.InIndia,therehasbeenasignificantgrowthinthenumberofindexfundsfrom2002onwards.Todaytherearemorethan20indexfundsimitatingtheNIFTYorSENSEX.Inthisarticle,wereviewandcompareanumberofIndianindexfunds.TheCRISILcompositerankingofanindexfundreflectsthequarterlyperformanceofthatfundandissubjecttofluctuations.Weareinterestedinthoseindexfundsthatdonotdeviatesignificantlyfromtheunderlyingbenchmarkindexinthelongrun.Thisensuresthataninvestorgetsthebenefitofanystrongrallyinthebenchmarkindex,whichtheindexfundimitates.Weidentifysomeindexfundsthatsatisfyourcriteria,andarealsorankedabovethree(indicatingaboveaverageperformance)intheCRISILrankingsofMarch2011andDecember2010.

KeywordsIndianindexfunds,cointegration,CRISILcompositeranking

Introduction

Often a stock or a certain portfolio depreciates significantly during a correction in the stock market, but does not participate in the recovery rally. This is often the situation faced by retail investors indulging in momentum trading, without exit rules such as stop loss. When the speculations are wrongs and the markets correct sharply, often investors hold their portfolio with the hope of a future recovery. But in general there is no guarantee that stocks that participated in one bull rally will also participate in the next rally.

However, there are certain funds, known as index funds, where the portfolio is designed by imitating a benchmark index as closely as possible. In principle, an index fund should move with the benchmark index that it imitates, as far as possible. So an investor investing in an index fund, imitating a broad index

Subhrangshu Sekhar Sarkar isProfessorattheDepartmentofBusinessAdministration,TezpurUniversity,Assam,India.E-mail:[email protected] DuttaisAssociateProfessorattheDepartmentofMathematicalSciences,TezpurUniversity,Assam,India.E-mail:[email protected] DuttaisResearchScholarattheDepartmentofBusinessAdministration,TezpurUniversity,Assam,India.E-mail:[email protected]

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90 Subhrangshu Sekhar Sarkar, Santanu Dutta and Pinky Dutta

such as the Sensex or Nifty, can expect that his portfolio will participate in a bull rally in the market. So an investor can take advantage of significant correction in a stock market by investing in an index fund. This is perhaps one of the reasons for the increase in popularity of index funds among retail investors.

Index Funds versus Traditional Mutual Funds

Traditional fund management is based on the assumption that fund managers will try to enhance the value of fund by continuous efforts and monitoring. However, many researchers have suggested that many actively managed funds have not acquired excess returns with respect to broad market indices (see Rey and Seiler, 2001).

The first index fund was launched by Wells Fargo Bank in 1971. It was a simple S&P 500 Index Fund, started with $6 million from the Samsonite Corporation (Jorion, 2002). During the 1980s, index funds gained impetus in the UK, Europe and Japan. Over the past 30 years, index funds have gained immense popularity among institutional equity investors and individual investors. In India the first index fund was started by the Unit Trust of India in 1998. At present, almost all mutual fund houses provide the facility of investing in index funds (for instance, see the AMFI website, www.amfiindia.com, for the list of Indian index funds).

Advantages of an Index Fund

There are a number of advantages of an index fund. For instance, the low maintenance cost is one of the key advantages of index funds. It does not require the services of a portfolio manager, analytical work by security analysts, operating expenses or advisory fees. The fund managers construct a portfolio that mirrors the return and risk of the index at the lowest possible cost (see Chen and Singal, 2006). Consequently, an index fund can be offered to an investor with a much lower entry and exit charge than an actively maintained fund. For instance, in most Indian index funds, there are no entry or exit loads (if exited after 15 days) imposed on the investor.

Index funds are suitable for long-term risk-averse investors. It provides investors the facility to invest in a diversified portfolio, at the same time lowering the risk exposure. The investor is exposed only to the market-specific risk factors. Portfolio diversification avoids unique or company specific risk factors. Another advantage is that index funds are highly liquid. There is no lock-in period; investors may redeem the entire investment at any point of time. Given the advantages of index funds, they are becoming increasingly popular investment instruments among Indian retail investors.

Statement of the Problem

CRISIL regularly ranks the performance of Indian index funds based on a number of criteria such as assets under management on a monthly average basis, tracking error, etc. These rankings reflect the quarterly performance of the index funds and are subjected to fluctuations (CRISIL, 2011). For instance,

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A Review of Indian Index Funds 91

the CRISIL rankings of March 2011 and December 2010 of Kotak Nifty ETF, Kotak Sensex ETF, LIC NOMURA MF Index Fund - Sensex Plan, Franklin India Index Fund – BSE Sensex Plan - Growth Plan exhibit fluctuations. While the CRISIL rankings reflect short-term (quarterly) performance of an index fund, a criterion that ensures that an index fund will not deviate from the underlying index significantly in the long run will be of obvious interest to a long-term investor.

In this article, we investigate whether an index fund deviates significantly from the benchmark index over a long period of time. Since an index fund aims to imitate an index, it is expected that an ideal index fund should not deviate too much from the index it aims to track.

Data and Objective

In this article we compare 23 Indian index funds, which track the Sensex or Nifty. For each fund we have collected data on daily NAV (or closing price for an exchange traded fund) and the closing price of the underlying index from 1 April 2007 (or since inception, for funds that have been launched after 1 April 2007) to 31 March 2011. We also report the CRISIL composite ranks, for March 2011 and December 2010, of the index funds. The data are collected from AMFI, NSE and CRISIL websites.1

We investigate whether these funds are cointegrated with the underlying benchmark index, i.e., whether these index funds exhibit co-movement with the underlying benchmark index.

Literature Review

Although the number of index funds seems to have increased quite significantly in India, the number of papers studying Indian index funds seems to be quite less. In fact, we have come across only two such papers. The papers by Sethu and Baid (2002) and Fernandes (2003) have evaluated index fund imple-mentation in India using tracking error analysis. Sethu and Baid (2002) have pointed out that the tracking error may arise from factors that are not under the index fund manager’s control. Fernandes (2003) has observed that the tracking error of some of the index funds (imitating Nifty) is positively correlated with Nifty volatility. This observation suggests that a slightly high tracking error for a particular period need not imply poor long-term performance of the portfolio.

Equity markets in India have witnessed high volatility since 2007 (see Dutta, 2011). Have the index funds, based on the Sensex and Nifty, imitated these indices during this volatile period? We have not come across any study that reviews the performance of the index funds in India during recent times. The aim of this article is to fill this gap. We use a criterion called cointegration, rather than tracking error, to assess the performance of a number of Indian index funds during the last four financial years. Such a study seems to be new.

It is natural to question the motivation for investigating whether an index fund is cointegrated (with the underlying index), instead of simply computing its annualized tracking error. Since the Indian and global stock markets have been highly volatile during the last few years, the annualized tracking error of an index fund can be rather high during this period (as tracking error can be positively correlated with index volatility (Fernandes, 2003). So a high tracking error during this period need not necessarily imply poor long-term performance of the index fund. The aim of passive investment is to imitate an index, as

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92 Subhrangshu Sekhar Sarkar, Santanu Dutta and Pinky Dutta

far as possible. Hence, our goal is to identify index funds that imitate or exhibit co-movement with the underlying index. This naturally leads to the concept of cointegration as a criterion for assessment, as two time series are said to cointegrated if the two series exhibit co-movement or are tied to one another (see Engle and Granger, 1987).

Measuring the Performance of Index Funds

Tracking Error

An index fund is subjected to tracking error, which is usually defined as the annualized standard devia-tion of the difference in daily returns between the index fund and its target index (see Fernandes, 2003; Lee, 1998; Pope and Yadav, 1994; Wolter and Zimmermann, 1999). There are other definitions of track-ing error as well. For instance, Clarke et al. (1994) and Roll (1992) have defined tracking error as the difference between portfolio returns and the benchmark portfolio returns.

There are several sources of tracking error, such as holding buffer cash to meet redemption and index volatility (see Fernandes, 2003). Tracking error is also caused by attempts to outperform the benchmark index and passive portfolio replication of the benchmark index by a sampled portfolio (see NSE, 2011).

A low tracking error implies that the returns on the index fund closely resemble the underlying bench-mark index returns over a given period of time. Usually an index fund aims to minimize the tracking error as far as possible. However, Alexander and Dimitriu (2004) have mentioned several demerits of designing a portfolio with an aim to minimize tracking error. Fernandes (2003) also provides insight into a number of important properties of tracking error. We discuss them briefly.

1. A portfolio that aims to minimize the tracking error may need frequent rebalancing (Alexander and Dimitriu, 2004), which involves extra monitoring effort and cost.

2. If the tracking error follows a non-stationary process (such as random walk), the portfolio can diverge significantly from its benchmark, unless frequently rebalanced (Alexander and Dimitriu, 2004).

3. Fernandes (2003) has pointed out that the annualized tracking error of a portfolio is highly sensi-tive to any discrepancy between the returns of the portfolio and the benchmark index even for a single day. Therefore, a slightly high (say, above two) tracking error for a particular period, espe-cially when the market is volatile, need not imply poor long-term performance of the portfolio.

4. The 250-day tracking error of an index fund can vary widely over different periods of time. For example, the tracking error of UTI Nifty Index Fund was low (below two) during the period from June to September 2002, but jumped up abruptly during the period from December 2002 to March 2003 (see Figure 5 in Fernandes, 2003). It is difficult to assess the long-term performance of such an index fund based on the recent annualized tracking error.

Due to the above-mentioned limitations of tracking terror, we use a very different criterion to assess the long-term performance of some Indian index funds. An index fund aims to mimic the movements of the underlying benchmark index as closely as possible. Hence, a good index fund should be tied to the benchmark in the long run. This phenomenon is known as cointegration (see Engle and Granger, 1987).

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A Review of Indian Index Funds 93

Therefore, one criterion for assessing the performance of an index fund is to test whether the NAV of that fund and the price of the underlying index are indeed cointegrated over a long period of time. Using this criterion we assess the performance of index funds imitating the Nifty or Sensex. The concept of cointegration is discussed briefly in the following paragraph.

Cointegration and Its Test

Engle and Granger (1987) formalized the idea of integrated variables sharing an equilibrium rela-tion, which turned out to be either stationary or have a lower degree of integration than the original series. They denoted this property as cointegration, signifying co-movements among trending vari-ables. Cointegration is the situation where we can form a linear combination of time series that is stationary, from two or more time series that are not individually stationary. By stationary we mean that the time series has constant mean, standard deviation over time, and the autocorrelation func-tion is purely a function of the ‘lag’, i.e., for a time series {yt}t=1,2,… the correlation between yt and yt+h is same as the correlation between y1 and y1+h, for any value of t. Cointegration, between two or more time series, ensures that in the long run the series do not drift arbitrarily far away from each other. Therefore, it is natural to expect that a good index fund is cointegrated with the underlying benchmark index.

A time series {yt} is said to be integrated of order d, in short I (d), if it has a stationary, invertible, non-deterministic ARMA representation after differencing d times. Let {y1t}, {y2t} be two I (d) time series. In general, any linear combination of {y1t}, {y2t} will also be I (d). However, if there exists (a,b) such that {zt = y1t – a – b y2t} is I(d-b), d ≥ b > 0, then {y1t}, {y2t} are defined as cointegrated of order (d, b), and denoted by yt = (y1t, y2t) ∼ CI(d, b). (a, b) is called the cointegrating vector (see Engle and Granger, 1987).

Most of the cointegration literature focuses on the case where variables contain a single unit root, i.e., by yt = (y1t, y2t) ∼ CI (1, 1), since few economic variables prove in practice to be of higher order.

Test for Cointegration

Engle and Granger (1987) suggested a procedure for testing whether by yt = (y1t, y2t) is cointegrated. It is as follows.

We fit an OLS regression model:

y1t = a + b y2t + zt (1)

to the observed data on yt = (y1t, y2t). Let a, b be the OLS estimates of a and b respectively.

Then the residual series { }tz of the fitted model is defined as

yt t t= − −1 2z y a bˆ ˆ (2)

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94 Subhrangshu Sekhar Sarkar, Santanu Dutta and Pinky Dutta

The Phillips–Perron test2 (Phillips and Perron, 1988), and the Augmented Dickey–Fuller (ADF) test3

are applied to the estimated residual series { }tz . The null hypothesis is that the residual series is explo-

sive or non-stationary, and the alternative hypothesis is that the residual series is stationary. If the null hypothesis is rejected, i.e., p-value is small, then

y y y CIt t t= ( , ) ( , )1 2 1 1∼ (3)

In statistics, the Augmented Dickey–Fuller (ADF) test and the Phillips–Perron (PP) test are unit root tests. That is, they are used in time series analysis to test the null hypothesis that a time series is inte-grated of the order 1. These tests are built on the Dickey–Fuller test of the null hypothesis δ = 0 in

∇ = − +y y ut t tδ 1 , (4)

where ∇ is the first difference operator.The ADF test and the PP test address the issue that the process generating data for yt might have a

higher order of autocorrelation than is admitted in the test equation– making yt − 1 endogenous and thus invalidating the Dickey–Fuller t-test. Whilst the ADF test addresses this issue by introducing lags of ∇yt as regressors in the test equation, the PP test makes a non-parametric correction to the t-test statistic. The test is robust with respect to unspecified autocorrelation and heteroscedasticity in the disturbance proc-ess of the test equation.

Data Analysis

We apply both these tests to the 23 index funds imitating the Nifty and Sensex. In both these tests the null hypothesis is that the index fund is not cointegrated, therefore a low p-value (less than say, 5 per cent) indi-cates that the data supports the alternative, i.e., the index fund is cointegrated with the benchmark index.

In Table 1, we have evaluated the PP and ADF test statistics and p-values for the 14 Nifty index funds, using R software. In Table 2, we have reported these statistics for seven Sensex funds. For each fund we have also reported the CRISIL ranks in March 2011 and December 2010.

Table 1. NiftyIndexFunds:CointegrationandCRISILRanks

NiftyIndexFundsPPTestStatistic p-value ADFtest p-value Comment

CRISILMarch

2011Rank

CRISILDecember2010Rank

UTINiftyIndexFund(G)

–1.58 0.76 –1.59 0.75 NotCointegrated 3 3

NiftyBeES –12.75 0.01 –3.98 0.01 Cointegrated 1 1KotakNiftyETF –175.46 0.01 –3.781 0.020 Cointegrated 1 *ICICIPruIndexFund

–1030.6 0.01 –7.46 0.01 Cointegrated 3 3

FranklinIndiaIndexFund

–1.876 0.631 –1.84 0.64 NotCointegrated 3 3

LICNAMURAMFIndex

–15.726 0.232 –3.08 0.12 Notcointegrated 4 5

(Table 1 continued)

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A Review of Indian Index Funds 95

NiftyIndexFundsPPTestStatistic p-value ADFtest p-value Comment

CRISILMarch

2011Rank

CRISILDecember2010Rank

CanaraRobecoNiftyIndex

–31.39 0.01 –10.04 0.01 Cointegrated * *

SBIMagnumIndexFund

–5.20 0.01 –1.25 0.895 NotCointegrated 5 5

HDFCIndexFund-NiftyPlan

–11.66 0.459 –1.30 0.873 Notcointegrated 4 4

BirlaSunLifeIndexFund

–30.99 0.01 –9.61 0.01 Cointegrated 4 4

UTISunder –2.89 0.199 –2.57 0.338 Notcointegrated * *PrincipalIndexFund-Growth

–2.78 0.944 –1.05 0.931 Notcointegrated 2 2

TataIndexFund-NiftyA

–30.42 0.01 –8.59 0.01 Cointegrated * *

INGNiftyPlusFund

–11.66 0.459 –2.42 0.397 NotCointegrated * *

FranklinIndiaIndexTaxFund

–1.76 0.681 –1.78 0.67 NotCointegrated * *

Sources: http://www.crisil.com/capital-markets/crisil-mf-ranking-list.html; http://www.amfiindia.com/NavHistoryReport_Frm.aspx;http://www.nseindia.com/;andAuthors’findings.

Note: *NotratedbyCRISIL.

Table 2. SensexIndexFunds:CointegrationandCRISILRanks

SensexFundsPPTestStatistic p-value ADFTest p-value Comment

CRISILMarch

2011Rank

CRISILDecember2010Rank

SensexICICIPrudentialETF

–346.8 0.01 –3.87 0.015 Cointegrated * *

TataIndexFund-SensexA

–742.52 0.01 –7.30 0.01 Cointegrated * *

LICNOMURAMFIndexFund-SensexPlan

–604.28 0.01 –6.90 0.01 Cointegrated 5 4

LICMFIndex-SensexAdv(G)

–279.66 0.01 –6.30 0.01 Cointegrated * *

KotakSensexETF –10.86 0.50 –2.59 0.33 NotCointegrated 2 1FranklinIndiaIndexFund-BSEPlan-GrowthPlan

–643.21 0.01 –7.48 0.01 Cointegrated 3 2

UTIMasterIndexFund –735.69 0.01 –9.29 0.01 Cointegrated 2 2HDFCIndexFundSensexPlan

–85.17 0.01 –2.20 0.4916 Notcointegrated 3 3

Sources: http://www.crisil.com/capital-markets/crisil-mf-ranking-list.html;http://www.amfiindia.com/NavHistoryReport_Frm.aspx;http://www.nseindia.com/;andAuthors’findings.

Note: *NotratedbyCRISIL.

(Table 1 continued)

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96 Subhrangshu Sekhar Sarkar, Santanu Dutta and Pinky Dutta

Findings

The following are the main observations of our empirical study.

1. We studied 23 index funds, based on the Nifty and Sensex. We found that 12 index funds are cointe-grated with the underlying benchmark index (see Tables 1 and 2). From Table 1 we see that out of the I5 Nifty index funds, only six funds are cointegrated with the underlying benchmark index. But, out of the eight index funds imitating the Sensex, six funds are cointegrated (see Table 2).

2. While there seems to be no direct relation between cointegration and CRISIL composite ranking, we see that most of the cointegrated funds do not perform poorly in CRISIL rankings. The CRISIL composite rankings are based on a number of factors, such as assets under management on a monthly average basis, tracking error, etc. (CRISIL, 2011). Those index funds that exhibit less than ` 100 million of assets under management, on a monthly average basis for the last month of the period for which the funds are ranked, are not ranked by CRISIL. Out of the 23 index funds studied in this article, only 15 funds are ranked in the March 2011 ranking by CRISIL. Out of these 15 funds ranked by CRISIL, seven funds are cointegrated with the underlying benchmark index. Interestingly only two out of these seven cointegrated funds are ranked below three (indicating three) in the CRISIL rankings of December 2010 and March 2011. Therefore, it seems that while cointegration is a long-term characteristic, it may also ensure that the short-term performance of an index fund is not poor in terms of CRISIL rankings.

3. Relationship between cointegration and tracking error: The tracking error of funds that are not cointegrated may exhibit wide fluctuations over time. For example, the tracking error of a UTI Nifty Index Fund, which is not cointegrated, varies widely between March 2001 and March

Table 3. TrackingErrorofIndexFundsduring2009

TrackingError(Percentage)

Data March2009 June2009 September2009 December2009

Nifty BirlaIndex 1.60 1.40 1.29 0.93CanaraRobecoIndex 2.69 2.82 2.39 2.25FranklinIndiaIndexFund-Nifty 1.01 1.06 1.05 0.42HDFCIndexFund-Nifty 1.72 1.89 1.91 1.44ICICIPrudentialIndexFund 0.97 0.97 0.98 1.33LICIndex-Nifty 3.07 3.28 3.35 2.64PrincipalIndexFund 0.97 0.96 0.78 0.75SBIMagnumIndex 2.36 2.04 1.55 0.56TataIndexFund-Nifty 0.92 0.99 1.00 0.71UTINiftyIndex 0.76 0.87 0.86 0.54

Sensex FranklinIndiaIndexFund-Sensex 0.93 1.00 0.95 0.54HDFCIndexFund-Sensex 3.29 3.42 3.30 2.09LICIndex-Sensex 6.23 5.49 2.80 2.12TataIndexFund-Sensex 1.55 1.55 1.46 1.30UTIMasterIndex 1.37 1.41 1.41 0.74

Source: http://www.canararobeco.com/upload/UploadMedia/DoesYourIndexFundMirrorIndexReturns%20-%20Mint_07042010.pdf

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A Review of Indian Index Funds 97

2003 (see Figure 5 in Fernandes, 2003). The tracking error of this fund is below two during the period from January to September 2002, but increases drastically during the period from December 2002 to March 2003. In contrast, the tracking error of cointegrated funds does not appear to vary widely. For instance, from Table 3 we see that the tracking error of cointegrated funds such as Birla Index, Canara Robeco Nifty Index, Franklin India Index Fund-Sensex, ICICI Prudential Index fund and Tata Index Fund-Sensex fund do not vary abruptly over the four quar-ters of 2009. It is important to emphasize that cointegration does not imply low tracking error; rather cointegration ensures that the tracking error will not fluctuate widely over different periods of time.

Conclusion

Cointegration is an important feature of an index fund, as it ensures that the fund is actually tied to the underlying benchmark index that it aims to imitate. We observe that if an index fund is not cointegrated then its tracking error may vary widely over different periods of time. Consequently, low tracking error in the recent past need not necessarily ensure that the fund will continue to track the benchmark index closely in future, especially in the long run. In contrast, cointegration ensures that the index fund does not deviate significantly from the underlying index that it imitates. So, along with low tracking error, cointegration is a desirable property that a good index fund is expected to exhibit, especially for an inves-tor with a long investment horizon.

CRISIL composite ranking of index funds are based on a number of criteria, such as assets under management on a monthly average basis, tracking error, etc., which are important parameters for assess-ing the performance of an index fund. We see that most of the cointegrated funds are also ranked three or above in the CRISIL rankings of 2010 and 2011. While this is an encouraging observation, it not suf-ficient to conjecture that cointegration also leads to high CRISIL ranking. This is due to the fact that cointegration and CRISIL rankings measure different aspects, namely the long-term and short-term performances of an index fund.

Therefore, it is advisable to choose those index funds that are cointegrated and are also ranked three or above, indicating average or above average performance in the CRISIL rankings. Only 4 out of 23 Indian index funds considered in this article satisfy both these criteria. These funds are Nifty BeES, Kotak Nifty ETF, UTI Master Index Fund and HDFC Index Fund Sensex Plan.

Notes1. See www.amfiindia.com; www.nseindia.com and http://www.crisil.com/capital-markets/crisil-mf-ranking-list.

html2. Phillips–Perron test. Retrieved from http://en.wikipedia.org/wiki/Phillips%E2%80%93Perron_test (accessed on

4 June 2011)3. See http://en.wikipedia.org/wiki/Augmented_Dickey%E2%80%93Fuller_test (accessed on 4 June 2011)

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