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First Major Study on the Use of Derivatives by Indian Equity Mutual Funds during the Pandemic

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Submitted:

29 April 2024

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29 April 2024

Withdrawn:

18 December 2024

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Abstract
Emergence of COVID-19 had profound impact on global stock markets, including Indian mar-ket. Key indices like NIFTY50 and Sensex dropped by approximately 40% within two months in 2020, which also affected major mutual funds, leading to significant depreciation of their Net Asset Value. Securities and Exchange Board of India (SEBI) allows mutual funds to use deriva-tives for hedging purposes, capped at 100% of the scheme's net assets covering debt, equity, and derivatives. However, circular amendment by SEBI in January-2019 permitted covered call strat-egies on constituent stocks of Sensex and NIFTY50 for mutual fund schemes, excluding ETFs and Index Funds. This study investigated whether mutual funds increased their derivative us-age as risk mitigation strategy during COVID-19 pandemic, analyzing derivative holdings from 2019-2023. Surprisingly, findings indicated a decline in derivative holdings in 2020 compared to pre-pandemic levels. Statistical tests and performance evaluation metrics such as T-test, F-test, Treynor Ratio, Sharpe Ratio, and Jensen's calculations were employed to assess mutual fund performance. Although derivative-holding mutual funds didn't outperform benchmarks in aver-age returns, it showcased significantly reduced volatility, offering investors favorable risk-return trade-offs. research sheds light on derivative utilization in Mutual Fund industry, potentially in-forming regulators, fund managers, and investors in their decision-making
Keywords: 
Subject: Business, Economics and Management  -   Finance

1. Introduction

An MF is a kind of collective investment plan that is professionally managed and pools money from numerous individuals to invest in the assets like stocks, bonds, short-term money market instruments, along other financial instruments (Rehmani 2018). Investors like mutual funds for a number of reasons. Purchasing shares directly from the market is one approach to investing. Achieving this, however, requires research into the track record of the firm whose shares are being bought, understanding the company’s future business strategies, understanding the promoters’ résumé, researching the company’s dividend and bonus issuance history, etc. Mutual funds have gained immense importance in recent years, particularly because they are an effective, low-cost way for investors to contribute to financial markets by spreading risks through portfolio diversification. They are crucial for the financial sector, in particular, and also play an essential role in the overall growth of the capital market in India. The combined assets managed by mutual fund houses are over INR 43 lakhs crores.
COVID-19 was a major shock to worldwide stock markets and the Indian stock market suffered with the major indices NIFY50 and Sensex falling by almost 40% within two months from their peak in January 2020. Leading Mutual Funds also bore the brunt witnessing similar/ higher erosion of the Net Asset Value during the same period, which could have been lessened if the Mutual Funds had used derivatives to hedge the exposure. Mutual funds are permitted to utilize derivatives as a hedge by the SEBI, provided that the cumulative gross exposure from debt, equity, and the derivatives does not surpass 100 percent of the scheme’s net assets (Circular Number: Cir/ IMD/ DF/ 11/ 2010). The SEBI updated its circular in January 2019 to allow mutual fund schemes (other than ETFs and Index Funds) to write call options on constituent stocks of the Sensex indices and Nifty 50 only using a covered call strategy. The entire notional value of the call options issued by a plan, including the strike price and premium value, may not be more than 15 percent of the equity shares’ overall market value owned by the plan. “The total number of shares supporting all written call options cannot exceed 30 percent of the overall number of unencumbered shares of a certain business owned in the plan. (Circular No.: SEBI/HO/IMD/DF2/CIR/P/2019/17.)”
Retail investors could opt to trade derivatives via mutual funds instead of on their accounts for a variety of reasons. For small investors, there are entrance obstacles, particularly for currency derivatives contracts and interest rates, which are frequently too big for the majority of retail investors. Retail investors might not be well-informed on derivatives and how they are used, and they could also choose not to take personal risks (Johnson and Yu 2004). According to the study SEBI in 2023, individual traders’ 89 percent (i.e. 9 out of 10 individual traders) in the equity derivatives segment suffered losses. Additionally, mutual funds benefit from scale economies in their transactions and in the costs they incur. Liquidity restrictions may be placed on small investors by contracts that demand daily marking to market.
Derivatives are used extensively by Arbitrage Mutual Funds (which hedge 100% of their exposure) and by debt funds to manage against interest rate risk. We examined the utilization of derivatives by the Equity, Hybrid, and other funds which have significant investment in equity shares. By undertaking this research, we are able to derive insights on this unexplored topic. While derivative volumes have been growing leaps and bounds due to continued interest by retail investors and FPOs, our study looks into its use by Indian mutual funds. By reviewing the data from 2019 to 2023, we have been able to analyze the decisions made by Mutual funds during the critical period of COVID-19 by comparing the holdings pre, during, and post-COVID. Our analysis revealed that the total holdings in derivatives as a percentage of total investment by all Equity Funds is insignificant. This is significant as an instrument that has been permitted to reduce the risk from unanticipated global or domestic events is not being used. This observation is stark in the face of a global pandemic like COVID-19, wherein stocks fell over 40% which led to a similar decline in the majority of mutual funds, resulting in stressful times for retail investors. To the relief of the investors, the market has turned around and has now touched all-time highs. However, the question as to why Equity Fund Managers stay away from using derivatives to hedge their market exposure remains. Is it perhaps because of the restrictions placed by SEBI, wherein a mutual fund can only hedge its exposure, which will result in lower performance during bull markets? Another reason could be the cost of hedging due to the availability of only short maturities in the Derivatives market. The study on hedging becomes equally important as according to a report released by Morgan Stanley, the Indian stocks could fall by 25-40% if the current government is not re-elected. Having said that, there are few funds that have investments in derivatives of anywhere between 2-15% of their portfolio.
Our analysis also provides information on the types of derivatives i.e. Stock future, Index future, Index Call and put option, stock call and put option, and derivatives of commodities. Our analysis reveals, that despite SEBI granting approval for MFs to invest in Options, the mutual funds primarily use investment in Index and stock futures. Our analysis also revealed that the disclosure on holding of derivatives by Mutual Funds in their portfolio is not uniform, as some MFs show short positions as a positive figure in their holdings on account of the margin place while few others report short positions as negative while reporting their exposure to derivatives. This is a key insight for the regulator SEBI to ensure that all MFs utilize a uniform approach to report their derivative exposure. This is how the remaining of the paper is structured. We present the relevant literature for review in Section II. The goal of the study, the empirical methodology, and the data used are described in the Section III. The outcomes and their implications are covered in Section IV. The research’s main conclusions are presented in the Section V.

2. Literature Review

This section may be divided by subheadings. It should provide a concise and precise description of the experimental results, their interpretation, as well as the experimental conclusions that can be drawn. While there have been a lot of studies on the Indian Equity fund’s performance, there is limited research on the derivatives usage by Indian Equity Mutual Funds. Our literature review mainly covers studies across the Globe on the usage of derivatives by MFs and select studies on the Indian markets. The most conclusive evidence to date comes from a study of MFs by (Koski and Pontiff 1999). which indicates that the majority of MF managers utilize derivatives for the hedging and that a very small percentage utilize them for speculating & amplification. The use of derivatives may have advantages, according to an earlier study. According to various studies (Almazan et al. 2004; Deli and Varma 2002; Frino, Lepone, and Wong 2009; Koski and Pontiff 1999) benefits could include improved information use, lower costs of transaction, lower costs of liquidity-motivated trading, and more effective ways to maintain a certain level of the risk exposure. (Cao, Ghysels, and Hatheway 2011) found that risk along with return characteristics of funds which utilize derivatives are significantly dissimilar from the funds employing derivatives sparingly. (Mandal 2011) analyzed the hedging effectiveness of stock index futures and found that using model LLS models to hedge portfolios can reduce risk. On the basis of an argument first put forth by (Glode 2011), a logical conjecture that explains the observed underperformance and extra flows is that the derivative strategies used by these funds may have been designed to outperform during times of crisis when investors place a premium on a strong performance. The managers of Canadian mutual funds don’t use derivatives in their holdings (Johnson and Yu 2004). According to a study on Spanish mutual funds, using derivatives does not increase the funds’ performance (Marin and Rangel 2006). The usage of derivatives in Italian equities MFs between December 2002 and May 2007 was examined by (Garcia-Appendini and Rangel 2009) and was discovered that throughout this period, the average asset allocation to derivatives grew by about 50%, closely corresponding with the management of Italian mutual fund legislation to European norms. A study on the usage of options by US-based Mutual found that neither permanent nor transient users of options engaged in excessive risk-taking, but rather that certain funds used options to successfully reduce risk (Cici and Palacios 2015). During the first outbreak, funds which utilized derivatives for the hedging prior to the crisis substantially outperformed nonusers by over 9% as their derivative return’s distribution shifted to the right (Kaniel and Wang 2020). Derivative users considerably improved their risk-adjusted performance, grew their exposure to market risk, decreased idiosyncratic as well as overall risk, decreased skewness, as well as raised kurtosis during the same period. (Kaniel and Wang 2022) most recent analysis, which used new data, discovered that almost 30% of US mutual funds employ derivatives, even though there is now little proof of a connection among fund performance as well as derivative usage.
There have been several studies on the COVID-19 impact on mutual allocation, company performance, and investor preferences. According to (Bansal et al. 2020) Indian companies with larger cash balances performed better than similar competitors with less financial flexibility. Regarding the significance of financial flexibility in the US, (Ramelli and Wagner 2020) have similar conclusions. Our results on US institutional investors’ trading preferences also support those of (Glossner et al. 2020; Jacob, Gupta, and Gopalakrishnan 2024) found at the time of the initial stages of the pandemic, funds showed a preference for companies with lower risk, greater financial adaptability, and large market presence. This inclination towards less risky ventures, which later shifted, indicates a redirection towards more secure investments.

3. Objective, data, and Methodology

The study’s objectives are as follows:
  • To find out whether equity mutual funds’ use of derivatives increased/decreased during COVID?
  • To find out whether the equity mutual funds that use derivatives outperformed their peers pre- during and post-COVID-19?
  • Did investment in derivatives assist equity mutual funds reduce their volatility and improving their overall performance based on risk/return matrices?
  • The authors reviewed over 500 hundred equity mutual funds with Assets Under Management of INR 15 lakhs crores. The authors reviewed the derivative holdings of mutual funds from January 2019 till December 2023, to study the use derivatives of derivatives pre-COVID and during COVID and post-COVID periods to examine which mutual funds used derivatives to hedge exposure and their performance versus their peers and their benchmark.
There is a huge amount of scholarly research on how to evaluate Indian mutual fund performance. (Sapar and Madava 2003) used risk-return analysis, the Sharpe ratio, Jensen & Fama, Treynor ratio, and other methods to determine the Indian mutual fund sector performance at the time of the bear market. For the period of September 1998 to April 2002, AMFI provided statistics on monthly closing NAV. For the study, a sample of 58 open-ended designs was selected. The study’s conclusions showed that, in terms of both total and systematic risk, the majority of the sample schemes were able to provide better returns than predicted returns. (Devi and Kumar 2010) evaluated the investment performance of equity MFs within India at the time of 2003 - 2007 by using mean rate of return, SD (Standard Deviation), and risk-return analysis. Furthermore, risk-adjusted measures of performance assessment like the Treynor ratio, Sharpe ratio, and Jensen measure were also used. A total of 102 schemes were taken as sample schemes - 56 equity diversified funds, 18 equity tax saving funds, 21 equity index funds, and seven equity technology funds. This research findings comparative research of the investment MFs’ performance from the public and private sectors in India showed that there was no discernible difference between their performance. Using the rate of return, Treynor & Sharpe ratios, SD, beta. (Dhanda, Batra, and Anjum 2012) analyzed the investment performance of a few open-ended “mutual fund plans in terms of risk-adjusted returns and risk-return from April 2009-March 2011. The findings revealed that only 3 schemes, namely HDFC Capital Builder Fund, HDFC Top 200, and UTI Opportunities Fund” had outperformed the market. (Zaheeruddin, Sivakumar, and Reddy 2013) examined the of 3 private-sector MFs performance from July 1, 2009, to April 2, 2012. Besides risk-return analysis, risk-adjusted measures of performance analyses like Sharpe &Treynor ratios and Jensen Alpha have been also utilized to assess the performance. The findings of the research indicated that ICICI generated the highest returns; whereas, Birla Sun Life was the riskiest one. (Pal and Chandani 2014) attempted to investigate the performance of the top 10 equity MF plans for a period of 5yrs, that is, from 2007 to 2012. With the statistical measures like SD, R-square, beta, expense ratio, and Sharpe ratio, the analysis revealed that among all the sample schemes, HDFC Mid Cap Opportunities as well as Quantum Long Term Equity emerged as top performers during the period of the study. (Dr. M.M. Goyal 2021) assessed the top 10 MFs’ performance and contrasted it with that of the CNX Nifty and S&P benchmark indices. The research discovered that generally, all of the schemes worked well since they produced greater and better returns than the market index utilizing the Treynor ratio, Sharpe ratio, and Jensen measure. Franklin India Opportunities Fund has been determined to be the top performer among all the sample schemes since it produced greater average returns while also having reduced risk. (TOMER and KHAN 2015) analyzed the mutual funds’ performance in India with risk-return measures, Sharpe & Treynor ratio, Jensen - differential measure, and Sharpe - differential measure from January 1, 2005, to December 30, 2010. The results showed mixed performance of sample schemes. Moreover, the private sector funds performed better in comparison to public sector funds in all aspects.

3.1. Measures Used for Performance Evaluation

Return Measures: Investments are done to earn a reward. Returns may be defined as the reward earned from an investment. Monthly returns of the selected MF schemes were calculated with month-end NAVs by utilizing the formula mentioned below:
R p t = N A V t − N A V t − 1 N A V t − 1
where, R p t = fund returns, N A V t = NAV current day, N A V t − 1 = NAV in previous day
Likewise, the bench mark index was computed as:
R m t = I n d e x t − I n d e x t − 1 I n d e x t − 1
where, R m t represents the market return, I n d e x t and I n d e x t − 1 present the market index on day t and the previous day.
Risk Measures: Investments are risky. Risk may be defined as the potential for variability in returns. Risks are neither good nor bad. Risk in an investment usually refers to the probability that the actual returns may be lesser as compared to expected returns. The higher the risk in an investment, the higher the returns generated by it. There are two types of risks - total risk, measured by SD(σ), and systematic risk, determined by beta coefficient (β). The risk involved with the chosen mutual fund schemes has been determined based on month-end NAV.
The research has used the following risk measures:
Standard Deviation (σ): It is a measure of return volatility since it compares the actual returns of a mutual fund to its predicted returns. Higher SD indicates higher risks involved in the investment.
Beta (β): Beta (β) measures the volatility in returns of an investment in terms of systematic risk and is calculated by relating the portfolio returns with the market returns.
Risk-Free Rate: It has 0 variability of returns. It has no association with risky assets. It is the base for performance evaluation of risky investments. In the present work, the average monthly yield of 91 days of treasury bills has been considered a risk-free rate, particularly because it is guilt-edged and of course, because of its easy accessibility.
Sharpe Ratio: (Sharpe 1966) constructed an index to measure portfolio performance. It is recognized as a reward-to-variability ratio. It is the excess return ratio average of fund portfolios and the SD of the returns in a given period. It measures the return in relation to the portfolio’s total risk and is based on the CML (Capital Market Line). Sharpe ratio judges the efficacy of fund managers in the diversification of overall risk and is a beneficial tool to assess the excess return/unit of overall risk. It is believed that the greater the Sharpe ratio, the better it is.
Treynor Ratio: (Treynor and Mazuy 1966) gave another measure of performance evaluation, popularly known as the Treynor ratio. It is quite alike to the Sharpe ratio as it also determines excess returns created by an investment over the risk-free rate. Treynor ratio evaluates excess returns per unit of systematic risk, i.e. beta, unlike the Sharpe ratio which uses total risk. It is also recognized as the ratio of reward to volatility. Similar to the Sharpe ratio condition, the larger the “Treynor ratio,” the better it is.
Jensen Measure: (Jensen 1968) developed another methodology to measure the average return of a fund portfolio (above or below) as predicted by SML (Security Market Line). It is popularly referred to as Jensen’s alpha. It is beneficial as it assesses the fund managers’ capability to make higher returns for investors. A positive as well as significant Jensen alpha value is an indication that the fund has generated higher returns than CAPM returns.

4. Analysis and Results

The authors downloaded the data of derivative holdings at the time the period from the January 2019 to December 2023 and the results are shown in the Figure 1 below:
It is clear from the above chart that the total derivative holding decreased significantly between pre-COVID and during COVID and started increasing slowly post-COVID. To check the robustness of our assessment, we did a t-test to compare the mean of derivative holdings during the period Jan 2019 to Dec 2019 (pre covid) with Jan-Dec 2020 (During Covid) and similarly for the following years and results are given below in Table 1. The results establish that the derivatives volumes decreased significantly from the time the market started declining due to fears over the pandemic. Except for 2023, the downward movement in 2020 and the upward movement in 2021 & 2022 are statistically significant.
We collated the break-up of derivative volumes into various categories, see Table 2 below. The figures corresponding to the first line of the table below are the cash margin placed by Mutual Funds with the exchange for trading in derivatives. We can clearly see similar results with the figure of Derivatives of stock futures falling by almost 50% during COVID and rising by 50% post-COVID.
We selected ten mutual funds that had an average holding over 2% of the average of the total derivative holdings during the period from January 2019 to December 2023 and their names are given below in Table 3 and descriptive statistics of the funds are given in Table 4.
We calculated the daily average returns of the above-mentioned ten MFs for the period from 01 January 2019 till 31st December 2023 and of select benchmarks and results are given below in Table 5. The authors did a t-test using daily returns and found that there was an insignificant difference in means between the indices and mean returns of the mutual funds investing in derivatives, as shown in Table 6.
We also did an F test to compare the variances between the average daily returns of mutual funds that invest in derivatives against the indices. We found there was a significant difference, see Table 7
This perhaps explains the high Sharpe ratio, positive Treynor ratio as well as Jenson’s alpha. We also did Levine’s test for homogeneity and ANOVA and the statistics are given below in Table 8 and Table 9.

5. Conclusions

The authors examined the derivatives utilization by Indian Equity Funds as a means to hedge their exposure during COVID-19. We found a significant drop in derivatives volumes between pre-COVID and during COVID and a significant increase between during COVID and post COVID which reveals that the mutual funds did not use derivatives to hedge their exposure. However, with sharp-up run in the market coinciding with an increase in derivatives indicates that the Fund Managers may be using derivatives to safeguard their profits in case of a drop in the market.
Authors conclude that the derivatives utilization by equity MFs did not assist in their returns major benchmarks. We found that the volatility as calculated by the SD of returns was significantly lower for mutual funds that invest in derivatives as having a positive effect on the Jensen’s alpha, Sharpe & Treynor ratio of mutual funds. Investors
Our Analysis of data reveals that as an industry, the majority of Indian equity mutual funds invest insignificant amounts in derivatives. The authors spoke with several fund managers on the reasons and were given the following reasons:
• High transaction costs: The maturity of the Indian futures market is very short with the majority of the trades happening within two months of maturity. If a mutual fund, decides to hedge the exposure using a NIFTY futures short position, it has to roll over every two months to be able to hedge its exposure. This increases transaction costs and makes derivatives unattractive
• SEBI rules: As per SEBI guidelines, the total exposure of the fund including the derivative should not exceed 100%. If a mutual fund invests in derivatives of INR 1000, for which it will place a margin of 25% of INR 250, it has to necessarily set aside INR 750 in fixed deposits. Since there is no benefit of leverage to mutual funds, as against individuals who can trade in margin, the Mutual Fund houses restrict purchasing derivatives. The second reason is that mutual funds cannot short any stock and use only NIFTY contracts to hedge against FII which holds long on certain equities and short on others.
The research provides valuable insights into the derivatives utilization by Equity MFs to hedge their exposure for investors, fund managers, and regulators. The main limitation of this research is that we restricted the sample to ten funds that had significant holdings. A more elaborate study would surely provide better insights. A comparative study of derivative holdings over the last two decades will also reveal if, in previous years, derivatives were more popular amongst fund managers.

Author Contributions

Conceptualization, J.K.; methodology, J.K.; formal analysis, J.K.; investigation, J.K.; writing—original draft preparation, J.K.; writing—review and editing, J.K. and S.P.S; All authors have read and agreed to the published version of the manuscript

Funding

This research received no external funding.

Data Availability Statement

The data used in this research will be available upon request.

Conflicts of Interest

The authors declare no conflicts of interest.

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Figure 1. Data of derivative holdings at the time the period from the January 2019 to December 2023.
Figure 1. Data of derivative holdings at the time the period from the January 2019 to December 2023.
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Table 1. T-test results for comparison of mean derivative holdings pre-COVID (Jan 2019 - Dec 2019) and during COVID (Jan 2020 - Dec 2020) years.
Table 1. T-test results for comparison of mean derivative holdings pre-COVID (Jan 2019 - Dec 2019) and during COVID (Jan 2020 - Dec 2020) years.
Year Derivative Volume in T Test-p value
2019 7,555.98 -
2020 5,070.52 0.0001
2021 6,539.40 0.0019
2022 8,016.27 0.0039
2023 8,541.87 0.5022
Table 2. Break-up of derivative volumes by category.
Table 2. Break-up of derivative volumes by category.
Description 2019 2020 2021 2022 2023
Derivatives 18.70% 49.60% 38.30% 43.00% 36.00%
Derivatives - Index Call 0.00% 0.00% 0.00% 0.00% 0.00%
Derivatives - Index Future 6.30% 9.70% 14.60% 3.60% 1.40%
Derivatives - Index Put 0.10% 0.70% 0.80% 1.80% 1.00%
Derivatives - Stock Call 0.00% 0.00% 0.00% 0.10% 0.30%
Derivatives - Stock Future 74.90% 36.40% 46.30% 51.30% 56.40%
Derivatives - Stock Put 0.00% 0.00% 0.00% 0.10% 0.00%
Derivatives - Commodity 0.00% 0.00% 0.00% 0.00% 4.80%
Grand Total 100% 96.40% 100% 100% 100%
Table 3. Selected Mutual Funds with Average Derivative Holdings Over 2% from January 2019 to December 2023.
Table 3. Selected Mutual Funds with Average Derivative Holdings Over 2% from January 2019 to December 2023.
Name of the Fund INR Crores as at 31st December 2023
Aditya Birla SL Frontline Equity Fund (G) 21,840
AXIS Bluechip Fund (G) 34,580
ICICI Pru Bluechip Fund (G) 47,928
ICICI Pru Multi-Cap Fund 10,340
Parag Parikh Flexi Cap Fund - Direct (G) 52,007
Quant Active Fund (G) 7,413
Quantum Mid Cap Fund 4,222
Quant Flexi Cap Fund (G) 2,901
Quant Small Cap Fund - (G) 13,001
SBI Magnum Global Fund (G) 4,253
Table 4. Descriptive statistics of the funds.
Table 4. Descriptive statistics of the funds.
Name of Scheme Base Date 5 Years
CAGR		 Annualised SD Annualised Sharpe Ratio Beta Treynor Ratio Jensons Alpha R Squared
Aditya Birla SL Frontline Equity Fund (G) 29-12-2023 14.93 18 0.71 0.91 0.06 0 0.96
AXIS Bluechip Fund (G) 29-12-2023 13.65 12.4 0.82 0.85 0.07 0.01 0.85
ICICI Pru Bluechip Fund (G) 29-12-2023 16.98 17.79 0.82 0.9 0.06 0.01 0.96
ICICI Pru Multi-Asset Fund (G) 29-12-2023 18.29 13.53 1.11 0.6 0.1 0.03 0.73
Parag Parikh Flexi Cap Fund (G) 29-12-2023 22.79 14.42 1.31 0.58 0.13 0.05 0.61
Quant Active Fund (G) 29-12-2023 26.22 20.06 1.13 0.81 0.11 0.05 0.61
Quant Flexi Cap Fund (G) 29-12-2023 26.6 19.41 1.18 0.78 0.12 0.05 0.61
Quant Mid Cap Fund (G) 29-12-2023 26.82 22.04 1.02 0.85 0.08 0.03 0.56
Quant Small Cap Fund - (G) 29-12-2023 32.22 21.31 1.3 0.73 0.15 0.07 0.44
SBI Magnum Global Fund (G) 29-12-2023 15.64 13.75 0.92 0.54 0.09 0.02 0.58
Average 21.41 17.27 1.03 0.76 0.1 0.03 0.69
Scheme: Indices
Nifty 200 TRI 29-12-2023 16.74
S&P BSE Tech TRI 29-12-2023 19.75
S&P BSE 200 TRI 29-12-2023 17.2
Table 5. Daily Average Returns of Selected Mutual Funds and Benchmarks from January 1, 2019, to December 31, 2023.
Table 5. Daily Average Returns of Selected Mutual Funds and Benchmarks from January 1, 2019, to December 31, 2023.
Fund name Average Daily returns*
Aditya Birla SL Frontline Equity Fund (G) 0.0631
AXIS Bluechip Fund (G) 0.0583
ICICI Pru Bluechip Fund (G) 0.0708
ICICI Pru Multi-Asset Fund (G) 0.0719
Parag Parikh Flexi Cap Fund - Direct (G) 0.0912
Quant Absolute Fund (G) 0.0859
Quant Active Fund (G) 0.1022
Quant Flexi Cap Fund (G) 0.129
Quant Small Cap Fund - (G) 0.1203
SBI Magnum Global Fund (G) 0.0904
Average 0.0883
Nifty 200 TRI 0.0756
S&P BSE 500 TRI 0.073
S&P BSE 200 TRI 0.0709
Nifty Large Midcap 250 TRI 0.0756
Table 6. Results of T-Test on Daily Returns of Indices and Mutual Funds Investing in Derivative.
Table 6. Results of T-Test on Daily Returns of Indices and Mutual Funds Investing in Derivative.
t-Test: Paired Two Sample for Means Variable 1 Variable 2
Mean 0.086044949 0.072962727
Variance 0.914180339 1.79103125
Observations 1232 1232
Pearson Correlation 0.077456913
Hypothesized Mean Difference 0
df 1231
t Stat 0.290008581
P(T<=t) one-tail 0.385929257
t Critical one-tail 1.646092395
P(T<=t) two-tail 0.771858515
t Critical two-tail 1.961892958
Table 7. Results of F-Test on Variances of Average Daily Returns between Mutual Funds Investing in Derivatives and Indices.
Table 7. Results of F-Test on Variances of Average Daily Returns between Mutual Funds Investing in Derivatives and Indices.
F-Test Two-Sample for Variances Average returns of mutual funds S & P BSE 500 TRI
Mean 0.085682364 0.072962727
Variance 0.880617247 1.79103125
Observations 1232 1232
df 1231 1231
F 0.491681676
P(F<=f) one-tail 0
F Critical one-tail 0.910466185
Table 8. Levine’s test for homogeneity.
Table 8. Levine’s test for homogeneity.
Test of Homogeneity of Variances Levene Statistic df1 df2 Sig.
MF Based on Mean 2.255 248 845 0
Based on Median 1.252 248 845 0.012
Based on the Median and with adjusted df 1.252 248 217.295 0.045
Based on trimmed mean 2.138 248 845 0
Table 9. ANOVA.
Table 9. ANOVA.
ANOVA Sum of Squares df Mean Square F Sig.
MF Between Groups 581.954 386 1.508 2.537 0
Within Groups 502.212 845 0.594
Total 1084.17 1231
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