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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
ELSSEquity
35
600
10
GoldETF
5
6
OtherETFs
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 3year 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. 0706.
Available at SSRN: http://ssrn.com/abstract=918250 Electronic copy available at: http://ssrn.com/abstract=1420522 4. The average Riskfree interest was computed using the coupon (interest) offered by Government
of India’s longterm debt securities during the period 200609. 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 (n2, 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 (n2, 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 (n2, 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 (n2, 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 (n2, 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 BSE200 1.7368 8.7109 0.1994 1.1178 BSE500 2.6779 8.8710 0.3019 1.2037 Stock
Market
Index
BSE30 Return Risk 0.0552 BSE100 Period
Period 3year
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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 Winter '11
 BARNARD
 Physics, pH

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