SCMHRD Market Risk and Investment performance of equity mutual funds in India Tushar Alva -2009A06 Shaleen Agarwal -2009A12 Sarath Ruthvic Prabhala- 2009A56 1
Market risk and investment performance of equity mutual funds in india
Jan 22, 2015
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- 1. SCMHRD
Market Risk and Investment performance of equity mutual funds in India
Tushar Alva -2009A06
Shaleen Agarwal -2009A12
Sarath Ruthvic Prabhala- 2009A56
Mayank Agarwal- 2009B12
Subhodeep Bandhopadhyay- 2009B48
Ankit Kumar- 2009B50
INDEX
Serial No.TopicPage Numbers1Executive summary4-52Introduction6-73Significance of the study84Literature review9-155Data156Research methodology16-197Data Analysis and interpretation20-298Findings and conclusion30-319References32-3310Appendix34-51
APPENDIX
Appendix No.DescriptionPage NumbersAppendix 1List of funds selected for study34Appendix 2Average Returns of selected funds35Appendix 3Absolute Returns of selected funds37Appendix 4Standard Deviation of selected funds38Appendix 5Betas of selected funds38Appendix 6 Relative Performance Index (RPI)39Appendix 7Mann-Whitney U-Test of Average Returns40-48Appendix 8Mann-Whitney U-Test of Absolute Returns49-50Appendix 9Hierarchical multiple clustering - Agglomeration method51
Executive Summary:
This study has been undertaken to evaluate the performance of the Indian Mutual Funds vis--vis the Indian stock market. For the purpose of this study, 21 open ended equity based growth mutual funds were selected as the sample. The data, which is the weekly NAVs of the funds and the closing of the BSE Sensex, were collected for a period of 5 years starting 19/03/2004 to 13/02/2009.
Different statistical tools were used on the data obtained to get the average returns, absolute returns, standard deviation, Fund Beta, R-squared value, residual value, Relative Performance Index were calculated. These variables of the funds were compared with the same variables of the market to assess how the different funds have performed against the market.
A Statistical test, Mann Whitney U-Test, was done on the returns of the fund with respect to the Sensex returns. Another U-Test was done taking absolute return as the variable. These U- Test were done to test the hypothesis which was that the fund returns over the period of time are similar to the market returns over the period of time.
All the funds were classified into a hierarchical cluster on the basis of their average returns, absolute returns, standard deviation, fund beta, and relative performance index. This classification was to see whether the funds have similar properties or not.
All the mutual funds gave similar returns with respect to the market expect for certain time period which was during the late 2005 and early 2006. There is a positive correlation with the absolute returns of the market and the mutual funds over the period of time. The study showed that the standard deviation of the funds were high during the boom period in comparison with the market and were comparatively lower when the recessionary trend started. The fund betas also show that there is significant correlation between the fund returns and the market returns. Of the 21 funds considered for this study, 7 funds had RPI less than 0.7, 3 funds had RPI of almost 1 and 11 funds had RPI of more than 1.
The results of the U-Test showed that all the funds are accepting the hypothesis that is they are giving returns in sync with the market except for one fund which is UTI CCP Advantage growth fund, whose returns vary significantly from the market returns. With the help of clustering it was seen that a lot of different funds have similar properties and so were classified into one cluster. There were a few outliers who didnt have any property in common with the other funds but still behaved more or less in the same way as the market and other funds. A U-Test was also done on the absolute returns and the results of this were also similar to the U-Test on average returns, that is, for UTI CCP Advantage Fund the returns were not similar to the market returns and varied significantly.
Introduction:
The mutual fund industry has been in India for a long time. This came into existence in 1963 with the establishment of Unit Trust of India, a joint effort by the Government of India and the Reserve Bank of India.The next two decades from 1986 to 1993 can be termed as the period of public sector funds with entry of new public sector players into the mutual fund industry namely, Life Insurance Corporation of India and General Insurance Corporation of India.
The year of 1993 marked the beginning of a new era in the Indian mutual fund industry with the entry of private players like Morgan Stanley, J.P Morgan, and Capital International. This was the first time when the mutual fund regulations came into existence. SEBI (Security Exchange Board of India) was established under which all the mutual funds in India were required to be registered. SEBI was set up as a governing body to protect the interest of investor. By the end of 2008, the number of players in the industry grew enormously with 46 fund houses functioning in the country.
With the rise of the mutual fund industry, establishing a mutual fund association became a prerequisite. This is when AMFI (Association of Mutual Funds India) was set up in 1995 as a nonprofit organization. Today AMFI ensures mutual funds function in a professional and healthy manner thereby protecting the interest of the mutual funds as well as its investors.
The mutual fund industry is considered as one of the most dominant players in the world economy and is an important constituent of the financial sector and India is no exception. The industry has witnessed startling growth in terms of the products and services offered, returns churned, volumes generated and the international players who have contributed to this growth. Today the industry offers different schemes ranging from equity and debt to fixed income and money market.
The market has graduated from offering plain vanilla and equity debt products to an array of diverse products such as gold funds, exchange traded funds (ETFs), and capital protection oriented funds and even thematic funds. In addition investments in overseas markets have also been a significant step. Due credit for this evolution can be given to the regulators for building an appropriate framework and to the fund houses for launching such different products. All these reasons have encouraged the traditional conservative investor, from parking fund in fixed deposits and government schemes to investing in other products giving higher returns.
It is interesting to note that the major benefits of investing in a mutual funds is to capitalize on the opportunity of a professionally managed fund by a set of fund managers who apply their expertise in investment. This is beneficial to the investors who may not have the relevant knowledge and skill in investing. Besides investors have an opportunity to invest in a diversified basket of stocks at a relatively low price. Each investor owns a portion of the fund and hence shares the rise and fall in the value of the fund. A mutual fund may invest in stocks, cash, bonds or a combination of these.
Mutual funds are considered as one of the best available investment options as compare to others alternatives.They are very cost efficient and also easy to invest in. The biggest advantage of mutual funds is they provide diversification, by reducing risk & maximizing returns.
India is ranked one of the fastest growing economies in the world. Despite this huge progression in the industry, there still lies huge potential and room for growth. India has a saving rate of more than 35% of GDP, with 80% of the population who save. These savings could be channelized in the mutual funds sector as it offers a wide investment option.In addition, focusing on the rapidly growing tier II and tier III cities within India will provide a huge scope for this sector. Further tapping rural markets in India will benefit mutual fund companies from the growth in agriculture and allied sectors. With subsequent easing of regulations, it is estimated that the mutual fund industry will grow at a rate of 30% - 35% in the next 3 to 5 years and reach US 300 billion by 2015.
As it can be noted, there is huge growth and potential in the mutual fund industry. The development of this sector so far has been commendable and with the above positive factors we are looking at a more evolved industry.
Significance of the Study:
Over the last couple of years mutual funds have given impressive returns, especially equity funds. The growth period first started during early 2005 with markets appreciating significantly. With 2006 approaching more towards 2007, markets rallied like never before. The financial year 2007-08 was a year of reckoning for the mutual fund industry in many ways. Most stocks were trading in green. All fund houses boasted of giving phenomenal returns. Many funds outperformed markets. Equity markets were in the limelight. Investors who were not exposed to equity stocks suddenly infused funds. AUM grew considerably and fund houses were on a spree of launching new schemes.
Growth funds which aim at giving capital appreciation invest in growth stocks of the fastest growing companies. Since these funds are more risky providing above average earnings, investors pay a premium for the same. These funds have grown to become extensively popular in India. All the leading fund houses offer several schemes under the growth funds today.
The remarkable performance of this industry has attracted many researchers to study and examine the growth, the performance of funds, the players in the market and the regulators. It is interesting to learn the growth phase of these funds over this period.
The study aims at:
Comparing the performance of the selected funds vies-a-vies the benchmark index, BSE (Bombay Stock Exchange) Sensex
Capturing differences in the performance levels, if any.
Ascertaining whether the returns generated by the funds are purely attributable to market movement or individual fund performance.
Literature Review:
Performance evaluation of mutual funds is one of the preferred areas of research where a good amount of study has been carried out. The area of research provides diverse views of the same.
For instance one paper evaluated the performance of Indian Mutual Fund Schemes in a bear market using relative performance index, risk-return analysis, Treynors ratio, Sharpes ratio, Jensens measure, Famas measure. The study finds that Medium Term Debt Funds were the best performing funds during the bear period of September 98-April 2002 and 58 of 269 open ended mutual funds provided better returns than the overall market returns.
Another paper used Return Based Style Analysis (RBSA) to evaluate equity mutual funds in India using quadratic optimization of an asset class factor model proposed by William Sharpe and analysis of the relative performance of the funds with respect to their style benchmarks. Their study found that the mutual funds generated positive monthly returns on the average, during the study period of January 2000 through June 2005. The ELSS funds lagged the Growth funds or all funds taken together, with respect to returns generated. The mean returns of the growth funds or all funds were not only positive but also significant. The ELSS funds also demonstrated marginally higher volatility (standard deviation) than the Growth funds.
One study identified differences in characteristics of public-sector sponsored & private-sector sponsored mutual funds find the extent of diversification in the portfolio of securities of public-sector sponsored and private-sector sponsored mutual funds and compare the performance of public-sector sponsored and private-sector sponsored mutual funds using traditional investment measures. They primarily use Jensens alpha, Sharpe information ratio, excess standard deviation adjusted return (eSDAR) and find out that portfolio risk characteristics measured through private-sector Indian sponsored mutual funds seems to have outperformed both Public- sector sponsored and Private-sector foreign sponsored mutual funds and the general linear model of analysis of covariance establishes differences in performance among the three classes of mutual funds in terms of portfolio diversification.
Another study examined the risk-adjusted performance of open-end mutual funds which invest mainly in German stocks using Jensons measure and Sharpes measure. The study finds out that the rates of return of the mutual funds and the rates of return of the chosen benchmark both must include identical return components. Either both must include dividends or exclude them. The performance estimates are not very sensitive with respect to the benchmark choice. When we look at an investment strategy in which the investment in a specific fund has the same risk as the chosen benchmark, the average underperformance is small when we weight the individual fund returns equally. The average performance is neutral, when we weight the individual fund returns according to fund size, measured by assets under management.
One more paper analyzed whether it was more appropriate to apply a factor-based or a characteristic-based model - both known as benchmarks in portfolio performance measurement using the Linear model, asset pricing model and Fama and French factors. The study showed that if information on returns was used and a linear model was proposed that adjusted return to a set of exogenous variables, then the right side of the equation reported the achieved performance and the passive benchmark that replicated the style or risk of the assessed portfolio. While, a factor model utilizes a replicate benchmark with short positions implicitly symmetrical to the long positions. Performance of Russell indexes was analyzed by applying various factor models, constructed from the indexes themselves, and other models that use the indexes directly as benchmarks; the presence of biases was detected. Therefore, according to the empirical findings, selection of exogenous variables that define the replicate benchmark would appear to be more relevant than the type of model applied.
Another study aimed at analyzing performance of select open-ended equity mutual fund using Sharpe Ratio, Hypothesis testing and return based on yield. The most important finding of the study had been that only four Growth plans and one Dividend plan (5 out of the 42 plans studied) could generate higher returns than that of the market which is contrary to the general opinion prevailing in the Indian mutual fund market. Even the Sharpe ratios of Growth plans and the corresponding Dividend plans stand testimony to the relatively better performance of Growth plans. The statistical tests in terms of F-test and t-Test further corroborate the significant performance differences between the Growth plans and Dividend plans.
Another study investigated mutual fund performance using a survivorship bias controlled sample of 506 funds from the 5 most important mutual fund countries using Carhart (1997) 4-factor asset-pricing model. The study revealed a preference of European funds for small and high book-to-market stocks (value). Secondly, it showed that small cap mutual funds as an investment style out-performed their benchmark, even after control for common factors in stock returns. Finally 4 out of 5 countries delivered positive aggregate alphas, where only UK funds out-performed significantly.
One more studylooked at some measures of composite performance that combine risk and return levels into a single value using Treynors ratio, Sharpes ratio, Jensons measure. The study analyzed the performance of 80 mutual funds and based on the analysis of these 80 funds, it was found that none of the mutual funds were fully diversified. This implied there is still some degree of unsystematic risk that one cannot get rid of through diversification. This also led to another conclusion that none of those funds would land on Markowitzs efficient portfolio curve.
Another paper aimed to evaluate if mutual fund managers exhibit persistently superior stock selection skills over a short-horizon of one year using risk-adjusted abnormal returns (RAR), One-factor capital asset pricing model or CAPM three-factor, Fama-French model, Four-factor Carhart model. Their study demonstrated that short-term persistence in equity mutual funds performance does not necessarily imply superior stock selection skills. Common factors in stock returns explained some of the abnormal returns in top ranking mutual fund schemes. Only the winner portfolios sorted on four-factor alphas' provided an annual abnormal return of about 10% on post-formation basis using daily data. The short-term persistence results were much better when daily data was used rather than monthly observations, thus implying that data frequency does affect inferences about fund performance.
A similar study examined the empirical properties of performance measures for mutual funds using Simulation procedures combined with random and random-stratified samples of NYSE and AMEXsecurities and other performance measurement tools employed are Sharpe measure, Jensen alpha, Treynor measure, appraisal ratio, and Fama-French three-factor model alpha. The study revealed that standard mutual fund performance was unreliable and could result in false inferences. In particular, it was easy to detect abnormal performance and market-timing ability when none exists. The results also showed that the range of measured performance was quite large even when true performance was ordinary. This provided a benchmark to gauge mutual fund performance. Comparisons of their numerical results with those reported in actual mutual fund studies raised the possibility that reported results were due to misspecification, rather than abnormal performance. Finally, the results indicated that procedures based on the Fama-French 3-factor model were somewhat better than CAPM based measures.
One more paper evaluated whether or not the selected mutual funds were able to outperform the market on the average over the studied time period. In addition to that by examining the strength of interrelationships of values of PCMs for successive time periods , the study also tried to infer about the extent to which the future values of fund performance were related to its past by using single index model. The study revealed that there were positive signals of information asymmetry in the market with mutual fund managers having superior information about the returns of stocks as a whole. PCM also indicated that on an average mutual funds provided excess (above-average) return, but only when unit of time period was longer (1 qtr or 4 qtr). Therefore, they concluded that for assessing the true performance of a particular mutual fund, a longer time horizon is better.
Another study examined the effect of incorporating lagged information variables into the evaluation of mutual fund managers performance in Indian context with the monthly data for 89 Indian mutual fund schemes using Treynor - Mazuy Model, Merton-Henriksson Model. The study revealed the use of conditioning lagged information variables causing the alphas to shift towards the right and reducing the number of negative timing coefficients, though it could not be concluded that alphas of conditional model were better compared to its unconditional counterpart as they were not found to be statistically significant. The noticeably different results of the unconditional timing models vis--vis conditional timing models testified superiority of the model
One more study talked about a 4-step model for selecting the right equity fund and illustrated the same in the context of equity mutual funds in Saudi Arabia. The 4 step model was as follows:
1. Compare returns across funds within the same category.
2. Compare fund returns with the returns of benchmark index.
3. Compare against the funds own performance.
4. Risk-related parameters : as indicated by the Standard Deviation (SD) and risk-adjusted returns as calculated by the Sharpe Ratio (SR).
The study revealed that most of the funds invested in Arab stocks had been in existence for less than a year and the volatility of the GCC stock markets contributed to the relatively poor performance of these funds and the turnaround of these funds could take place only with the rallying of GCC and other Arab markets. Out of the six categories of equity mutual funds in Saudi Arabia discussed above, Funds invested in Asian and European stocks were more consistent in their performance and yielded relatively higher returns than other categories, though funds invested in Saudi stocks yielded higher 3-year returns. Given the future outlook of Asian economies, particularly China and India and the newly emerging economies such as Brazil and Russia, funds invested in the stocks of these countries are likely to continue their current performance in near future.
One more paper studied the performance and portfolio characteristics of 828 newly launched U.S. equity mutual funds over the time period 1991-2005 using Carhart (1997) 4-factor asset-pricing model. Their study revealed new U.S. equity mutual funds outperformed their peers by 0.12% per month over the first three years. However, there were distinct patterns in this superior risk-adjusted performance estimated using Carharts (1997) 4-factor model. The number of fund that started to outperform older funds shrunk substantially after one to three years. These results suggested that the initially favorable performance was to some extent due to risk taking and not necessarily superior manager skill. Scrutinizing the returns further confirmed that the returns of fund started to exhibit higher standard deviations and higher unsystematic risk that could not be explained by the risk exposure to the four factors of the Car hart model.
Another paper, analyzed the Indian Mutual Fund Industry pricing mechanism with empirical studies on its valuation. It also analyzed data at both the fund-manager and fund-investor levels. It stated that mispricing of the Mutual funds could be evaluated by comparing the return on market and return on stock. During the pricing period, if the return on stock is negative, then it indicates overpricing and if are positive indicates under pricing. Relative performance measurement was used to measure the performance of the MF with SENSEX and it used Standard Deviation, Correlation analysis, Co-efficient of Determination and Null Hypothesis. This study revealed that standard deviations of the 3-month returns were significant with the increase in the period. The Standard Deviation increase indicated higher deviations from the actual means. The variance and coefficient of variation (COV) were also significant. Variance increases in the later periods indicated higher variability in the returns. As the time horizon increased COV decreased implying value are less consistent as compared to small duration of investments.
One more study, provided extensive evidence on portfolio characteristics of mutual funds and studied the relation between fund performance and the fund manager's investment strategy using both the traditional unconditional alpha model, as in Jensen (1968), and the conditional alpha, following Ferson and Schadt (1996). The study showed that a weak negative relation exists between performance and past stock returns in the portfolio. Investing in value stocks could help to improve overall performance. It also showed that mutual funds with a more diversified portfolio performed somewhat better than funds with a less diversified portfolio. However, diversification could be achieved by extending the funds' investment universe and investing in non-listed stocks. Elton, Gruber, Das and Hlavka (1993) showed that funds investing in these types of assets could achieve superior performance simply because these assets were not captured within the benchmark model. This paper, however, found no evidence to indicate that investment outside the fund's primary investment universe would enhance performance. Moreover, the effects of cash holdings on performance were explored, and some weak evidence suggested that large cash holdings implied better tactical decisions.
Another paperexamined the performance of equity and bond mutual funds that invested primarily in the emerging markets usingTreynors ratio, Sharpes ratio, Jensens measure. With this research they found that on an average the U.S. stock market outperformed emerging equity markets but the emerging market bonds outperformed U.S. bonds. They also found that overall emerging market stock funds under-performed the respective MSCI indexes. These were evident by their lower return, higher risk, and thus lower Sharpe ratios.
One more paper studied the performance of mutual funds around the world using a sample of 10,568 open-end actively managed equity funds from 19 countries using different models, mainly, domestic market model,international market model, Carhart (1997) domestic four-factor model, Carhart (1997) international four-factor model. With the help of this research they came to a conclusion that the funds size was positively related with fund performance. Larger funds performed better suggesting the presence of significant economies of scale in the mutual fund industry worldwide. This conclusion is consistent among domestic and foreign funds, and in several other robustness tests. Fund age is negatively related with fund performance indicating that younger funds tend to perform better. This finding seemed mainly driven by the samples of foreign and U.S. funds. When investing abroad, young mutual funds seemed to offer investors higher returns.
Data:
For the purpose of this study, out of 46 fund houses available in India, 21 Funds across 5 fund houses have been selected. On the basis of the highest AUM (assets under management); these 5 fund houses were selected. All the funds were selected by simple random sampling. First the sample size was 30, but because of the non availability of data for 9 funds, only 21 funds were considered for the study. All the funds selected for the study are open-ended equity funds under the growth option. The Net Asset Values (NAV) for all the 21 funds are from March 2004 to March 2009, which is the period of this study.
Since, all these are equity funds, the BSE Sensex (Bombay Stock Exchange Sensitive Index); which is the oldest, most widely and commonly used benchmark index in India; has been considered as the benchmark index. The funds selected for this study can be found in Annexure - appendix 1.
Research Methodology:
The funds which have been evaluated for this study have been randomly selected from the Indian fund houses like Reliance, Birla, UTI, HDFC, and ICICI. The data, which is the weekly NAVs (Net Asset Value), of the selected fund was collected from Reuters.
To compare the funds with a market index the BSE Sensex was selected for the only reason that it is Indias most widely and commonly used Benchmark index. The weekly NAVs and the Sensex closing were collected over a period of 5 years. The NAVs and the Sensex closing were then divided into 32 periods with 8 weekly NAVs (on an average) in each group.
After this the returns were calculated for both the funds and the BSE Sensex. Once the grouping of weekly NAVs of the funds and the BSE Sensex were done the average return, standard deviation, and absolute returns were calculated both for Fund NAVs and the Sensex closing. These calculations were done for each group for all the 21 funds.
Hierarchical Clustering:
For the purpose of this study we have used agglomerative hierarchical clustering, which is a method which builds a hierarchy of clusters using a bottom up approach, wherein it starts with a single cluster and then merges a pair of cluster as it moves up the hierarchy.
For the purpose of clustering, an appropriate metric should be used and for this study, Euclidean distance method is used. This is a metric which is an ordinary distance between and two given points on a scale and can be measured by a ruler, proven by the Pythagoras theorem.
This can be represented by the following formula:
These results are then graphically represented using a dendogram, which an arrangement of clusters obtained from hierarchical clustering.
Hypothesis Testing:
It is a method of making statistical decisions using experimental data. For this study, we have 21 funds with a 5 year weekly data, which is divided into 32 periods which effectively gives us 32 average returns and 32 absolute returns for the period. The main purpose of this exercise is to obtain significant sample size in order to conduct a non-parametric Mann-Whitney U-Test which was proposed by Mann and Whitney (1947). This kind of hypothesis testing is used on samples which are not normally distributed and since the sample used for the purpose of this study is not normally distributed, we have used the Mann-Whitney U-Test.
Mann-Whitney U-Test for Average Returns:
For the purpose of this study, hypothesis is used to test the changes in the average returns over the given 32 periods and compare these average returns with the BSE Sensex returns for the same period, to conclude whether the average returns of the fund and the benchmark index are the same.
The U-test can be represented in an equation as per the below:
Where,
n1 and n2 = sample size of the mutual fund and BSE Sensex index.
The following formula is used to compute the Z value:
Where,
U = U value,
mu = mean of the U values and
u = standard deviation of the U values.
On the basis of the above inputs, the U-test hypothesis is established as per below:
H0: x1 = x2
Ha: x1 x2
x1 = Mean returns for the BSE Sensex Index.
x2 = Mean returns for the Mutual Fund.
Mann-Whitney U-Test for Absolute Returns:
For the purpose of this study, hypothesis is used to test the changes in the absolute returns over the given 32 periods and compare these absolute returns with the BSE Sensex returns for the same period, to conclude whether the absolute returns of the fund and the benchmark index are the same.
U-test hypothesis is as per below:
H0: x1 = x2
Ha: x1 x2
Where,
x1 = Absolute returns for the Base Sensex Index.
x2 = Absolute returns for the Mutual Fund.
Data analysis and Interpretation:
Returns:
Returns are the yield that an asset generates over a period of time. It is the percentage increase or decrease in the value of the investment over a period of time.
In this study the fund returns and the Sensex returns have been calculated for each of the period.
There are 21 funds with a 5 year weekly data, which is divided into 32 periods which effectively gives us 32 betas and 32 average returns for the period. The main purpose of this exercise is to obtain significantly large sample size in order to conduct a non-parametric Mann-Whitney U-Test.
The fund returns for each of the period were calculated as follows:
Current NAV Previous NAV x 100
Previous NAV
The BSE Sensex returns were calculated as follows:
Current Closing Previous Closingx 100
Previous Closing
Average Returns:
Average return is the simple average of the returns generated by an asset. In this study daily average return of both the Sensex and the funds were calculated for each of the 32 periods.
Average returns of the BSE Sensex returns and the funds returns have been calculated with this formula:
Where,= average return,
n = number of weeks in the period,
x1 xn = return of the corresponding week
In the data collected for the study, the selected mutual funds have given average returns in varying degrees. During late 2004, funds posted average returns in the range of 0.50% - 2.75% while markets in the same period gave average returns of 0.69%. Similar average returns were seen in late 2005 and early 2006 when markets went up significantly. However, with the fall in markets in mid 2006, negative average returns were seen. Average returns posted by these funds were in the range of -1.7% to -3.75% while markets had returns of roughly -2%. Beginning of 2008 and onwards faced worse returns to the extent of -6% by funds and similar returns by markets. On the whole, mutual funds provided average returns in the same range as markets with the exception of certain time periods as represented in Table 1 and Table 2 in the Appendix 2.
The average returns of the funds are not significantly different over the period, this has been proved by conducting a Mann Whitney U-test on the average returns of the 21 funds and with 95% confidence we can conclude that the average returns of the funds were not significantly different from the average returns of the BSE Sensex index. This study shows that although the markets slumped in the later half of the 2nd period, the gains out of the bull run in the 1st half where the average returns for these funds were in the range of 0.5% to 2.75% of the 2nd period offsets the losses where the average returns of these funds were in the range of -1.7% to -3.75%, and hence the overall returns in the 1st period and the 2nd period are quite similar.
Absolute Returns:
After analyzing the average returns a clears no conclusion could be drawn hence absolute return were calculated to give a clearer indication of the returns generated. Absolute Returns refers to the returns that an asset achieves over a period of time. It measures the percentage appreciation or depreciation in the value of an asset over a certain time frame.
The absolute returns of the BSE Sensex returns and the fund returns were calculated as follows:
Return of the last week Return of the first weekx 100
Return of the first week
Absolute return measures the appreciation or fall in the funds performance as a percentage of the initial invested amount. These returns were compared to the benchmark index to in order to ascertain the extent to which the portfolio has outperformed / underperformed in relation to the index. Typically there should be a low correlation between the funds performance and the index (refer), as the fund is expected to outperform and deliver positive absolute return vis--vis index.
Form the analysis in appendix 3 Table 3 and 4, it can be noted that mutual funds have delivered varying returns over different time periods. During the last quarter of 2004, mutual funds delivered impressive returns. On an average the selected mutual funds had returns of approximately 10% whilst markets gave returns of around 6% during the same period. A similar phase was witnessed in mid 2005 where on an average funds gave returns of 13% and markets posted returns on the same lines. During 2006 and 2007 funds gave comparable returns to the previous years but this time around the index outperformed the funds significantly.
The absolute returns of the funds till the end of 2007 was in the range of 10% to 13% and the absolute returns of the BSE Sensex in the same period ranged from 6% to 17%, in the period between 2004 to end of 2005 the funds have managed to outperform the BSE Sensex, however, we observe that in the period between 2006 to end of 2007 the funds have significantly underperformed compared to the BSE Sensex. However, there was massive slump in the period of September 2008 to October 2008, during which the funds returns fell to -35% as compared to BSE Sensex returns of -40%. This study shows the correlation in the absolute returns of the funds and the BSE Sensex and shows us that in the long-run the absolute returns of the fund and index are quite similar as represented in Table 3 and Table 4 in the appendix.
Hence it can be seen, that on the whole, it can be concluded that in terms of absolute returns, funds have been performing in line with markets. However, the extent of the impact and movement has been lesser or more in relation to markets in certain periods.
Standard Deviation:
Standard Deviation is a tool which measures the variability of the data set. It is the square root of the square of the mean deviations from the arithmetic mean of a data series. It is calculated to measure the riskiness of a fund, stock or portfolio. Higher the standard deviation means higher the risk and higher the returns of the asset and a low standard deviation mans that the asset is less risky and will generate less returns.
The standard deviation of the fund returns and the BSE Sensex returns were calculated with the following formula:
Where, s = Standard Deviation,
N = number of weeks in the period,
= mean of the period,
xi = return of the corresponding week.
Standard deviation which measures variability and extent of dispersion from data, expresses the volatility of the fund. It mainly indicates the risk associated with the given fund.
Form the analysis in appendix 4 table 5 and table 6; it was observed that mutual funds have witnessed high standard deviation in booming markets. During mid 2004 and mid 2006 Standard deviation is in the range of 3% - 9%; which is fairly high compared to the market. The markets in the same period had an average volatility of approximately 2%. This shows that during these periods, funds were more volatile compared to the other time periods. This shows that the risk associated with these funds were much higher during these periods compared to the market.
This also meant that since the mutual funds were having much higher risks and volatility; they were susceptible to high returns also.During this period, standard deviation in the range of 1% - 14 % was seen. However, with the fall of markets in 2008 and recession beating down the markets, returns collapsed and the funds posted negative returns. Standard deviation marginally came down and is currently hovering in the range of 2% - 6.5%.
The standard deviation of the fund returns were significantly high during the 2007 to 2008 period when the BSE Sensex moved up sharply from 12000 levels in March 2007 to 21000 levels in December 2007, here the standard deviation moved up sharply from the 3% to 8% levels to 3% to 14% levels. This trend was observed in the period from January 2008 to June 2008 when the BSE Sensex plummeted from the 21000 levels to 13000 levels, this shows that sudden rise or fall in the markets result in the similar movement in the standard deviation of the fund returns.
Regression:
Regression is a statistical tool to analyze the fund returns with respect to the market returns to calculate the fund beta and the R squared value. Here the fund returns are the dependent variables and the market returns are the independent variables. The regression Equation is as follows.
Y = a + bx + c
Where, Y = dependent Variable
X = independent variable
a = y intercept of the line
b = slope of the regression line
c = residual value.
With the help of this the fund beta is calculated. Beta is the measure of volatility of a stock, fund, portfolio, etc with respect to the market. If the beta is positive then the fund returns are directly proportional to the market returns and if the beta is negative then the fund returns are inversely proportional to the market.
Beta of a fund is calculated with the following formula:
Where, a = fund beta
Cov (ra,rp) = covariance of the returns of the fund and the market,
Var rp = variance of the market returns.
The beta of the portfolio expresses how the expected return of the mutual fund is correlated with the returns of the markets in the given period.
The study takes into consideration each beta of the 32 periods of 21 funds, here the average betas of 20 funds is in the range of 0.6 to 0.9 and for one fund the average beta exceeds 1 as per appendix 5 in Table 7 and Table 8. This shows that there is a significant level of correlation in the returns of the funds as compared to BSE Sensex index and that most the funds have performed as much or near the market performance.
Overall it can be concluded that from the data collected for the study, most of the funds are sensitive to the market and have given returns as much as the market has or near the market returns.
Residual Value:
Using the regression equation and the regression analysis the c value or the residual value has been calculated for all the 32 periods for each of the 21 funds.
The residual value shows that how much portion of the return can be attributed to the fund or the portfolio and how much is the attributed to the market. Residual value shows what percentage of return is independent of the market and is that because of the fund properties.
The residual value for each of the 21 funds for all the 32 periods is coming up to 0. So it can be inferred that the funds are responding to the markets only.And the funds returns cannot to attributed to the fund properties or the fund components. This is true for all the funds during each of the 32 periods.
Relative Performance Index:
The Relative Performance Index for the sample size has been computed. This is calculated to show how each fund has performed in relation to the market. Here, we take the market index as the BSE Sensex Index.
On the basis of the RPI analysis, we graded the funds as:
Under-performers (X
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