Active versus Index Equity Investing – Early Evidence from India

Rajan Raju, Ananya Mittal
May 27, 2020


This paper examines the relative performance of actively managed equity mutual funds against liquid, low-cost index-tracking exchange-traded-funds in India and investigates the merit of investing in index trackers. This is an important discussion as a majority of flows to equity schemes in the Indian fund industry currently go to share classes of actively managed funds with the highest total expense ratios. This high expense ratio raises the question of whether an investor would be better off investing in a low-cost index tracker. To deal with the active-vs-index decision for an investor, we build a simple yet robust framework using In-formation Ratio and R2 and use this framework to examine the performance of key equity scheme categories against two index trackers in India. The paper preliminarily affirms that low-cost index ETFs in India are credible alternatives to actively managed funds both in terms of performance and cost to the investor. The results provide preliminary evidence of, broadly defined, closet indexing in the Indian active fund management industry and raises issues of reasonableness and relevance of choice of benchmarks by active fund managers specifically in fund categories like focused schemes.

1 Introduction and Literature Review

Mutual funds play a very important role in the financial development of a country. They allow inclusion and active participation of a large volume of participants in markets while abating the risks for small investors. At the same time they improve the efficiency and stability of financial markets. They are one of the key instruments of wealth creation and retirement savings for all types of investors, and therefore their performance is always a subject of attention. In India, as at end-March 2020, The Association of Mutual Funds in India (AMFI) reported 89.75 million folios and net assets of ₹2.2 million crores under management. Of these, Growth/Equity Oriented schemes had 62.7 million folios and net assets of ₹578.5 thousand crores. AMFI’s Industry Trend shows equity-oriented schemes derive 87% of their assets from individual investors1 (AMFI, 2020b). Domestic equity index funds had a mere 544 thousand folios and just ₹8,089 crores under management.

In the developed markets, there has been a transformational shift of capital from active funds to passive funds. In Jan 2020, Morningstar reported that over the past decade index funds dominated inflows: ‘passive funds had inflows of $3.8 trillion, while actively managed funds had outflows of $185 billion. Meanwhile, overall active market share – as measured by total assets – fell from 78.3% to 59.0%’ (Morningstar, 2020). Globally, it is a matter of time before assets under indexed funds surpass assets with actively managed funds. In India, there is a long way to go before indexed funds are a significant portion of investor assets.In the developed markets, there has been a transformational shift of capital from active funds to passive funds. In Jan 2020, Morningstar reported that over the past decade index funds dominated inflows: ‘passive funds had inflows of $3.8 trillion, while actively managed funds had outflows of $185 billion. Meanwhile, overall active market share – as measured by total assets – fell from 78.3% to 59.0%’ (Morningstar, 2020). Globally, it is a matter of time before assets under indexed funds surpass assets with actively managed funds. In India, there is a long way to go before indexed funds are a significant portion of investor assets.
Broadly mutual funds can be classified as either actively managed funds or as passive/index funds. Actively managed funds aim to produce returns that are higher than and/or have a lower risk than a particular benchmark. The benchmark is chosen by the manager. The fund manager makes a careful selection of securities that fit the fund’s investing style and that she expects will collectively outperform the chosen benchmark. By contrast, index funds closely track a specific benchmark and accordingly deliver performance approximately equal to the performance of the benchmark followed. There is no selection expertise in index funds. Generally, index funds have lower expense ratios as compared to active funds.

A mutual fund that substantially delivers the performance of a much cheaper passive index fund is what we call a ‘closet index fund’. This is broader than the more traditional definition which defines a closet index fund as one where ‘asset managers claim, according to their fund rules and investor information documentation, to manage their funds in an active manner while the funds are, in fact, staying very close to a benchmark and therefore implementing an investment strategy which requires less input from the investment manager. At the same time, it is alleged that these funds charge management fees in line with those of funds that are considered to be actively managed’ (European Securities and Markets Authority, 2016). We differ from this traditional definition because an investor should be as concerned about outcomes themselves as to the means of achieving the outcomes.

In addition to the risk and returns of funds, expenses of funds are critically important in determining the investors realized returns. Closet indexers deliver similar performance to a low-cost index fund but charge a higher fee. An investor can effectively earn a higher return by investing in a low-cost index tracker rather than the closet indexing active fund. Total expense ratios (TER) for mutual funds are determined by a complex of factors. As we show, TERs are widely dispersed even amongst funds similar strategies.
Closet indexing raises a range of issues from the effectiveness of investor disclosure to the actual performance of the fund versus the expectations of investors. Using a US perspective, Cremers and Curtis (2015) argue that ‘persistent closet indexing implicates a number of legal issues, including possible liability for fund advisors under the Securities Act and the Investment Company Act’. Cremers et al. (2016) show that closet indexing is a global issue: ‘While 10% of United States mutual fund assets are invested in funds classified as closet index funds, closet indexing in other countries sometimes exceeds 50% of assets invested. For example, in Sweden, 56% of assets are invested in closet index funds, 58% in Poland and 44% in Finland’.

There has not been any formal study on closet indexing in India. Before 2018, the structure of the mutual fund industry allowed for fund managers to decide on their strategy, the universe of securities they could consider, and the choice of benchmark for the fund making it difficult to compare performance across funds. In late 2017, this inherent structural ambiguity was addressed by The Securities and Exchange Board of India (SEBI) through its circular titled ‘Categorization and Rationalization of Mutual Fund Schemes’ (Securities and Exchange Board of India, 2017). The rationalization was a significant step in setting a common framework across the industry laying the foundation for a more transparent fund management industry. The Board defined the investment universe for equity schemes into:
     • Large Cap: the top 100 companies in terms of full market capitalization
     • Mid Cap: 101st – 250th company in terms of full market capitalization
     • Small Cap: 251st company onwards in terms of full market capitalization

It has been two years since the rationalization by SEBI, and while the period is still short2 we develop and test a framework allowing investors to choose between actively managed funds and index tracking investment alternatives including identifying potential closet indexers. Ceteris paribus, an investor should be indifferent between an active fund or an index tracker having identical risk and return characteristics and costs. We use the SEBI standard-framework in our analysis, categorising funds in our sample by either the scheme category the fund or the benchmark chosen.

Further, in their circular titled ‘Benchmarking of Scheme’s performance to Total Return Index’ dated Jan 2018, SEBI (Securities and Exchange Board of India, 2018) required mutual funds to disclose the benchmark used to compare the performance of a scheme. The benchmark had to be the total return variant. Importantly, SEBI required that the ‘selection of a benchmark for the scheme of a mutual fund shall be in alignment with the investment objective, asset allocation pattern and investment strategy of the scheme’. This clarification allows for funds using similar benchmarks to be viewed as a category with similar characteristics.

There is a consensus that identifying closet indexers is a challenge. Cremers et al. (2016) cover a range of quantitative measures to determine closet indexers. The European Securities and Markets Authority used three metrics in their methodology to quantify closet indexing :
     • Active Share: the percentage of a fund portfolio that does not coincide with the underlying equity benchmark,
     • Tracking Error: the volatility of the difference between the return of the fund and the return of its benchmark, and
     • R2: the percentage of the fund performance that can be explained by the performance of the benchmark index.

While acknowledging the legitimate questions raised by ESMA on closet indexing, the European Fund and Asset Management Association (EFAMA) gave a robust argument why a quantitative analysis is not adequate to identify closet indexers (EFAMA, 2016). We are mindful of the issues with a quantitative-only analysis but remain steadfast in our view that a quantitative analysis is the best place for an investor to start their assessment between investment alternatives.
Like EFAMA, we believe investors are not necessarily better off selecting high-active-share managers. Active share focuses on the means (choice of instruments) rather than the outcomes (returns and risk). The similarity of returns is an indicator of similar strategies and therefore potential closet indexing3 From the range of options to examine the performance of funds4, we prefer one which reflects the relative performance of the actively managed fund against a relevant index tracker. Our first measure is none other than the familiar Information Ratio (IR). The IR is often used as a measure of a portfolio manager’s level of skill and her ability to generate excess returns relative to a benchmark, but it also attempts to identify the consistency of the performance by incorporating the tracking error. IRs above 0 indicates that the fund is outperforming the benchmark. As investors are concerned with outcomes, we prefer the IR to simply using the tracking error as the IR gives us a relative measure of outcomes.
Our second measure quantifies the relationship of returns between investment alternatives. If the returns of the cheaper alternative explain a significant portion of the returns of the expensive option, then the cheaper choice should be preferred.
We, therefore, use two measures in our framework : ‘Information Ratio’ and ‘R2’. The IR is the measurement of portfolio returns in excess of the returns of a benchmark divided by the volatility of those returns.
where Rp is the period portfolio return and Rb is the benchmark return for the same period.
The R2 follows ESMA’s definition. It is a statistical measure indicating goodness of fit of the regression to the relationship between the excess returns of the portfolio and the excess returns of the benchmark, similar to the traditional Capital Asset Model.
where rrf is the risk-free rate for period t. An R2 above 0.9255, we argue, indicates a high explanation of the period portfolio excess returns by the period excess returns of the benchmark.
We can now compare the performance of actively managed equity mutual fund schemes, against their respective index funds. The IR gives the relative measure of risk-adjusted performance and the R2 gives the explanatory power of the fund returns vis a vis the returns of the index tracker. If an actively managed fund has a negative IR ratio and an R2 against an index fund, we classify it as a potential closet indexer. Equivalently, a fund with a positive IR and an R2 less than 0.925 would likely not be a closet indexer. While we use zero (0) as our threshold for IR, we recognize that a practical implementation could use a higher threshold thereby giving an investor a ‘cushion-of-safety’. While the paper focuses on the active-vs-index choice, the framework can be used more generally to compare any two investment alternatives.
The debate on the relative value of actively managed funds against index funds is strong in many international markets. However, in India, this debate is still early. In this analysis, we lay out a framework to evaluate investment choices, use to specifically look at the active-vs-index choices for investors in India, and identify potential closet indexers. We believe this paper is one of the early efforts to understand actively managed equity fund performance against index trackers in India under SEBI’s rationalized regime. In doing so we attempt to contribute to the active-index tracker discussion within an Indian context.
The rest of the paper is set out as follows: Section 2 outlines the data we use. Section 3 is the bulk of the paper with specific analysis across several subsections: Section 3.1 looks at benchmarks; Section 3.2 examines total expense ratios; Section 3.3 looks at returns and risk for actively managed funds and index trackers; Section 3.4 examines rolling returns. In Section 3.5, 3.6, and 3.7 we build our core framework of using Information Ratio and R2. Section 3.8 analyses the performance of fund composites using the 4-factor Fama French Model. Finally, Section 4 concludes.

1 Defined as retail plus HNI (High Net Worth Individuals).
2 Data pre-2018 cannot be used for the analysis given the significant changes to funds across the industry.
3 We believe the burden of demonstrating out-performance should rest with the fund manager/distributor based on the fund’s track record. We recognize that past performance is no guarantee of future performance. Equally, if the fund manager has not outperformed in the past, an investor should remain skeptical of any promise of out-performance in the future.
4 Sharpe Ratio, Sortino Ratio, Treynor Ratio to name a few.
5 longer time series will allow more precise calibration.

2 Data

For this study, we use a sample of open-ended actively managed Indian equity mutual funds with minimum assets under management of ₹265 crores6 which existed continuously between Jan 2018 and April 2020. Only regular Growth variants of the funds were included. All sectoral funds, thematic funds, solution-oriented schemes, small-cap funds, dividend yield funds, and equity-linked savings schemes were excluded. Our sample has 82 funds is summarized in Table 1 and listed in full in the Appendix (Table A2).
Table 1: AMFI Categories of Funds in Sample
Table 2: Benchmarks adopted by Funds in Sample
For index trackers, unfortunately, in India, although there are 32 index-tracking exchange-traded funds (ETFs) listed the assets under management of index trackers are still small compared to actively managed mutual funds. To be a practical investment alternative for retail investors, an ETF needs to be both sizeable and liquid. Otherwise, investors are exposed to idiosyncratic risks like liquidity and bid-ask spreads. As of April 30, 2020, there are only 10 ETFs with assets over ₹500 crores. The equity ETFs within this 10 track in the main two indices: the NSE NIFTY 507 and the S&P BSE Sensex8 indices. We select the two trackers with the largest assets for the study – the SBI ETF NIFTY and the SBI ETF Sensex.

Instead of ETFs, we could also consider index tracking fund schemes. Again, mutual fund companies do not have a range of low-cost index-tracking schemes. The few existing funds are similar to the index ETFs and we do not see merit in analysing both index-tracking ETFs and index-tracking funds as they are effectively fungible except for operational aspects and nuances. We, therefore, only use the index-tracking ETFs.

Data for monthly returns, benchmarks, and total expense ratios (TERs) for each of these funds and the index trackers were taken from Refinitiv. If any specific data point was not available on Refinitiv, we update the data point from the fund manager’s or index provider’s website.

We use the 4 Factor Fama French Dataset from CMIE and the Indian Institute of Management, Ahmedabad (Agarwalla et al., 2013)9. The monthly survivorship-bias adjusted dataset has been used. This dataset stops 31 December 2019, so our factor analysis period is truncated between Jan 2018 and Dec 2019.

To calculate risk-free rates after Dec 2019, we adopt the same methodology followed by Agarwalla et al. (2013). We source the 91-day T-bill rate from the Reserve Bank of India’s weekly auction data10. The implied yields are converted to daily rates based on the number of trading days in the year following the issue. Data on trading days is from Refinitiv.

6 We use a size criteria to eliminate small-sized funds that will be liquidity constrained.
7 The NIFTY 50 is a diversified 50 stock index accounting for 13 sectors of the economy and represents about 66.8% of the free-float market capitalization of the stocks listed on NSE as on March 29, 2019.
8 tracks the performance of the 30 largest, most liquid, and financially sound companies across key sectors of the Indian economy that are listed at BSE Ltd.
10 available on RBI’s Database for the Indian Economy (

3 Analysis

3.1 Benchmarks

By laying out a standardized framework and clear definitions of the universe in late 2017, SEBI has created a level playing field across the industry. Importantly, an investor has more transparency in evaluating and comparing funds and fund performance. The benchmarks adopted by the funds in the sample are summarized in Table 2. The skew of fund schemes towards the Multicap and Large & Mid Cap funds is reflected in the choice of benchmark. Benchmarks from the managers’ website are still a mix of Total Returns and Price Returns. For this analysis, we only consider Total Return variants of the benchmark where available.
Figure 1 shows the heatmap of the pairwise correlation between the monthly returns of the individual benchmarks between Jan 01, 2018, and April 30, 202011. The range of the correlations is between 0.9 and 1.0. The benchmarks, in the main, are highly correlated for the period under investigation. Longer time-series data would allow for more robust statistical analysis, but the immediate practical implication for an investor is that there are little diversification benefits by investing across benchmarks. The top companies by capitalization will always weigh heavily on market-cap-weighted benchmarks in India. The high correlation between benchmarks makes the investment choice simpler for an investor. Conversely, the high correlation makes choosing a benchmark ‘in alignment with the investment objective, asset allocation pattern, and investment strategy of the scheme’ more challenging for the fund manager. We cover this in more detail later in the paper.
Figure 1: Pairwise Correlation between Benchmark Monthly Returns

11 The appendix has the full table with the pairwise correlations – Table A3.

3.2 Total Expense Ratios

We look at the expense ratios to determine if the TERs of actively managed funds have a substantial difference to the TER of index funds. If there is a significant difference, then an investor will need to determine if the active funds justify their higher TER through better performance (returns and/or risk). If not, an investor should prefer to invest her money into the lower-cost index tracker.

Figure 2 shows the distribution of TERs for all 82 funds by their AMFI Scheme Category. The TERs range between 1.18% and 2.98% with a mean TER of 2.15%. In comparison, the TER for the SBI ETF NIFTY and SBI ETF Sensex is only 0.07%, which is 2.08% lower than the mean actively managed fund TER. This implies that over 5 years, an investor can potentially earn an additional 10.86% cumulatively by investing into the index ETF rather than an actively managed mutual fund with the current average TER.

Figure 2: Regular share class TER by AMFI Category
Figure 3: Direct share class TER by AMFI Category

Such a wide gap in TERs is troubling. The wealth management industry (both the fund managers and the distributors) is appropriating significant costs from investors’ returns. Wahal and Wang (2011) show that the entry of new active funds which are close in style to incumbent actively managed funds creates competitive pressures leading incumbent funds to lower their fees. Cremers et al. (2016) build on this work and ‘find that actively managed funds are more active and charge lower fees when they face more competitive pressure from low-cost explicitly indexed funds’.

The availability of direct share classes offers investors a lower-cost alternative – one where the share of economics paid to the distribution channel is minimized/eliminated. In reality, most of the investments into mutual fund schemes are still in the regular higher TER share class. AMFIs data for March 2020 shows that 86% of flows from individual investors into Equity-oriented schemes are to regular share classes, while distributors drive only a third of individual flows into ETFs and Fund of Funds (AMFI, 2020a). This starkly illustrates the structural issue – wealth managers dominate flows into the more expensive regular scheme classes thereby reducing the realized returns of investors. The behaviour of distributors is driven by the economics of the share of the TER12.
Figure 3 shows the distribution of TERs of the direct share classes of the 82 funds by their AMFI Category. The direct share class TERs range between 0.46% and 2.20% with a mean TER of 1.16%. The TER for the SBI ETF index trackers is 1.09% lower than the average TER for the direct share class. Over 5 years an investor can potentially earn an additional 5.59% cumulatively by investing into the ETF rather than an actively managed direct share class of a mutual fund with the current average TER assuming the same gross returns between the two.
It is reasonable to split in the economics of the TER between the fund manager and the distributor. We can deduce that the direct TER is the share of the fund manager and the difference between the direct TER and the regular TER as the distributor’s share of the economics.
where Share is the split of economics.
The distributor is in effect earning 0.99% or 45.9% of the total economics. This is a significant share of the economics. An investor should ask whether the distributor is adding adequate value to the investor’s realized investment returns to justify the imputed fee13. Figure 4 shows the spread between the TERs of a fund’s direct and regular share classes, grouped by their chosen benchmark. We eliminate benchmarks which are used by single funds14. Given that the two largest index funds by assets are those tracking the NIFTY 50 and the S&P BSE Sensex benchmarks, it is not surprising to see that funds using these two as their benchmark show the biggest differential in the TERs between share classes (Table 3).
Figure 4: Difference in TERs between Direct and Regular Share classes by Benchmark

This may indicate early evidence that the increased competition from index funds is indeed causing TERs of actively managed funds to be reduced. Given the TER differential between actively managed funds and index funds, there is a strong case for investors to demand a wider range of low-cost index funds in India. Both Wahal and Wang (2011) and Cremers et al. (2016) have argued that competition drives expense ratios down. Having a larger range of sizeable, liquid index trackers will drive TERs of regular actively managed funds down.

Table 3: Mean Difference in TERs of Direct and Regular Share Classes by Chosen Benchmark

12 This raises a whole range of issues around conflicts of interest inherent in the wealth management industry which is beyond the scope of this paper.
13 There are broader issues around the sustainability of this economic model of the wealth management industry which are closely tied to the legal-regulatory framework that underpins the industry. The issues of fairness, fiduciary obligations, ethical responsibilities, and obligations are intertwined.
14 As a broad research paper, we will not publish any analysis that would highlight any individual fund.

3.3 Returns and Risks

Having determined that actively managed funds have significantly higher expense ratios than index trackers, we consider the returns of actively managed funds versus index trackers. Would higher returns from actively managed funds justify their higher costs? To explore this, we first calculate monthly excess returns of the funds and the index trackers. A priori, we expect active funds out perform index-trackers either by generating more return for the same risk (defined as volatility) as the trackers or alternately giving the same return with lower risk.

Figure 5 plots the average Monthly Excess Returns of each of the 82 funds grouped according to the AMFI fund categories against the Volatility of these monthly excess returns. For comparison, the corresponding return and volatility values for the two SBI ETFs are also plotted on the same chart and marked with a ‘+’ and a diamond sign. The chart is further divided into 4 portions with the SBI ETF NIFTY taken as the center.

Figure 5: Monthly Excess Returns and Volatility

The area shaded red highlights those funds that have delivered lower monthly returns and have taken higher risks than the SBI ETF NIFTY. 65.9% of funds in the sample fall under this area and represent funds that have underperformed the index fund. The green area, likewise, represents those funds that have delivered higher monthly returns while taking lower risks than the SBI ETF NIFTY and has only 11.0% of the funds in sample. These are funds that have bettered the SBI ETF NIFTY on both the metrics: Risks as-well-as Returns. The rest of the funds underperformed the ETF in at least one of the two metrics.

We note two points. First, there is a crowding of risk-adjusted return around the performance of the SBI ETF NIFTY. This is not surprising given the high correlation between benchmarks. Active managers have struggled to deliver significant outperformance during the sample period. Second, this crowding of performance is a sign of potential closet indexing.

We recognize that the period under consideration, Jan 2018 through Apr 2020, is short. In addition, the only index funds we have to compare the sample of funds are tracking the performance of the top 30 and top 50 companies by market capitalization.

3.4 1 Year Daily-Rolling Returns

Point-in-time returns do not show the full impact of volatility of returns. Rolling returns provide a more holistic way of looking at investment returns as they show the variation of returns over a period. We use a 1-year rolling window to calculate returns. To calculate category returns, we average the returns of all funds in the category on an equal weight basis. Rolling returns with a higher mean return and a lower spread are preferred over rolling returns with lower mean returns and larger spreads.

We recognize that there is likely to some base effect in the price data. The industry rationalized schemes to comply with the SEBI circular. This could have affected the normal course of prices of underlying stocks creating the base effect. The effect is likely to have persisted for a short period. The rolling returns analysis would fully account for any base effect. The point-in-time returns do not show the full impact of volatility of returns.

Figure 6 plots a box plot showing the category wise 1-year daily-rolling returns for each AMFI Fund category.

Figure 6: 1-year rolling returns

This chart indicates that the mean 1-year rolling returns for the two SBI ETFs are higher than the mean 1-year rolling returns for each of the active fund categories. The ETFs also show a lower range of 1-year returns over the evaluation period (1-year rolling returns with a mean of 6.2%, 7.7% and are in the range: 20.2% to -27.0% and 22.5% to -22.1% for the SBI ETF NIFTY and S&P BSE Sensex respectively), thereby illustrating a steadier annual performance by the index trackers than actively managed funds on a rolling basis.

Our review of returns indicates that actively managed funds have not demonstrated clear out- performance compared to the low-cost index trackers. They do not deliver a consistently higher return on average of 1.09%15 to justify a clear preference of active funds over an index fund. From both point-in-time and rolling-returns there is no clear bias toward choosing actively managed funds in particular. The low-cost index funds make a solid case to be included in an investor’s choice set.

3.5 Information Ratio

Having shown that there is a significant difference in expense ratios and that returns do not show a clear justification for the higher costs of active funds, we explore the first of our two measures – the Information Ratio. The IR gives an objective measure of risk-adjusted performance against a bench- mark. Under ideal circumstances, we would have liked to use actual index funds tracking large-cap, mid-cap, and small caps so that we could use these (or combinations of these index funds) to evaluate the performance of the actively managed funds. Unfortunately, the range index funds are not available and/or do not have the necessary scale currently. We run the analysis against the two SBI ETFs16. Active funds with IRs above zero (0) are funds that have a risk-adjusted performance at least in line with the index tracker. An investor should be indifferent between two instruments with an IR of zero, provided their costs of holding are equal. Figure 7 summarizes the IR for funds grouped within their respective Fund category. We use the SBI Sensex index tracker to calculate the IRs for actively managed funds that use the S&P BSE Sensex as their benchmark and the SBI NIFTY tracker for all the other funds.

Figure 7: Box Plot of Information Ratio of Funds within AMFI Category
Figure 8: Box Plot of Information Ratio of Funds by Fund Benchmark
The green area in the figure shows funds that have had an IR above 0 (zero)17: only 13.4% of our sample of 82 funds. Investors would have had higher risk-adjusted returns simply buying into one/any of two low-cost index funds over the past 27 months as compared to investing in all the other funds in our sample. We can also analyse IRs of funds grouped by their benchmarks rather than scheme categories. Figure 12 is the box plot by fund benchmark. All funds that use the S&P BSE Sensex as their benchmark have negative IRs for the period. 33.3% of funds with a stated benchmark of the NIFTY50 have negative IRs. Funds tracking other benchmarks have generally done worse than the SBI NIFTY tracker, but we do not have a liquid index tracking the 100, 200, or 500 companies by market capitalization to make a direct comparison.

Despite this lack of available instruments, the dispersion of performance within each benchmark is wide and clear. Our analysis shows that fund managers in India have not shown a consistent relative outperformance of index trackers since Jan 2018.

15 Assuming that an investor would choose the direct share class in favor of the regular share class.
16 For this paper, we do not see the merit of comparing the active funds against the theoretical indices. Investors should compare between two accessible investment options.
17 A practical implementation of the model may use a higher threshold to build a ‘cushion of safety’ for an investor. Any such cushion reduces the number of funds that would meet the threshold.

3.6 R2

The R2 represents the percentage of fund performance that can be explained by a change of performance in an index tracker. The higher the R2, the more the fund performance is explained that of the tracker. The higher R2, the higher the preference of the lower-cost index-tracker over a more-expensive actively managed fund, cetris paribus.  We calculate the R2 as per Equation 2 using S&P BSE Sensex as the benchmark if the active fund has the S&P BSE Sensex as its chosen benchmark. Otherwise we use SBI ETF NIFTY. We take an R2 equal to or over 0.925 as a threshold to signify that there is a close relationship between the returns of the actively managed fund and its index fund. Figure 9 shows the distribution of R2 in buckets18. 37.8% of the funds have an R2 equal to or greater than 0.925 and 17.1% over 0.95. The median R2 is, not surprisingly, high at 0.91, indicating, on average, the performance of actively managed equity funds closely reflects the excess returns of the lower-cost index funds. While not in itself conclusive, the high R2 raises the possibility of the existence of closet indexing within the Indian market.
Figure 9: Distribution of R2

Figure 10 plots the distribution of R2 for regressions across monthly returns of funds against an index fund by fund category. Funds with a large-cap bias show a significantly higher R2 to our two large-cap focused low-cost tracker ETFs. The significant tails of multi-cap funds in the box-plot points toward different investment styles by the fund managers. The Mid-Cap themed funds have the lowest R2. The overall high R2 to our large-cap index tracker indicates that active managers have maintained a reasonable large-cap tilt since Jan 2018.

Figure 10: Box Plot of R2 of Funds by Fund Category

Figure 11 plots the distribution aggregated by the choice of benchmark19. Interestingly, not all funds that track the S&P BSE Sensex have followed the index closely. However, the performance of funds tracking the NIFTY 100 have a high R2 to the index ETF performance. Overall though, the chart exhibits evidence of a large-cap tilt across the funds in the sample. We do have outlier funds with R2 less than 0.875 – but these are 25.6% of the total sample.

Figure 11: Box Plot of R2 of Funds by Fund Benchmark

If all active managers have a tilt towards large-cap stocks, an investor could allocate some part of her portfolio to a low-cost large-cap index tracker. She would thereby avoid the high TERs of actively-managed funds and enhance her realized returns. Within each category or chosen benchmark some funds have avoided having high R2s. There are actively managed funds which an investor could consider including into her equity portfolio. So it is not all-or-nothing: actively managed funds and index trackers can co-exist.

18 We have intentionally chosen buckets which are not equal in size
19 Note our earlier caveat on taking out data points that can identify individual funds

3.7 Combining Information Ratio (IR) and R2

We finally combine the two measures to build a practical and simple approach to determine which funds are potential ‘winners’ and which are likely to be closet indexers. The framework compares the actual performance of alternative investment options available to the investor rather than using a theoretical index for evaluation. Winner funds deliver excess returns above those of the index ETFs (having a positive IR) while maintaining a ‘lower’ R2. Funds with negative IRs and having R2 higher than 0.925 are preliminarily classified as closet indexers20. Investors looking to invest in funds with negative IRs and lower R2 should assess the fund very carefully. These funds do not have a solid economic case for investment. The relevant index fund does. Likewise, investors evaluating funds with positive IRs but with R2 above 0.925 must do so with care. The factors contributing to the excess re- turn over the index tracker must be understood. We cover examining factor returns in the next section.

Figure 12 is a scatter plot between the IR of actively managed funds and the respective index ETF versus their R2. Funds have been colour coded to represent their respective categories. The scatter plot is divided into 4 coloured areas. The dark orange area (top-left) contains funds with a negative IR and with R2 equal to or greater than 0.925. 32.9% of our sample are such funds. These are potential closet index candidates that can be replaced by low-cost index ETFs in an investor’s portfolio. The investor must deliberate the reason to invest in or retain such funds. The area coloured light green (bottom-right) has funds with low R2 and positive IR. Continuing with such funds in an investor’s portfolio would be the economically rational choice, as funds in this category can deliver relative outperformance. Unfortunately, these represent only 8.5% of our sample. If investors add a ‘cushion of safety’ to the IR threshold, the consideration set of funds will be smaller.

Using the IR / R2 framework, only a small percentage of funds in our sample offer relative out- performance over the two index trackers we compare the funds’ sample against. This leads to the preliminary conclusion that low-cost index ETFs should be an integral part of an investor’s equity portfolio. We are mindful of the short time series and therefore treat this conclusion as preliminary. The AMFI data however points to an overwhelming proportion of funds going into the regular share class of actively managed mutual funds. Consequently, investors in equity mutual funds have possibly suffered both an opportunity loss (of being invested in a fund which has underperformed) and a real loss (lower realized returns resulting from paying higher fees) by being invested so overwhelmingly into the highest TER share classes of actively managed funds.

Figure 12: R2 and Information Ratio of Funds

20 A robust analysis with a longer time series would need to be completed to determine a statistically robust R2 cut-off.

3.8 Analysing performance using the 4-factor Fama-French Model

SEBI’s standardization framework of the mutual fund industry in late 2017 allows for factor analysis to be meaningfully applied to funds and scheme categories. Factor theory originates from Fama and French’s (1993) seminal work on the topic.  Factors are investment styles that deliver returns over the long run.  Stocks  have  exposure  to  style  factors  like  size,  value,  momentum,  and  quality.  Equity mutual funds are made up of stock portfolios. Therefore, mutual funds can be decomposed into specific factors. Investors can reassemble these factor exposures using available index trackers.  If  a particular fund is exposed to, say, large-cap stocks (the Size factor), we can replicate the exposure to the factor using low-cost index trackers tracking the S&P BSE Sensex or the NIFTY 50. Then we can quite precisely compare the performance after costs between the mutual fund and the index-tracking factor equivalent. Factor analysis, therefore, provides a formal basis to choose between investment alternatives with similar factor exposure using the IR / R2 framework.

To understand the drivers of returns of funds, we use the traditional approach of examining excess returns against the Fama and French four-factor model (FF4), which includes Market, Size (small- minus-big), Value (high-minus-low ) and Momentum (winner-minus-loser ) (Fama and French (2011), Agarwalla et al. (2013)). Table A4 in the appendix describes the characteristics of the scheme categories of the sub-set of equity schemes in our sample.  A priori, we would expect Large Cap Funds21, Mid Cap Funds22 to have statistically significant tilts to the size factor; Value Funds23 to have statistically significant exposure to the value factor. Large & Mid Cap Funds24, Multi-Cap Funds25, Contra Funds26 and Focused Funds27 are more generic in scope for a priori hypothesis of factor exposures.

We first compute fund composites by calculating equal-weighted returns of all funds in the relevant Fund Category. We use equal weights to ensure that the composite reflects equally the effects of actions of all the fund managers. We prefer this approach to an asset size weighted approach to avoid size bias in the treatment of the fund manager’s actions.

where FCt is the excess return of the fund composite for period t, Rft is the excess return of fund f for period t, and n is the number of funds. We group all funds within a fund category to create the fund composite for the category. Besides, we analyse composites by grouping funds using the same benchmark28 using the same methodology.

More formally, we examine excess returns of fund composite portfolios and look at the intercept (α) for the Fama and French four-factor model (FF4), which includes MKT (Market), SMB (Size), HML (Value) and WML (Momentum) (Fama and French (2011), Agarwalla et al. (2013)). The intercepts are from the regression equation 5 with the four right-hand-side variables included:

where FCt is the return of the composite portfolio for period t, MKTt is the Market excess return for period t and SMB, HML and WML the size, value, and momentum factors for period t. We use the CMIE/Indian Institute of Management Factor Dataset (Agarwalla et al., 2013). While the time series is short, it is long enough to perceive some preliminary trends. We also note that the market prices and hence returns in the first few months are likely to be affected by the restructuring of the portfolios across the fund industry. As the factor dataset consists of all listed companies with number-of-days- traded and liquidity filters, it has significantly more companies that most of the public indices. The market betas (MKT) will, therefore, be different from those available on financial websites or providers.

Tables 4 and 5 give the summary results. Sharpe is the annualized Sharpe Ratio using monthly excess returns; Info Ratio is the information ratio of the fund composite against the SBI ETF Sensex if the benchmark used is S&P BSE Sensex by the fund composite or SBI ETF NIFTY otherwise. The Adjusted R2 is calculated for the Fama French 4 Factor regression.

Table 4: FF4 Analysis of monthly returns of a composite of funds grouped by Fund Category

Table 4 shows the results by AMFI Fund category composites. All fund composites have FF4 betas lower than the market and the two index trackers. Only the two index trackers show a positive Sharpe for the period. All fund composites show negative IRs. As expected, the Large & Mid Cap and Mid Cap categories show statistically significant positive coefficients to the size factor. A positive SMB coefficient indicates a tilt towards small-cap companies, while a negative coefficient indicates a tilt towards large-cap companies. Only the two index trackers show significant negative coefficients indicating that they are correctly large-cap focused. Surprisingly, the Large-Cap Fund composite does not have a statistically significant Size coefficient. Our R2 analysis (Figure 10) shows one outlier fund. This outlier seems to have affected the category fund composite’s coefficient.

While exposure to size is possible driven by fund strategy and regulatory regime, it is interesting to see the convergence of various fund categories into the Value factor. Fund managers across all scheme categories seem to follow some form of a value strategy in their stock selection. Contra, Large & Mid Cap, Mid Cap, Multi-Cap, and Value categories all report significant and positive coefficients indicating their tilt towards value. As expected, the two index trackers have p values that do not reject the null hypothesis of no exposure to the value factor. Both the S&P BSE Sensex and the NIFTY indices are based solely on market capitalization. Finally, turning to Momentum, none of the fund categories nor the index trackers have any statistically significant exposure to this factor29

Table 5: FF4 Analysis by composite Funds using the same Benchmark

Table 5 shows the FF4 analysis summary for fund composites based on Benchmarks that funds follow. This provides a different perspective to analyse the fund manager’s approach to building portfolios SEBI’s requirement that a benchmark ‘shall be in alignment with the investment objec tive, asset allocation pattern and investment strategy of the scheme’ lays out three parameters. All schemes using the same benchmark must be broadly aligned on the three parameters. Table A1 in the Appendix gives the breakdown of fund categories by the chosen benchmark. Immediately, the choice of benchmarks by fund managers shows the challenge of adherence.  The large-cap S&P BSE Sensex and the NIFTY50 benchmark are used by schemes in the Large Cap, Focused, and Value Fund Categories. The last two categories allow fund managers significant flexibility in choosing stocks that are not large-cap despite their choice of a benchmark. For example, one fund categorised as Focused uses the NIFTY as a benchmark.  It has the following asset allocation mix ‘The  Asset  Allocation  pattern would be as follows:- Equity & Equity related instruments of Large-Cap Companies 65%-100%, Other Equities 0-35%, Fixed Income, Money Market instruments and Cash & Cash Equivalents 0%-35%, Investment in REITs & InvITs 0%-10% ’. The fund manager is perfectly within the SEBI Guidelines which require ‘65% of total assets in equity and equity-related instruments’ for a fund classified as Focused. The fund manager has chosen to keep at least 65% in large-cap stock (the top 100 companies by market cap).  Another Focused fund using the same benchmark states ‘Under normal circumstances, the asset allocation pattern shall be as under: Equity and Equity related Securities (max 30 companies)65%-100%  -Debt  /  Money  market  instruments  0%-35%.’  Is the NIFTY index (which consists of the top 50 companies by market capitalization) aligned with ‘the investment objective, asset allocation pattern, and investment strategy ’?  If a fund has 35% exposure to other equities or 35% exposure to Money Market instruments, is the choice of index relevant or reasonable?  To ensure transparency of the risks inherent in a mutual fund and appropriateness of the chosen benchmark, a review of the alignment between the mutual fund’s strategy and its chosen benchmark seems appropriate and required.

With that important context, recall Figure 11, the box plots of R2 by Fund Benchmark, showed significant variance between funds following the same benchmark. For example, within funds tracking the S&P BSE Sensex, there was a large difference in individual fund performance reflected as differences in the R2s. Consequently, we would expect to see factor coefficients at odds with the factors implied by the benchmarks. In the case of the two funds above, the exposure to large-cap size is likely to be small, if the fund manager allocates only the minimum required 65% to large-cap stocks. It is therefore not surprising that the NIFTY 50 tracking fund composite does not have the expected statistically significant negative coefficient to Size. Of the NIFTY benchmarked funds, 5 of the 9 funds are Focused funds. As we have shown, these funds take exposures beyond large caps. Similarly, only 2 of 4 funds tracking the S&P BSE Sensex are Large Cap schemes. Therefore, while the S&P BSE Sensex tracking composite shows a tilt towards size, the tilt is smaller than what is seen with the S&P BSE Sensex index tracker. The NIFTY 100 index tracker, on the other hand, shows a statistically significant tilt towards the large caps. Of the 5 funds using the NIFTY 100 as the benchmark, 4 of them are large-cap funds. Funds benchmarked to NIFTY Large Midcap 250 show a tilt away from Large-cap stocks (statistically significant positive coefficient for SMB). All 11 funds tracking the index are in Large & Mid Cap schemes. As there is a spread of funds tracking the S&P BSE 200, NIFTY 500, or S&P BSE 500 benchmarks across Multi-Cap, Focused, and Value fund categories there is no statistically significant tilt away from Large Cap. As we have noted, fund managers seem to keep a significant exposure to large-cap stocks irrespective of the choice of benchmark.

In terms of exposure to value, only the composite of funds tracking NIFTY Large Midcap 250, BSE 200 and BSE 500 show statistically significant coefficients. Finally, the fund composite of funds tracking the NIFTY 50 shows statistically significant exposure to the momentum factor (WML). Figure 14 in the Appendix shows that Focused schemes, in particular, are exposed to this factor. 5 of the 12 Focused schemes in our sample track the NIFTY 100. This could explain the exposure to momentum for this composite.

The FF4 analysis reveals the factor exposure taken by funds. There is a logical alignment between fund categories and factors. Investors are well-advised to look at the underlying factors of returns in their evaluation of investment choices. Specifically, if an investor was looking at an active fund with positive IR and high R2, she could look to decomposing the returns by factors as a first step. She could objectively assess if she is comfortable taking on these factor exposures. If a significant portion of the positive IR comes from returns attributable to, say, the Momentum factor, she has a more reliable way of determining if the fund meets her risk appetite and investment considerations. The IR/ R2 process can shortlist a choice set. The FF4 analysis could be the second stage of the evaluation process that evaluates the choices against risk tolerance and investment objectives.

The FF4 analysis additionally flags a couple of important issues. First, whether the chosen fund benchmarks are relevant and reasonable. We posit that fund benchmarks are powerful anchors for investors in making their decisions. Any benchmark is implicitly associated with risk and return pro- files. The NIFTY 50, consisting of the 50 largest companies market capitalization, will be viewed very differently than the NIFTY 500, consisting of the 500 largest companies by market capitalization. This difference is driven by a range of factors – knowledge, perception, risk appetite. The choice of a benchmark can lead to an anchoring bias by an investor. Two funds with the same performance are likely to be viewed differently if the benchmarks are different. Our analysis raises issues of benchmark selection for schemes categories like Focused funds.

Second, the FF4 analysis highlights the importance of having a wide range of liquid index trackers. These trackers offer direct alternatives to actively managed funds. They create a competitive environment for the industry to reduce costs, increase performance, and in general, offer investors better returns for their investment. We hope for the introduction of a wider range of index trackers in the Indian market.

21 with 80% of total assets in ‘equity or equity-related instruments of large-cap companies’.
22 With 65% of total assets ‘in equity and equity-related instruments of Mid Cap companies’.
23 ‘scheme should follow a value investment strategy’.
24 with 35% each of total assets in equity and equity-related instruments of large-cap and mid-cap companies are respectively.
25 with 65% of total assets in equity and equity-related instruments.
26 ‘follow a contrarian investment strategy with 65% of total assets in equity and equity-related instruments’.
27 focused on max 30 stocks, with 65% of total assets in equity and equity-related instruments.
28 Like the rest of the paper, we exclude benchmarks that are followed by single funds from this analysis.
29 Charts showing the variation of factor exposures by Fund Category are in the Appendix. These give further detail into the factor tilts taken by active fund managers.

4 Conclusion

Since the watershed rationalization of the Indian mutual fund industry following SEBI’s 2017 circular, the preliminary aggregate evidence shows a few trends:
     • Costs/TERs: There remains a significant differential in costs to investors between regular share classes, direct share classes, and index trackers. Investors would be well advised to review these costs as a higher cost directly translates into lower realized investment returns for the investor. We show that these costs translate into a significant drag to returns. The current flow of investor funds into the highest TER equity funds leads to lower realized returns for investors.
     • Performance : Performance of actively managed equity funds do not show a clear outperformance against low-cost index trackers. A significant majority of actively managed funds have negative information ratios and lower rolling 1-year returns. When combined with the higher TER of the regular and direct share classes of these funds, investors have lost out through both the opportunity loss of lower returns in aggregate of actively managed funds and the realized loss of investment returns due to the higher TER of the class of funds they have invested in.
     • Performance against index trackers: For the period since Jan 2018, only a small proportion of actively managed funds have a higher IR than generic index trackers. Simultaneously, for the same period, a significant proportion of actively managed funds have over 92.5% of their performance explained by the performance of index trackers. There are a few funds that have positive IRs. This demonstrates that fund managers do outperform. Investors should look for such opportunities. We argue, therefore, that Index trackers are credible alternatives to a large number of actively managed funds. The range of index trackers available for investment by retail investors is still limited. The industry should look to create a vibrant set of index-tracking products. This will increase competition in the industry and benefit investors.
     • Factor analysis is a useful tool to understand the risks being taken by actively managed funds to ensure that the risks are aligned to the benchmark chosen and the fund category of the fund. Most funds have a significant exposure to large-caps. This argues for investors to consider adding low-cost large-cap index trackers as part of their portfolio at a minimum. While funds are largely aligned to factor exposures implicit in the standardized scheme categories, the choice of benchmarks for specialist categories raises questions of relevance and reasonableness.

We set out a framework using IR and R2 to evaluate any actively managed fund against a chosen low cost index tracker. As a next step we show that using factor analysis allows for the identification of products with similar factor risks. This two-step process offers a simple and robust framework to choose between the actively managed fund and the low-cost index tracker. Using the framework, there is a small proportion of funds that show outperformance against index trackers. This shows that some actively managed funds can outperform low-cost index trackers. In the main though, we should that a significant proportion of funds are potential index trackers. The IR / R2 framework can be easily incorporated into regular portfolio reviews. The framework’s biggest advantage is that it compares two alternative investment choices, rather than some abstract benchmark.

The underperformance of the actively managed funds in aggregate since Jan 2018 should imply that there should be more flows into the index trackers than there currently is. There is a saying in the fund management industry: ‘mutual funds are sold, not bought’. The current TER structure ensures that distributors will keep selling the highest cost variant – which often leads to sub-optimal realized investment outcomes for the investor. As in more developed economies, a robust index fund industry is a necessary condition to create the right competitive environment in the Indian fund management industry which will lead to lower costs and more transparent performance for investors.

Having a wide set of index funds across multiple benchmarks and including factor funds will further increase the alternatives for investors. Given the slow but steady growth of the passive/index industry in India, it seems likely that India too will follow the international trend of index funds being a significant share of the total assets under management by the fund management industry.

It has been a little over 27 months since Jan 2018. While this paper lays out some preliminary trends and findings, a longer data series is required for more robust statistical conclusions.


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A Appendix

Table A1: List of Benchmarks used within Fund Categories
Table A2: List of Funds in Sample
Table A3: Pairwise correlation between Benchmark monthly returns
Distribution of factors in funds by AMFI Fund Category.
Figure 13: Contra Fund: 4 Factor Fama French Regression
Figure 14: Focused Fund: 4 Factor Fama French Regression
Figure 15: Large Cap Fund: 4 Factor Fama French Regression
Figure 16: Large & Mid Cap Fund: 4 Factor Fama French Regression
Figure 17: Mid Cap Fund: 4 Factor Fama French Regression
Figure 18: Multi Cap Fund: 4 Factor Fama French Regression

The details of the scheme categories, their characteristics and uniform description are in Table A4

Table A4: Equity Schemes Characteristics (Securities and Exchange Board of India, 2017)

Nothing herein is investment advice in any form, it does not take into account your personal investment objectives or financial situation and makes no representation and assumes no liability as to the accuracy or completeness of the information.