Editorial Board

A Refereed Monthly International Journal of Management

Testing of Performance Measures on Mutual Fund Debt Schemes: An Empirical evidence in India

Shruthi M P

Research Scholar, Department of M.B.A,

Visvesvaraya Technological University

BDT College of Engineering, Davangere-577004

Karnataka, India,

Email: mpshruthigvt@gmail.com

Dr. T. Manjunatha

Professor, Department of Management Studies (MBA)

Visvesvaraya Technological University

B D T College of Engineering, Davangere -577004

Karnataka, India,

Email: tmmanju87@gmail.com

ORCID: 0000-0003-2322-0498

Dr. V. Rajesh Kumar

Founder and Managing Partner,

Vittam Pravina Gurushala, Bangalore-560011, 

Karnataka, India

Email: vrkumar27@yahoo.com

Abstract

We examine the performance of private and public mutual fund debt schemes in India. We use yearly NAVs of two hundred thirty-four debt schemes, Sensex and Treasury bill yield for the study period from April 2006 to March 2021. We apply time series plot, Quandt likelihood ratio (QLR) test, cumulative sum (CUSUM) test, compounded annual growth rate (CAGR using Geo-mean), performance measures and comparison with Nifty 10 yr. benchmark G-sec Index. The result of time series plot QLR test shows no structural break in the data and no change in parameter and further result show that no significance difference between private and public sector mutual fund debt schemes.

Keywords: NAV, CAGR, Sharpe, Treynor, Jensen, Sortino and time series plot.

Introduction

A mutual fund is an investment scheme that collects money from individuals and invests it in a variety of assets. The funds raised from various investors are typically invested in financial securities such as stocks and money-market instruments such as certificates of deposit and bonds. Asset classes are broadly classified as equity, debt, and money-market instruments. These investments could be made in the short, medium, or long term. Nalini and Tripathy (2005) found that analysed the market timing abilities of Indian fund manager in form of two models. There is only one scheme where market timing ability of the fund managers was shown. Rao(2006) focused on selected open-ended shares. The results exhibited that open ended schemes have made high returns than that of higher risk. Kavita (2009) focused on ELSS schemes analysing performance measures the results shows that ELSS performance is better comparison with its benchmarks. Debashish (2009) found that tax plans have performed intensely performance when measured against the benchmark. Khalid and et.al (2009) found that the Sortino Ratio, which dealt only with downside risk, the results measures given under different ratios had a nearly identical relationship between risk and return. Koulis and et.al(2011) found to attract new domestic and foreign investors, the management of mutual funds must become more significant, so that the return on their portfolio is more attractive than the typical market return. Rahman and et.al (2012) found that growth-oriented mutual funds have not outperformed their benchmark indicators. Some of the funds outperformed the benchmark for systemic risk, & most of the funds did not outperform the benchmark for volatility. Sahil Jain (2012) the results show that, over the last 15 years, private sector mutual fund companies have outperformed public sector mutual fund companies. Vanaja and Karrupawamy (2013) study focused on the performance measures of selected five private sector balanced schemes out of five only two schemes are earned returns above the average returns and Sharpe ratio is positive for all the schemes. Jitendra and Anindita (2015) found that private sector tax saving mutual fund schemes have outperformed as compared to its market return and the performances of public sector tax saving mutual fund schemes were not satisfactory. Nandhini and Rathnamani (2017) found that there is an impact of mutual fund flow in the Indian equity markets. Volatility and uncertainty are part and parcel of equity investing. Shruthi and Manjunatha (2018) argue that 10 per cent of the schemes have high return and lower risk, 10 per cent of the schemes have negative return and 80 per cent of the schemes have high risk and lower return. Chitra and Hemalatha (2018) found that measures results were useful for investors. Antoch et.al (2019) found that testing procedure works well in the framework of the four factors CAPM model and estimate the breaks in the monthly returns of US mutual funds. Shruthi and Manjunatha (2019) argue that investing in equity schemes would be beneficial for investors during the study period. The literature review shows that many researchers are focused on risk return analysis and performance measures. Our study is particularly focusing on comparison analysis of private and public mutual fund debt schemes performance in India using structural break, CAGR, performance measures and comparison of schemes with benchmark.

Objectives and Methodology

We have set following objective based on the evidence of review of literature 

• To measure the performance of private and public sector mutual fund debt schemes in India.

Data Sample and Methodology

This paper focuses on analysis and comparison of performance of debt schemes both for private and public sector mutual funds. We use annual NAV of 169 debt schemes of private sector mutual fund and 65 debt schemes of public sector mutual funds for 15 years study period from April 2006-07 to March 2020-21 to calculate CAGR, Nifty 10 year benchmark G-sec Index returns as market proxy and 91-day treasury bill rate is considered as risk-free rate.  The time-series plot of the CAGR suggests the possibility of structural break.  Quandt Likelihood Ratio (QLR) test and Cumulative Sum (CUSUM) test for structural break indicates that there is no structural break.  Hence, entire 15-years window is considered for analysis.  Kolmogorov-Smirnov test and Shapiro-wilk test are used for testing the normality of the CAGR data. Further, Mann-Whitney test is performed to check whether there is significant difference in the returns of debt schemes of public and private mutual funds. We calculate performance of selected 234 debt schemes by using Sharpe, Treynor, Jensen and Sortino measure and tested for their normality. Mann-Whitney test is performed for ascertaining whether there is significant difference in these performance measures for debt schemes of public and private mutual funds.  Nifty 10 yr. benchmark G-sec Index returns is identified as benchmark and CAGR of return is calculated for the same 15-year window.  Classification of public and private sector schemes are made on the basis of their CAGR as ‘above’ and ‘below’ benchmark.  Chi-square test of independence is used for ascertaining whether there is significant relationship between ‘type of mutual fund scheme’ and ‘performance against benchmark’.

Tools for analysis:

Calculation of rate of return and average return

                                                                                            .... (1)

 Average Return (AR)

            AR =                                                                                                 … (2)

First criterion to check the performance of mutual fund we used CAGR using geomean: it is calculated using annual returns of the schemes and to plot time series to test structural break in sample data. For time series plot we used QLR test and CUSUM test. If there is no structural break entire 15-year data can be considered as single window for analysis. Formula for CAGR:

      CAGR = 1                                                                               … (3)

1. Kolmogorov-Smirnov Test and Shapiro-wilk test has been used for testing the normality of the CAGR Data. To choose parametric or non-parametric test for testing hypothesis.
2. Non-parametric test: Mann Whitney test is used for testing hypothesis for private and public mutual fund debt schemes.
3. Parametric test: Independent sample T-test used for testing hypothesis for private and public mutual fund debt schemes.

Second criterion is performance measures viz: Sharpe, Treynor, Jensen and Sortino are calculated. Related formulas are listed below:

1. Sharpe Measure (SM): It shows excess of return on portfolio over the risk-free rate in relative to its standard deviation.

S_i                                                                                                         … (4)

1. Standard deviation (SD): It is the square root of the variance & measures the spreading of a dataset comparative to its mean. Square root of variance is determined by calculating the variation between each data point values from the mean.

SD =√∑ (xi − x̅) 2/N                                                                                         … (5)

1. Treynor Measure (TM): If the measure is higher than benchmark and portfolio has overtaken the market & it indicates high risk adjusted performance.

       T_i =                                                                                                           … (6)

1. Beta(β): It is mainly related to volatility with the schemes compared with benchmark.

       β =                                                          … (7)

1. Jensen Measure (JM): To determine scheme is making the Systematic return for its risk. If it is positive than the scheme, it is earning more returns.

     JM = (Ri- Rf) + β (Rm-Rf)                                                                                … (8)

1. Sortino Measure (SoM): Total volatility by using the assets standard deviation of negative portfolio returns.

      S_id =                                                                                                         … (9)

1. Kolmogorov-Smirnov Test and Shapiro-wilk Test are used for testing the normality of the CAGR Data. To choose parametric or non-parametric test for testing hypothesis.
2. non-parametric test: Mann Whitney test is used for testing hypothesis for private and public mutual fund schemes.
3. Parametric test: Independent sample T-test used for testing hypothesis for private and public mutual fund schemes. For the calculation of these measures, annual 91-day T-bills (treasury bill) rate is considered as risk-free rate (Rf) wherever required.Nifty 10 yr. benchmark G-sec Index is identified as benchmark for debt schemes, drawn from BSE India.

Third criterion we used to compare the performance of mutual fund schemes with market proxies: Chi-square test of independence is used for ascertaining whether there is a significant relationship between ‘type of mutual fund scheme’ and ‘performance against benchmark.’ Post Hoc test is used if there is significant relationship between ‘type of mutual fund scheme’ and ‘performance against benchmark.

Results and Analysis

Graph 1: indicate a possibility of structural break of the data. For confirmation we use QLR test and CUSUM test. The QLR test results for structural break null hypothesis is no structural break and test statistic: chi-square (1) = 7.92787 at observation 2014 with asymptotic p-value = 0.0650168. CUSUM test results for parameter stability null hypothesis is no change in parameters and test statistic: Harvey-Collier t (13) = -0.500262 with p-value = P (t (13) > -0.500262) = 0.625252. Both the test suggests that there was no structural break (p-value is exceeding 5percent). Hence, entire 15-year period has been considered as a single window for analysis of performance of Mutual fund debt schemes.

Table 1: The average CAGR suggest that the performance of both public and private sector Debt schemes is similar, however the maximum and minimum returns of both the schemes indicate a contrary outcome. Hence, there is a need to check whether the performance of public sector and private sector mutual fund debt schemes are same or different. For enabling testing of the above, it is essential to check whether the data has been normally distributed or not. Kolmogorov-Smirnov and Shapiro-Wilk tests were applied to check for normality of the CAGR data.

Table 2: The test result indicates that the CAGR data is not normally distributed (being significant at 1percent). Hence, for ascertaining whether there is a significantdifferencein the returns of public and private sector mutual fund debt schemes, non-parametric test has to be applied. Since the variable ‘type of mutual fund’ which is a nominal data has only two classifications (public sector and private sector), and the other variable ‘CAGR’ is a scale data, Mann-Whitney U test has been used.

Table 3 The results shows that null hypothesis ‘there is no significance difference in the returns of public and private sector mutual fund Debt schemes’ is accepted (sig. value having exceeded 5percent).

Table 4 indicates for enabling testing of the above, it is essential to check whether the data has been normally distributed or not. Kolmogorov-Smirnov and Shapiro-Wilk tests were applied to check for normality of the performance measures data.

Table 5 The test result indicates that the performance measures data is not normally distributed for Sharpe, Treynor, Jensen and Sortino measures (being significant at 1percent). Hence, for ascertaining whether there is a significantdifferencein the performance of public and private sector mutual fund debt schemes, non-parametric test has to be applied for Sharpe, Treynor, Jensen and Sortino measures. Since the variable ‘type of mutual fund’ which is a nominal data has only two classifications (public sector and private sector), and the other variable ‘SM, TM, JM and SoM’ is a scale data, Mann-Whitney U test has been used.

Table 6 The null hypothesis ‘there is no significance difference in the performance of public and private sector mutual fund Debt schemes with regards to Sharpe, Treynor, Jensen and Sortino measures’ is accepted (sig. value having exceeded 5percent).

Table 7 indicates for ascertaining whether ‘performance against benchmark’ is dependent upon the type of scheme, Chi-square test is applied (since both criteria in the above table are nominal data).

Table 8 The results indicates that there is no significance relationship between types of schemes and benchmark returns of public and private sector Debt mutual funds with regard to performance against benchmark (since p value for Pearson Chi-square test has exceeded 5percent).

Summary and Conclusion

We examine the compounded annual growth rate of debt schemes in private and public mutual funds. Firstly, we used time series plot to check structural break in data, CAGR, Performance Measures and benchmark comparison. The results indicates that no structural break in the data and no parameter stability. The average CAGR and Performance measures suggest that the performance of both public and private sector schemes is similar, however the maximum and minimum returns of both the schemes indicate a contrary outcome. Hence, we test hypothesis to check whether the performance of public sector and private sector mutual fund schemes are same or different. The results shows that there is no significance difference between private and public sector mutual fund debt schemes.

Implication and Scope for further Research

The results of the study may be used by researchers to compare with other foreign mutual funds schemes which will help for investment decision. We have analysed only debt schemes and further studies can include hybrid schemesin private and public sector mutual funds. Further studies can be undertaken to test the relationship between mutual fund schemes return and risk by applying asset pricing models and R-squared calculation are used to analyse the mutual fund performance.

Reference

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Time Series Plot of Average Returns of all Private and Public Sector Debt Schemes

Graph 1 Time Series Plot of Average Returns of all Schemes

Note: X axis indicate years i.e., from 2008-2021. Y axis indicates average return of all 234 schemes of private and public sector Debt mutual fund.

Source: drawn by researcher using Gretel software.

Table 1: CAGR of Private and Public Sector Mutual Fund DebtSchemes:

Source: CAGR of private and public sector mutual funds Debt schemes.

Note 1: First, third and fifth column indicates the codes (for private sector schemes we coded as PVTMFD-001to PVTMFD -169 and for public sector schemes coded as PSMFD-001 to PSMFD-065).

Note 2: Second, fourth and sixth column of the table indicate CAGR of the schemes for the study period.

Table 2 Tests of Normality of Private and Public Sector Mutual Fund Debt Schemes.

Note: we have computed test of normality by using SPSS 22 software.

Table 3 Mann-Whitney Test Result of Private and Public Sector Mutual Fund DebtSchemes

Table 4 Performance Measures of Private and Public Sector Mutual Fund Debt Schemes:

Source: Computed performance measures of private and public sector mutual funds Debt schemes.

Note 1: First and sixth column indicates the codes (For private sector schemes coded as PVTMFD-001to PVTMFD -169 and for public sector schemes coded as PSMFD-001 to PSMFD-065).

Note 2: Second and seventh column indicates Sharpe measure (SM) of schemes.

Note 3: Third and eighth column indicates Treynor measure (TM) of schemes.

Note 4: Fourth and ninth column indicates Jensen measure (JM) of schemes.

Note 5: Fifth and tenth column indicates Sortino measure (SoM) of schemes for the study period.

Table 5 Tests of Normality of Private and Public Sector Mutual Fund Debt Schemes.

Table 6 Mann-Whitney Test of Private and Public Sector Mutual Fund Debt Schemes.

Table 7 Comparison of mutual fund return and Benchmark Return of Private and Public Sector Mutual Fund Debt Schemes:

Table 8 Chi square test of Private and Public sector Mutual Fund Debt Schemes.

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