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Unformatted text preview: Does Fund Size Affect the Performance of Equity Mutual Funds? An Empirical Study in the Indian Context * Rao, D.N. ** Rao, S.B. 1. 1. Background Historical returns, though they do not guarantee future returns and investment objectives often influence investment decisions of investors. Though there may be other factors such as investment style of fund managers, fund size and nature of ownership of Asset Management Companies etc which might affect the performance of funds the investors often ignore as these have been grey areas for them. It has been the dilemma of investors and fund managers whether size affects performance of mutual funds and this issue has been little researched and not much of empirical evidence is available in the literature and hence this study. The Mutual Fund Industry in India offers a large variety of schemes which can be seen from the Table given below. The principle of ‘Economies of Scale’ is not an exception to the field of finance and investment. If the fund size is sufficiently large, the Fund Manager would have liquidity, flexibility for timing his investment decisions and stock selection. Further, it gives added advantage of reducing transaction costs due to bulk transactions. The study focuses on empirically researching whether fund size affects performance of open end equity/growth mutual funds in the Indian context. The study is probably the first empirical research which tries to ascertain the degree or power of relationship between fund size and performance. ____________________________________________________________________________ * Rao, D.N., is currently associated with Centre for Management Education, All India Management Association, New Delhi, India as Professor of Finance and Director. ** Rao, S.B., is currently associated with Centre for Management Education, All India Management Association, New Delhi, India as Controller of Examinations. Electronic copy available at: http://ssrn.com/abstract=1420522 Table 1: Mutual Fund Schemes as at 31st March 2009 Fund Category Open End No. of Amount Schemes Close End No. of Amount Schemes Interval Fund No. of Amount Schemes Income 160 98,927 265 2027 Equity 243 1489 47 Balanced 30 189 5 Liquid/Money Market 56 508,762 GILT 34 1417 ELSS-Equity 35 600 10 Gold-ETF 5 6 Other-ETFs 11 75 Fund of Funds Investing Overseas 10 47 Total 584 611,512 327 2027 Source: Association of Mutual Funds in India (www.amfiindia.com) 66 2 1096 10 68 Total No. of Amount Schemes 1106 509 293 35 56 34 47 5 12 106,842 1549 189 508,762 1417 600 6 75 10 979 47 614,645 2. 2. Literature Review Wilson Wilson et al (2007) examined whether size affects mutual fund behavior and reported that funds suffer from diminishing returns to scale and funds should alter investment behavior as assets under management increase. Design 3. Research Design 1. Open end, Equity Mutual Fund schemes having at least three years track record are only considered for the study. 2. The time period chosen for the study is 3 years (1st April 2006 to 1st April 2009). 3. All the data is secondary and was obtained from AMFI website and respective home pages of Asset Management Companies. 4. The total number of Open end Equity/Growth Funds is 244 (Population) and the Sample size has been worked out at 95% Confidence Level and Confidence Interval of 20%. The Sample size is 22. Convenient sampling has been used for this purpose. 5. Net Asset Values (NAV) of the select Equity Funds were collected on the first trading day of each Quarter of the 3-year period for computing the return (CAGR), Risk and Return per unit of Risk, Risk Adjusted Return (Sharpe Ratio) of the funds. __________________________________________________________________________________________ Wilson, Mungo Ivor and Pollet, Joshua Matthew (2007), How Does Size Affect Mutual Fund Behavior? HKUST Business School Research Paper No. 07-06. Available at SSRN: http://ssrn.com/abstract=918250 Electronic copy available at: http://ssrn.com/abstract=1420522 4. The average Risk-free interest was computed using the coupon (interest) offered by Government of India’s long-term debt securities during the period 2006-09. The coupon rates are available on Reserve Bank of India website (www.rbi.org.in) and the average Risk free rate has been computed to be 8%. 7. The fund size details have been obtained Website of Asset Management Company. 8. Correlation coefficients between fund size and the four parameters of performance (Return, Risk, Return/Risk, Sharpe Ratio) have been computed to assess the degree of relationship between fund size and performance of select Equity/Growth funds. 9. Covariance of Fund size and the four parameters of performance (Return, Risk, Return/Risk, Sharpe Ratio) have been computed to assess how the fund size and each of these parameters move together. 10. Further, the concept of Momentum (Mass * Velocity), a popular concept in Physics and Mechanics, has been adapted in this study to introduce a new concept called ‘Fund Momentum’ which is computed by the product of Fund Size and CAGR. The Concept ‘Momentum’ in Physics is defined as "mass in motion." All objects have mass; so if an object is moving, then it has momentum - it has its mass in motion. The amount of momentum which an object has is dependent upon two variables: how much stuff is moving and how fast the stuff is moving. When the concept of momentum is related to mutual funds, mass is to be taken as fund size and the velocity, that is the speed or rate at which the mass is moving in a specific direction is to be taken as the rate of return which is nothing but the Compounded Annual Growth Rate (CAGR). The Fund Momentum signifies ‘wealth generated’ by the fund for its unit holders if the Fund Momentum is positive, while negative Fund Momentum indicates ‘erosion of wealth’ of the unit holders. 11. Two more new concepts have been introduced in the form of ‘Return per Fund Size Quotient’ and ‘Risk per Fund Size Quotient’ to ascertain the Return and Risk per unit of fund size. Electronic copy available at: http://ssrn.com/abstract=1420522 12. The sample of 22 Equity/Growth Funds have fund size varying from Rs.9.57 crores to Rs. 2472.36 crores and they have been classified as given below: Micro sized funds: Fund size less than Rs.100 crores Small sized funds: Fund size more than Rs.100 crores but less than Rs.500 crores Medium sized funds: Fund size more than Rs.500 crores but less than Rs.1500 crores Medium sized funds: Fund size more than Rs.500 crores but less than Rs.1500 crores Large sized funds: Fund size more than Rs.1500 crores but less than Rs.2500 crores 13. Following Hypotheses were tested at 5% significance level of the Correlation of the coefficients: (a) Equity/Growth Funds: Null Hypothesis: There is no relationship between Fund Size and Performance of Equity/Growth Funds (r=0) Alternate Hypothesis: There is relationship between Fund Size and Performance of Equity/Growth Funds (r ≠ 0) (b) Micro sized Funds Null Hypothesis: There is no relationship between Fund Size and Performance of Micro sized Equity/Growth Funds (r=0) Alternate Hypothesis: There is relationship between Fund Size and Performance of Micro sized Equity/Growth Funds (r ≠ 0) (c) Small sized Funds Null Hypothesis: There is no relationship between Fund Size and Performance of Small sized Equity/Growth Funds (r=0). Alternate Hypothesis: There is relationship between Fund Size and Performance of Small sized Equity/Growth Funds (r ≠ 0). (d) Medium sized Funds Null Hypothesis: There is no relationship between Fund Size and Performance of Medium sized Equity/Growth Funds (r=0). Alternate Hypothesis: There is relationship between Fund Size and Performance of Medium sized Equity/Growth Funds (r ≠ 0). (e) Large sized Funds Null Hypothesis: There is no relationship between Fund Size and Performance of Large sized Equity/Growth Funds (r=0) Alternate Hypothesis: There is relationship between Fund Size and Performance of Large sized Equity/Growth Funds (r ≠ 0) 4. Analysis The Compounded Annual Growth Rate (Return) and the Annualized Standard Deviation of the fund returns (Risk) was computed using the Net Asset Value (NAV) of the funds on the last trading day of each of the quarter of the three year period (31.03.06 to 31.03.09). Further Risk Adjusted Return (Sharpe Ratio), Return per Risk, Return per Unit Fund Size, Risk per Unit Fund Size and Fund Momentum were computed for each of the 22 sampled Equity/Growth Funds and they are presented in the Table given below: Table 2: Risk Metrics of the Equity/Growth Funds S.No Name of the Fund Fund Size (Rs. Crores) Return Risk (R) (S) (r) Return/Risk CAGR Return/Fund Risk/ Sharpe Fund Size (R/S) Fund Ratio (s) Momentum Quotient (R/r) Size (r/S) S * (R/r) Quotient 1 SBI Magnum Equity Fund 217.17 -10.55 0.3565 -29.60 -0.0486 0.0016 -52.0368 -6427.53 2 UTI Master Growth 217.4 -9.78 0.3476 -28.13 -0.0450 0.0016 -51.1414 -6114.62 63.87 -10.02 0.4137 -24.22 -0.1569 0.0065 -43.5581 -1547.10 1834.56 -15.82 0.3882 -40.74 -0.0086 0.0002 -61.3541 -74748.09 20.95 -3.28 0.2782 -11.79 -0.1566 0.0133 -40.5517 -247.09 36.45 -13.60 0.3746 -36.31 -0.3732 0.0103 -57.6648 -1323.49 227.19 -3.53 0.3271 -10.80 -0.0155 0.0014 -35.2557 -2452.79 Birla Sun Life Equity Fund 1128.28 -7.98 0.3862 -20.67 -0.0071 0.0003 -41.3858 -23325.31 HDFC Equity Fund 2472.36 -5.94 0.3189 -18.63 -0.0024 0.0001 -43.7137 -46061.35 250.66 -4.08 0.2902 -14.07 -0.0163 0.0012 -41.6413 -3527.76 93 -10.91 0.3992 -27.33 -0.1173 0.0043 -47.3711 -2541.88 1019.35 -1.15 0.3277 -3.50 -0.0011 0.0003 -27.9184 -3570.24 1378.48 -14.30 0.3323 -43.02 -0.0104 0.0002 -67.1013 -59308.20 137.14 -16.13 0.3788 -42.58 -0.1176 0.0028 -63.7043 -5840.06 2027.35 -3.79 0.3344 -11.34 -0.0019 0.0002 -35.2642 -22989.57 477.83 -1.41 0.3214 -4.40 -0.0030 0.0007 -29.2852 -2101.02 139.31 -1.05 0.3244 -3.22 -0.0075 0.0023 -27.8840 -449.06 23.29 -15.32 0.3859 -39.71 -0.6580 0.0166 -60.4334 -924.86 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 LIC Mutual Fund Equity Fund JM Equity Fund Quantum Long Term Equity Fund Tata Growth Fund Franklin Templeton India Growth Fund ICICI Prudential Growth Plan Sundaram BNP Paribas Growth Fund HSBC Equity Fund Morgan Stanley Growth Fund Principal PNB Growth Fund Fidelity Equity Fund Growth Baroda Pioneer Equity Fund DWS Alpha Equity Fund Taurus Bonanza Fund Growth Option 19 Kotak Opportunities 681.65 -5.47 0.4083 -13.41 -0.0080 0.0006 -33.0006 -9139.59 20 Reliance Equity Fund 1678.25 -3.22 0.2938 -10.96 -0.0019 0.0002 -38.1993 -18391.06 9.57 -11.27 0.3740 -30.14 -1.1779 0.0391 -51.5358 -288.44 39.85 -8.54 0.3584 -23.82 -0.2143 0.0090 -46.1429 -949.37 21 22 DBS Cholamandalam Growth Fund ING Core Equity Fund From the above Table it is observed that the total fund size/Assets managed by the sampled 22 Equity/Growth Funds is Rs.14,173.96 crores (approximately US Dollars 3 billions) and the total momentum of the sampled funds is Rs.292268.5 with a negative sign representing wealth erosion for the Unit holders over the three year period considered. The standard deviation of the Return per Fund size Quotient and Risk per Fund size Quotient are 0.2792 and 0.0089 respectively, which are not very large considering the standard deviation of the fund sizes of the 22 sampled funds (769.73) which clearly indicates that fund size does not much impact the performance of equity/growth funds. Correlation Correlation and Covariance of each of the Risk Metrics with Fund Size has been computed and is presented below: Table 3: Correlation and Covariance of the Risk Metrics with Size of Equity/Growth Funds Correlation (S, R) Correlation (S, r) Correlation (S, R/r) Correlation (S,s) 0.1403 Covariance (S, R) 519.2360 -0.2144 Covariance (S, r) -6.1465 0.1066 Covariance (S, R/r) 1018.2568 0.0740 Covariance (S, s) 638.4801 Observations Total Assets (Fund Size) Managed by 22 Sampled Funds: Rs.14, 173.96 crores Total Momentum: Rs (292,268.5) It is observed from the above Table that the Correlation Coefficients of Return, Risk, Return per Risk and Sharpe Ratio with Fund size are not significant for Equity/Growth Funds implying that the Fund size does not affect fund performance significantly. However, the Covariances (a measure of how much two variables change together) of fund size with return; fund size with return/risk and fund size with Sharpe Ratio are positive indicating that the fund size and these three performance variables moved in the same direction, while the contra has been observed in the case of Covariance of Fund size with Risk (due to negative covariance) implying that if the fund size increases the risk would go down. It is also interesting to note that the covariance of fund size with Return to Risk is highest among the positive covariances indicating that as the fund size increases Return per Risk would increase higher than that of other performance variables (Return and Sharpe Ratio). 4.1 Fund Size and Performance of Equity/Growth Funds: Hypothesis Testing The following Hypothesis testing was done: Null Hypothesis: There is no relationship between Fund Size and Performance of Equity/Growth Funds (r=0) Alternate Hypothesis: There is relationship between Fund Size and Performance of Equity/Growth Funds (r ≠ 0) At 5% significance level (Alpha=0.05), degrees of freedom 20 (n-2, where n= No. of Funds), and 2tailed test, the critical value of r = 0.423. All the four correlation coefficients do not fall in the rejection region and hence we do not reject Null Hypothesis. 4.2 4.2 Analysis of Micro sized Funds 7 of the 22 sampled Equity/Growth Funds have fund size less than Rs.100 crores and the total fund size (assets) managed by them is Rs.286.93 crores and they constitute 2.02 percent of the total fund size (assets) of the sampled Equity/Growth Funds. As outlined in the Methodology section these have been categorized as Micro sized Funds and the Risk Metrics for the same is given below: Table 4: Risk Metrics of the Micro sized Equity/Growth Funds Name Name of the Fund Fund Fund Size Size (S) (Rs. Crores) Return Return (R) (R) Risk Risk (r) (r) Return/Risk Return/Risk (R/r) (R/r) Return/Fund Return/Fund Size Size (R/S) Quotient Risk/Fund Risk/Fund Size Size (r/S) Quotient Sharpe Sharpe Ratio Ratio (s) Fund Fund Momentum Momentum S* S* (R/r) LIC LIC Mutual Fund Equity Fund 63.87 -10.02 0.4137 -24.2227 -0.1569 0.0065 -43.5581 -1547.10 Quantum Quantum Long Term Equity Fund Fund 20.95 -3.28 0.2782 -11.7944 -0.1566 0.0133 -40.5517 -247.09 36.45 -13.60 0.3746 -36.3096 -0.3732 0.0103 -57.6648 -1323.49 93 -10.91 0.3992 -27.3320 -0.1173 0.0043 -47.3711 -2541.88 23.29 -15.32 0.3859 -39.7105 -0.6580 0.0166 -60.4334 -924.86 9.57 -11.27 0.3740 -30.1404 -1.1779 0.0391 -51.5358 -288.44 39.85 -8.54 0.3584 -23.8237 -0.2143 0.0090 -46.1429 -949.37 Tata Growth Fund Tata Sundaram BNP Paribas Sundaram Growth Fund Growth Fund Taurus Taurus Bonanza Fund Growth Growth Option DBS DBS Cholamandalam Growth Growth Fund ING ING Core Equity Fund The standard deviation of the Return per Fund size Quotient and Risk per Fund size Quotient are 0.3883 and 0.0117 respectively, which are not very large considering the standard deviation of the fund sizes of the 7 micro sized funds (28.7302) which clearly indicates that fund size does not much impact the performance of equity/growth funds. Correlation and Covariances of fund size with Risk Metrics for Micro sized Funds is given below. It may be observed from the Table 5 that Correlation between Fund Size and Risk is significant and the other three correlation coefficients are found to be low and insignificant. Regarding the Covariances of Fund size with the Risk Metrics, it may be observed that the fund size, Risk, Return per Risk and the Risk Adjusted Return (Sharpe Ratio) move in the same direction while the fund size and Return move in opposite directions. Table 5: Correlation and Covariance of the Risk Metrics with Size of Micro Sized Funds Correlation (S, R) Correlation (S, r) Correlation (S, R/r) Correlation (S,s) -0.0504 Covariance (S, R) -4.8041 0.5202 Covariance (S, r) 0.5637 0.0657 Covariance (S, R/r) 14.8395 Observations Total Assets (Fund Size) Managed by 7 Sampled Micro size Funds: Rs. 286.93 crores Percentage of Equity/Growth Funds:2.0243 0.2838 Covariance (S, s) 51.1548 Total Momentum: Rs (7822.22) 4.2.1 4. 4.2.1 Fund Size and Performance of Micro sized Equity/Growth Funds: Hypothesis Testing The following Hypothesis testing was done: Null Hypothesis: There is no relationship between Fund Size and Performance of Micro sized Equity/Growth Funds (r=0) Alternate Hypothesis: There is relationship between Fund Size and Performance of Micro sized Equity/Growth Funds (r ≠ 0) At 5% significance level (Alpha=0.05), degrees of freedom 5 (n-2, where n= No. of Funds), and 2tailed test, the critical value of r = 0.754. All the four correlation coefficients do not fall in the rejection region and hence we do not reject Null Hypothesis. Weighted Averages of Return per Risk, Risk Adjusted Return (Sharpe Ratio) and Fund Momentum were computed and they are presented below: Table 6: Weighted Average Return per Risk, Risk Adjusted Return and Fund Momentum of Micro Funds Fund Fund Size (S) (S) Fund Fund Weightage Weightage (W) Return/Risk Return/Risk (R*) (R*) (W) (W) (R*) Sharpe Sharpe Ratio (s) (W) (W)* (s) Fund Fund Momentum Momentum Weighted Fund Weighted Fund Momentum Momentum 63.87 0.2225 -24.2227 -5.3909 -43.5581 -9.6942 -1547.10 -344.23 20.95 0.0730 -11.7944 -0.8610 -40.5517 -2.9603 -247.09 -18.0376 36.45 0.1270 -36.3096 -4.6117 -57.6648 -7.3241 -1323.49 -168.083 93 0.3240 -27.332 -8.8573 -47.3711 -15.3512 -2541.88 -823.569 23.29 0.0811 -39.7105 -3.2227 -60.4334 -4.9045 -924.86 -75.0061 9.57 0.0333 -30.1404 -1.0051 -51.5358 -1.7185 -288.44 -9.60505 39.85 0.1388 -23.8237 -3.3081 -46.1429 -6.4073 -949.37 -131.773 WAM (1570.3) Total: 286.98 WAR* (27.2570) WAs* (48.3605) 4.3 4. 4.3 Analysis of Small sized Funds 7 of the 22 sampled Equity/Growth Funds have fund size more than Rs.100 crores but less than Rs. 500 crores and the total fund size (assets) managed by them is Rs.1666.67 crores and they constitute 11.76 percent of the total fund size (assets) of the sampled Equity/Growth Funds. As outlined in the Methodology section these have been categorized as Small sized Funds and the Risk Metrics for the same are given below: Table 7: Risk Metrics of the Small sized Equity/Growth Funds Name Name of the Fund Fund Fund Size (S) (S) (Rs. Crores) Return Return (R) (R) Risk Risk (r) (r) Return/Risk Return/Risk (R/r) (R/r) Return/Fund Return/Fund Size (R/S) Size (R/S) Quotient Risk/Fund Risk/Fund Size Size (r/S) Quotient Sharpe Sharpe Ratio Ratio (s) (s) Fund Fund Momentum Momentum S* S* (R/r) SBI SBI Magnum Equity Fund 217.17 217.17 -10.55 0.3565 0.3565 -29.5968 -0.0486 0.0016 0.0016 -52.0368 -6427.53 UTI UTI Master Growth 217.4 217.4 -9.78 0.3476 0.3476 -28.1261 -0.0450 0.0016 0.0016 -51.1414 -6114.62 Franklin Franklin Templeton India Growth Growth Fund ICICI ICICI Prudential Growth Plan Plan Principal Principal PNB Growth Fund Fund Baroda Baroda Pioneer Equity Fund Fund DWS DWS Alpha Equity Fund 227.19 227.19 -3.53 0.3271 0.3271 -10.7962 -0.0155 0.0014 0.0014 -35.2557 -2452.79 250.66 250.66 -4.08 0.2902 0.2902 -14.0739 -0.0163 0.0012 0.0012 -41.6413 -3527.76 137.14 137.14 -16.13 0.37 0.3788 -42.5846 -0.1176 0.0028 0.0028 -63.7043 -5840.06 477.83 477.83 -1.41 0.3214 0.3214 -4.3970 -0.0030 0.0007 0.0007 -29.2852 -2101.02 139.31 139.31 -1.05 0.3244 0.3244 -3.2235 -0.0075 0.0023 0.0023 -27.8840 -449.06 The standard deviation of the Return per Fund size Quotient and Risk per Fund size Quotient are 0.0400 and 0.0007 respectively, which are not very large considering the standard deviation of the fund sizes of the 7 Small sized funds (114.43) which clearly indicates that fund size does not much impact the performance of equity/growth funds. Correlation and Covariances of fund size with Risk Metrics for Small sized Funds are given below. Regarding the Covariances of Fund size with the Risk Metrics, it may be observed that the fund size, Return, Return per Risk and the Risk Adjusted Return (Sharpe Ratio) move in the same direction while the fund size and Risk move in opposite directions. Table 8: Correlation and Covariance of the Risk Metrics with Size of Small Sized Funds Correlation (S, R) Correlation (S, r) Correlation (S, R/r) Correlation (S,s) 0.4667 Covariance (S, R) 257.6465 -0.3984 Covariance (S, r) -1.1174 0.46471 Covariance (S, R/r) 672.3409 Observations Total Assets (Fund Size) Managed by 7 Sampled Small size Funds: Rs. 1666.7 crores percentage of Equity/Growth Funds:11.76 0.4586 Covariance (S, s) 596.4411 Total Momentum: Rs (26,912.83) 4.3.1 4. 4.3.1 Fund Size and Performance of Small sized Equity/Growth Funds: Hypothesis Testing The following Hypothesis testing was done: Null Hypothesis: There is no relationship between Fund Size and Performance of Small sized Equity/Growth Funds (r=0) Alternate Hypothesis: There is relationship between Fund Size and Performance of Small sized Equity/Growth Funds (r ≠ 0) At 5% significance level (Alpha=0.05), degrees of freedom 5 (n-2, where n= No. of Funds), and 2tailed test, the critical value of r = 0.754. All the four correlation coefficients do not fall in the rejection region and hence we do not reject Null Hypothesis. Weighted Averages of Return per Risk, Risk Adjusted Return (Sharpe Ratio) and Fund Momentum were computed and they are presented below: Table 9: Weighted Average Return per Risk, Risk Adjusted Return and Fund Momentum of Small Funds Fund Size (S) Weightage (W) Return/Risk (R*) 217.17 0.1303 -29.5968 -3.8564 -52.0368 -6.7803 -6427.53 -837.507 217.4 0.1304 -28.1261 -3.6686 -51.1414 -6.6707 -6114.62 -797.346 227.19 0.1363 -10.7962 -1.4716 -35.2557 -4.8057 -2452.79 -334.315 250.66 0.1504 -14.0739 -2.1166 -41.6413 -6.2626 -3527.76 -530.575 137.14 0.0823 -42.5846 -3.5039 -63.7043 -5.2417 -5840.06 -480.637 477.83 0.2867 -4.397 -1.2605 -29.2852 -8.3958 -2101.02 -602.362 139.31 0.0836 -3.2235 -0.2694 -27.884 -2.3307 -449.06 -37.5414 Total: 1666.7 (W) (R*) Sharpe Ratio (s) (W) (s) WAR* -16.1473 Fund Momentum (M) WAs -40.4877 Weighted Average Fund Momentum WAM -3620.28 4.4 4. 4.4 Analysis of Medium sized Funds 4 of the 22 sampled Equity/Growth Funds have fund size more than Rs.500 crores but less than Rs. 1500 crores and the total fund size (assets) managed by them is Rs.4207.76 crores and they constitute 29.69 percent of the total fund size (assets) of the sampled Equity/Growth Funds. As outlined in the Methodology section these have been categorized as Medium sized Funds and the Risk Metrics for the same are given below: Table 8: Risk Metrics of the Medium sized Equity/Growth Funds Name Name of the Fund Fund Fund Size (S) (S) (Rs. Crores) Return Return (R) (R) Risk Risk (r) (r) Return/Risk Return/Risk (R/r) (R/r) Return/Fund Return/Fund Size Size (R/S) Quotient Risk/Fund Size Size (r/S) Qquotient Sharpe Sharpe Ratio Ratio (s) (s) Fund Fund Momentum Momentum S* S* (R/r) Birla Sun Life Equity Birla Fund Fund HSBC HSBC Equity Fund 1128.28 1128.28 -7.98 0.3862 0.3862 -20.6733 -0.0071 0.0003 0.0003 -41.3858 -23325.31 1019.35 1019.35 -1.15 0.3277 0.3277 -3.5025 -0.0011 0.0003 0.0003 -27.9184 -3570.237 Morgan Morgan Stanley Growth Fund Fund Kotak Kotak Opportunities 1378.48 1378.48 -14.30 0.3323 0.3323 -43.0243 -0.0104 0.0002 0.0002 -67.1013 -59308.2 681.65 681.65 -5.47 0.4083 0.4083 -13.4080 -0.0080 0.0006 0.0006 -33.0006 -9139.59 The standard deviation of the Return per Fund size Quotient and Risk per Fund size Quotient are 0.0040 and 0.0002 respectively, which are not very large considering the standard deviation of the fund sizes of the 4 Medium sized funds (289.04) which clearly indicates that fund size does not much impact the performance of equity/growth funds. Correlation and Covariances of fund size with Risk Metrics for Medium sized Funds are given below. Regarding the Covariances of Fund size with the Risk Metrics, it may be observed that the fund size, Return, Risk Return per Risk and the Risk Adjusted Return (Sharpe Ratio) move in opposite directions. The fund size and the four Risk Metrics correlation coefficients are negative and significant. Table 9: Correlation and Covariance of the Risk Metrics with Size of Medium Sized Funds Correlation (S, R) -0.6744 Covariance (S, R) -803.2833 Observations Correlation (S, r) -0.6897 Covariance (S, r) -5.9706 Correlation (S, R/r) -0.7244 Covariance (S, R/r) -2637.0917 Total Assets (Fund Size) Managed by 4 sampled Medium size Funds: Rs. 4207.76 crores. Correlation (S,s) -0.7910 Covariance (S, s) -2985.2494 Percentage of Equity/Growth Funds:29.69 Total Momentum: Rs (95343.3) 4.4.1 4. 4.4.1 Fund Size and Performance of Medium sized Equity/Growth Funds: Hypothesis Testing The following Hypothesis testing was done: Null Hypothesis: There is no relationship between Fund Size and Performance of Medium sized Equity/Growth Funds (r=0) Alternate Hypothesis: There is relationship between Fund Size and Performance of Medium sized Equity/Growth Funds (r ≠ 0) At 5% significance level (Alpha=0.05), degrees of freedom 2 (n-2, where n= No. of Funds), and 2tailed test, the critical value of r = 0.950. All the four correlation coefficients do not fall in the rejection region and hence we do not reject Null Hypothesis. Weighted Averages of Return per Risk, Risk Adjusted Return (Sharpe Ratio) and Fund Momentum were computed and they are presented below: Table 10: Weighted Averages of Return per Risk, Risk Adjusted Return and Momentum of Medium sized Funds Fund Size (S) Weightage (W) Return/Risk (R*) (W) (R*) Sharpe Ratio (s) (W) (s) Weighted Fund Average Momentum Fund Momentum 1128.28 0.2681 -20.6733 -5.54339 -41.3858 -11.0973 -23325.31 1019.35 0.2422 -3.505 -0.8485 -27.9184 -6.7633 -3570.237 1378.48 0.3276 -43.0243 -14.0949 -67.1013 -21.9827 -59308.2 681.65 0.1620 -13.408 -2.17207 -33.0006 -5.34604 -6253.52 -9139.59 -864.711 -19429.4 -1480.61 Total 4207.76 WAR* -22.6589 -63.7043 WAs -45.1894 WAM -28028.21 4.5 4. 4.5 Analysis of Large sized Funds 4 of the 22 sampled Equity/Growth Funds have fund size more than Rs.1500 crores but less than Rs. 2500 crores and the total fund size (assets) managed by them is Rs.8012.52 crores and they constitute 56.53 percent of the total fund size (assets) of the sampled Equity/Growth Funds. As outlined in the Methodology section these have been categorized as Large sized Funds and the Risk Metrics for the same are given below: Table 11: Risk Metrics of the Large sized Equity/Growth Funds Name Name of the Fund Fund Fund Fund Size (S) (S) Crores) (Rs. Crores) JM JM Equity Fund 1834.56 1834.56 HDFC HDFC Equity Fund Fund Fidelity Fidelity Equity Fund Fund -Growth Reliance Reliance Equity Fund Fund Return Return (R) (R) Risk Risk (r) (r) Return/ Return/ Risk Risk (R/r) Return/ Return/ Fund Size (R/S) Quotient Risk/Fund Risk/Fund Size Size (r/S) Quotient Sharpe Sharpe Ratio Ratio (s) Fund Fund Momentum Momentum S* S* (R/r) 2472.36 2472.36 -15.82 15.82 0.3882 0.3882 -40.7444 -0.0086 0.0002 -61.3541 -74748.09 -5.94 0.3189 -18.6305 -0.0024 0.0001 -43.7137 -46061.35 -3.79 0.3344 -11.3397 -0.0018 0.0002 0.0002 -35.2642 -22989.57 -3.22 3.22 0.2938 -10.9585 10.9585 -0.0019 0.0002 0.0002 -38.1993 -18391.06 2027.35 2027.35 1678.25 1678.25 The standard deviation of the Return per Fund size Quotient and Risk per Fund size Quotient are 0.0033 and 0.0000 respectively, which are not very large considering the standard deviation of the fund sizes of the 4 Large sized funds (343.86) which clearly indicates that fund size does not much impact the performance of equity/growth funds. Correlation and Covariances of fund size with Risk Metrics for Large sized Funds are given below. Regarding the Covariances of Fund size with the Risk Metrics, it may be observed that the fund size, Return, Risk Return per Risk and the Risk Adjusted Return (Sharpe Ratio) move in the same direction while the fund size and Risk move in the opposite direction. Table 12: Correlation and Covariance of the Risk Metrics with Large Sized Funds Correlation (S, R) Correlation (S, r) Correlation (S, R/r) Correlation (S,s) 0.1375 Covariance (S, R) 208.0055 -0.076 Covariance (S, r) -0.7821 0.0977 Covariance (S, R/r) 352.9578 0.1150 Covariance (S, s) 346.6927 Observations Total Assets (Fund Size) Managed by 4 sampled Large size Funds: Rs. 8012.52 crores percentage of Equity/Growth Funds:56.53 Total Momentum: Rs (162190) 4.5 4. 4.5.1 Fund Size and Performance of Large sized Equity/Growth Funds: Hypothesis Testing The following Hypothesis testing was done: Null Hypothesis: There is no relationship between Fund Size and Performance of Large sized Equity/Growth Funds (r=0) Alternate Hypothesis: There is relationship between Fund Size and Performance of Large sized Equity/Growth Funds (r ≠ 0) At 5% significance level (Alpha=0.05), degrees of freedom 2 (n-2, where n= No. of Funds), and 2tailed test, the critical value of r = 0.950. All the four correlation coefficients do not fall in the rejection region and hence we do not reject Null Hypothesis. Weighted Averages of Return per Risk, Risk Adjusted Return (Sharpe Ratio) and Fund Momentum were computed and they are presented below: Table 13: Weighted Averages of Return per Risk, Risk Adjusted Return and Momentum of Large sized Growth/Equity Funds Return/Risk (R*) Fund Momentum (M) Fund Size (S) Weightage (W) 1834.56 0.2289 -40.7444 -9.3289 -61.3541 -14.0477 -74748.09 2472.36 0.3085 -18.6305 -5.7486 -43.7137 -13.4884 -46061.35 2027.35 0.2530 -11.3397 -2.8692 -35.2642 -8.92265 -22989.57 1678.25 0.2094 -10.9585 -2.2953 -38.1993 -8.00098 -18391.06 Sharpe Ratio (s) (W) (R*) Total 8012.52 WAR* -20.2421 (W) (s) WAs -44.4597 Weighted Average Momentum (WAM) -17109.8 -14209.9 -5816.36 -3851.09 WAM -40987.2 Comparative performance of the funds in terms of WAR*, WAs and WAM is given below: Table 14: Comparison of the Performance of Funds Size wise Micro sized Equity/Growth Funds Small sized Equity/Growth Funds Medium sized Equity/Growth Funds Large sized Equity/Growth Funds Equity/Growth Funds WAR* -27.2570 -16.1473 -22.6589 -20.2421 -20.6190 WAs -48.3605 -40.4877 -45.1894 -44.4597 -44.2883 WAM -1570.30 -3620.28 -28028.21 -40987.20 -31953.60 The Indian Stock Market Returns (Bombay Stock Exchange) for the period of study is given below: Table 15: Return of Stock Market Indices for the three year period Return/ Sharpe 8.4221 Risk -0.0066 Ratio -0.9564 -0.6804 8.3462 -0.0815 -1.0400 BSE-200 -1.7368 8.7109 -0.1994 -1.1178 BSE-500 -2.6779 8.8710 -0.3019 -1.2037 Stock Market Index BSE-30 Return Risk -0.0552 BSE-100 Period Period 3-year period 5. 5. Conclusion All the performance parameters (Return, Risk, Return per Risk, Return per Fund size Quotient, Risk per Fund size Quotient and Sharpe Ratio) were negative as the Stock Market Return for the period of study (1st April 2006 to 1st April 2009) was negative which can be seen from Table 15. From the Hypothesis testing, it is clear that the correlation coefficients of fund size and performance variables are not significant and also the Null Hypotheses were not rejected. There is no conclusive evidence that the fund size affects performance of equity/growth funds, be it micro-, small-, medium- and large sized funds. The Covariances of fund size and performance variables show that barring risk the other three parameters (Return, Return/Risk and Sharpe Ratio) move together in the same direction and the values are random and no conclusions may be drawn regarding the fund size and performance of equity/growth funds, be it micro-, small-, medium- and large sized funds. Small sized funds have performed better than Micro-, Medium- and Large sized funds in terms of Return per Risk (WAR*) and Risk Adjusted Return (WAs). The Weighted Average Momentum of the Small sized Funds is the second best after that of Micro sized Funds whose fund size which is only 2.02 percent of the total fund size of Equity/Growth Funds. Considering that Micro sized funds constitute a small percentage of the total fund size of Equity Funds, we may consider that the performance of Small sized funds is the best in terms of WAM. This proves that the Small sized funds may not necessarily underperform than medium- and large sized funds. Further, the study points that the Indian Fund Managers of Medium- and Large sized Equity/Growth Funds were unable to outperform the stock market and also did not leverage the advantage of relatively large amount of funds at their disposal. ...
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