Description
This is a PPT on Portfolio Performance Measures. It is basically a risk return analysis of equity mutual funds using composite portfolio performance measures.
Risk-return analysis of equity mutual funds using composite portfolio performance measures
Mutual funds
Mutual Funds (Contd.)
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Number of fund houses – 35 Gaining visibility High scope for growth Advantages – Diversification, Transparency, Regulatory oversight, flexibility, convenience etc. Disadvantages – No guarantee, management risk, load charges etc.
Portfolio Management
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?
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Professional Management of various asset classes Two major objectives: Generate more than average returns Eliminate unsystematic risk completely Portfolio Management at Axis Bank Wealth managers handle portfolio of HNI clients Consists only of mutual funds
Objectives of the study
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To track the risk and returns of various schemes. To identify the relative performance of the selected schemes on risk adjusted theoretical parameters as suggested by Sharpe and Treynor. To track the market timing, diversification and net selectivity of the selected schemes on the basis of measures suggested by Jensen and Fama. To combine the individual rankings into a single comprehensive ranking and to be suggested to the branch.
Data collection
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?
? ? ? ?
Done at Sundaram BNP Paribas Period of study – 10 years Number of schemes selected – 30 Common Benchmark – Nifty 50 Risk Free Rate – 91 day T-Bill Rate Returns Rit = (EPit + Divit + Cap.Distit – BPit)/ BPit
Treynor Measure
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? ? ?
Risk premium per unit of risk T = (Rp - RFR)/?p Assumption – Elimination of unsystematic risk Applicable only for diversified funds Reward to volatility ratio
Sample Calc.
Fund Average Annual Rate of Return 15.329 25.015 33.796 Beta Treynor Rank
Birla Sun Life Advantage Fund (D)
1.117 1.269 1.206
9.618 16.104 24.219
3 2 1
Birla Sun Life Equity Fund (G)
Birla Sun Life Tax Relief '96 (D)
Fund Name
Block 1
Block 2
Treynor Rank Treynor Rank
Birla Sun Life Advantage Fund (D) Birla Sun Life Equity Fund (G) Birla Sun Life Tax Relief '96 (D) Canara Robeco Equity - Tax Saver (D) DBS Chola Opportunities Fund - (Regular)
…
9.618 16.104 24.219 -1.457 -8.941
…
21 18 12 26 30
…
18.789 26.050 15.328 26.921 19.456
…
23 7 25 6 22
…
Sharpe Measure
?
? ? ?
Risk premium return earned per unit of total risk S = (Rp - RFR)/?p Similar to Treynor Measure Reward to variability ratio Portfolios are compared to the Capital Market Line.
Sample Calc.
Fund
Birla Sun Life Advantage Fund (D) Birla Sun Life Equity Fund (G) Birla Sun Life Tax Relief '96 (D) Average Annual Rate of Return 15.329 25.015 33.796
Standard Deviation
10.658 11.114 11.130
Sharpe Rank
1.008 1.838 2.625
3 2 1
Fund Name
Block 1
Sharpe
Block 2
Rank Sharpe Rank
Birla Sun Life Advantage Fund (D) Birla Sun Life Equity Fund (G) Birla Sun Life Tax Relief '96 (D)
1.008
1.838 2.625 -0.169 -1.031 …
21
14 9 27 30 …
2.077
2.856 1.671 2.837 2.081 …
21
4 25 7 19 …
Canara Robeco Equity - Tax Saver (D) DBS Chola Opportunities Fund - (Regular)
…
Sharpe vs. Treynor
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?
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Disparities in ranking Higher the diversification – lesser the disparity Block 1 –Reliance Growth Fund 1 by Treynor and 10 by Sharpe Diversification – 0.125 Canara Robeco Equity – Tax Saver 26 by Treynor and 27 by Sharpe Diversification – 0.7
Jensen’s Alpha
?
Based on the CAPM model
E(Rp) = RFR + ?p (Rm - RFR) Superior fund managers – time the markets and/ or select undervalued securities Variant of the CAPM model Rp - RFR = ?p + ?p (Rm - RFR) Obtained through regression of (Rp – RFR) vs (Rm RFR)
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?
EViews Output
Fund Name
Block 1
Block 2
Jensen Rank Jensen Rank Birla Sun Life Advantage Fund (D) Birla Sun Life Equity Fund (G) Birla Sun Life Tax Relief '96 (D) 0.991 1.690 2.268 -0.026 -0.696 0.612 2.144 … 20 14 4 29 30 23 7 … -0.049 0.453 -0.275 0.525 0.087 0.744 0.211 … 23 7 27 5 21 3 15 …
Canara Robeco Equity - Tax Saver (D) DBS Chola Opportunities Fund (Regular) DSP BR Equity Fund (D) Franklin India Bluechip Fund (G)
…
Information Ratio
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? ?
?
Measures fund’s managers ability to use the information available to beat the benchmark Also known as appraisal ratio. IR = (Rp - Rb)/?ER Special case of Sharpe Ratio
IR (Contd.)
?
Can also be arrived at using: IR = ?p/?u
Fund Name
Block 1
Block 2
IR
Birla Sun Life Advantage Fund (D) Birla Sun Life Equity Fund (G) Birla Sun Life Tax Relief '96 (D) Canara Robeco Equity - Tax Saver (D) DBS Chola Opportunities Fund (Regular) … 0.140 0.264 0.322 -0.005 -0.142 …
Rank
22 7 2 29 30 …
IR
-0.018 0.153 -0.081 0.132 0.021 …
Rank
23 4 27 6 19 …
Fama’s Net Selectivity
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?
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Evaluates components of investment performance Overall performance = Excess Return = Rp – RFR Excess Return = Risk + Selectivity Risk Component = ?p (Rm - RFR) Selectivity = Diversification + Net Selectivity
Fama’s Net Selectivity (Contd.)
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?
?
?
Ratio of total risk = r = ?p/?m Using Ratio of Total Risk Rp = RFR + r (Rm - RFR) Using CAPM Model Rp = RFR + ?p (Rm - RFR) Difference yields the diversification component
Sample Calc.
Portfolio Average Standard Annual Rate Beta Deviation of Return
Reliance Growth Fund - (G) Nifty 50
36.757
0.935
9.429
24.563
1.000
8.668
Components
? ? ? ? ?
? ? ?
Overall performance = 32.172% Risk component = 18.676% [0.935*(24.563-4.5842)]. Selectivity component = 13.497%. Ratio of fund’s risk to the market risk = 1.088 [9.429/8.668]. New Risk Component = 21.73% Diversification Component = 3.058% Net Selectivity Component = 10.439%
Graphically
Fund Name
Overall Perfor mance Birla Sun Life Advantage Fund (D) Birla Sun Life Equity Fund (G) Birla Sun Life Tax Relief '96 (D) … 10.745 20.431
Block 1
Net Select Diversi- Selec Ra ivity fication tivity nk 9.663 0.348 0.262 9.315 21 18.93 14 9 27.71 8 …
Risk 1.082
1.229 19.201
29.211
…
1.169 28.043
… …
0.325
…
5
…
R^2 Vs Cost of Diversification
R^2 Vs Cost of diversification - Block 1
1.400 1.200
Cost of diversification
1.000 0.800 0.600 0.400 0.200 0.000 0.000
0.200
0.400
0.600
0.800
1.000
R^2
Contd.
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R^2 value for the Reliance Growth Fund - (G) (Rank = 1) is 0.738 Cost of diversification = 3.058%. R^2 value for Birla Sun Life Advantage Fund = (Rank = 20) 0.918 Cost of diversification is 0.905%. Reason : Poor Net Selectivity (-2.14 vs 10.439)
Rank Correlations
Block 1
Treynor Sharpe Jensen IR Treynor Sharpe Jensen IR Net Selectivity 0.917 0.918 0.804 0.929 0.912 0.952 0.964 0.883 0.965 0.923 Net Selectivity
Rank Correlations Block 2
Treynor Sharpe Jensen IR Treynor Sharpe Jensen IR Net Selectivity 0.976 0.986 0.973 0.980 0.952 0.984 0.995 0.963 0.958 0.98 3 Net Selectivity
Reliability Testing
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?
? ? ?
Cronbach’s Alpha – reliability coefficient Range = 0 to 1 Block 1, Value = 0.982 Block 2, Value = 0.995. Well above cut off values
Fund Name
Block 1 Rank based on returns 22 6 2 9 20 5 18 16 Final
Block 2
Rank based on returns 3 16 27 11 21 10 8 6 Final
DSP BR Equity Fund Franklin India Bluechip Fund - (G) Franklin India Prima Fund Franklin India Prima Plus HDFC Capital Builder HDFC Equity Fund HDFC Tax Saver Fund HDFC Top 200 Fund
Rank 22
5 4 10 18 2 20 17
Rank 3
15 27 9 18 13 10 7
…
…
…
…
…
Conclusion
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?
? ? ?
Very high correlation Distinct at individual level Final rank can be analyzed at the components level. Makes a significant difference to clients Helps wealth managers in better and informed decision making.
References
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?
?
?
Investment Analysis and Portfolio Management Sixth Edition by Frank K. Reilly & Keith C. Brown. NAV India – Internal Database of Sundaram BNP Paribas Fama Eugene. F (1972), “Components of Investment Performance”, Journal of Finance. www.amfiindia.com
doc_159303689.ppt
This is a PPT on Portfolio Performance Measures. It is basically a risk return analysis of equity mutual funds using composite portfolio performance measures.
Risk-return analysis of equity mutual funds using composite portfolio performance measures
Mutual funds
Mutual Funds (Contd.)
?
?
? ?
?
Number of fund houses – 35 Gaining visibility High scope for growth Advantages – Diversification, Transparency, Regulatory oversight, flexibility, convenience etc. Disadvantages – No guarantee, management risk, load charges etc.
Portfolio Management
?
?
? ? ?
Professional Management of various asset classes Two major objectives: Generate more than average returns Eliminate unsystematic risk completely Portfolio Management at Axis Bank Wealth managers handle portfolio of HNI clients Consists only of mutual funds
Objectives of the study
?
?
?
?
To track the risk and returns of various schemes. To identify the relative performance of the selected schemes on risk adjusted theoretical parameters as suggested by Sharpe and Treynor. To track the market timing, diversification and net selectivity of the selected schemes on the basis of measures suggested by Jensen and Fama. To combine the individual rankings into a single comprehensive ranking and to be suggested to the branch.
Data collection
?
?
? ? ? ?
Done at Sundaram BNP Paribas Period of study – 10 years Number of schemes selected – 30 Common Benchmark – Nifty 50 Risk Free Rate – 91 day T-Bill Rate Returns Rit = (EPit + Divit + Cap.Distit – BPit)/ BPit
Treynor Measure
?
? ? ?
Risk premium per unit of risk T = (Rp - RFR)/?p Assumption – Elimination of unsystematic risk Applicable only for diversified funds Reward to volatility ratio
Sample Calc.
Fund Average Annual Rate of Return 15.329 25.015 33.796 Beta Treynor Rank
Birla Sun Life Advantage Fund (D)
1.117 1.269 1.206
9.618 16.104 24.219
3 2 1
Birla Sun Life Equity Fund (G)
Birla Sun Life Tax Relief '96 (D)
Fund Name
Block 1
Block 2
Treynor Rank Treynor Rank
Birla Sun Life Advantage Fund (D) Birla Sun Life Equity Fund (G) Birla Sun Life Tax Relief '96 (D) Canara Robeco Equity - Tax Saver (D) DBS Chola Opportunities Fund - (Regular)
…
9.618 16.104 24.219 -1.457 -8.941
…
21 18 12 26 30
…
18.789 26.050 15.328 26.921 19.456
…
23 7 25 6 22
…
Sharpe Measure
?
? ? ?
Risk premium return earned per unit of total risk S = (Rp - RFR)/?p Similar to Treynor Measure Reward to variability ratio Portfolios are compared to the Capital Market Line.
Sample Calc.
Fund
Birla Sun Life Advantage Fund (D) Birla Sun Life Equity Fund (G) Birla Sun Life Tax Relief '96 (D) Average Annual Rate of Return 15.329 25.015 33.796
Standard Deviation
10.658 11.114 11.130
Sharpe Rank
1.008 1.838 2.625
3 2 1
Fund Name
Block 1
Sharpe
Block 2
Rank Sharpe Rank
Birla Sun Life Advantage Fund (D) Birla Sun Life Equity Fund (G) Birla Sun Life Tax Relief '96 (D)
1.008
1.838 2.625 -0.169 -1.031 …
21
14 9 27 30 …
2.077
2.856 1.671 2.837 2.081 …
21
4 25 7 19 …
Canara Robeco Equity - Tax Saver (D) DBS Chola Opportunities Fund - (Regular)
…
Sharpe vs. Treynor
?
?
?
Disparities in ranking Higher the diversification – lesser the disparity Block 1 –Reliance Growth Fund 1 by Treynor and 10 by Sharpe Diversification – 0.125 Canara Robeco Equity – Tax Saver 26 by Treynor and 27 by Sharpe Diversification – 0.7
Jensen’s Alpha
?
Based on the CAPM model
E(Rp) = RFR + ?p (Rm - RFR) Superior fund managers – time the markets and/ or select undervalued securities Variant of the CAPM model Rp - RFR = ?p + ?p (Rm - RFR) Obtained through regression of (Rp – RFR) vs (Rm RFR)
?
?
?
EViews Output
Fund Name
Block 1
Block 2
Jensen Rank Jensen Rank Birla Sun Life Advantage Fund (D) Birla Sun Life Equity Fund (G) Birla Sun Life Tax Relief '96 (D) 0.991 1.690 2.268 -0.026 -0.696 0.612 2.144 … 20 14 4 29 30 23 7 … -0.049 0.453 -0.275 0.525 0.087 0.744 0.211 … 23 7 27 5 21 3 15 …
Canara Robeco Equity - Tax Saver (D) DBS Chola Opportunities Fund (Regular) DSP BR Equity Fund (D) Franklin India Bluechip Fund (G)
…
Information Ratio
?
? ?
?
Measures fund’s managers ability to use the information available to beat the benchmark Also known as appraisal ratio. IR = (Rp - Rb)/?ER Special case of Sharpe Ratio
IR (Contd.)
?
Can also be arrived at using: IR = ?p/?u
Fund Name
Block 1
Block 2
IR
Birla Sun Life Advantage Fund (D) Birla Sun Life Equity Fund (G) Birla Sun Life Tax Relief '96 (D) Canara Robeco Equity - Tax Saver (D) DBS Chola Opportunities Fund (Regular) … 0.140 0.264 0.322 -0.005 -0.142 …
Rank
22 7 2 29 30 …
IR
-0.018 0.153 -0.081 0.132 0.021 …
Rank
23 4 27 6 19 …
Fama’s Net Selectivity
?
?
?
?
Evaluates components of investment performance Overall performance = Excess Return = Rp – RFR Excess Return = Risk + Selectivity Risk Component = ?p (Rm - RFR) Selectivity = Diversification + Net Selectivity
Fama’s Net Selectivity (Contd.)
?
?
?
?
Ratio of total risk = r = ?p/?m Using Ratio of Total Risk Rp = RFR + r (Rm - RFR) Using CAPM Model Rp = RFR + ?p (Rm - RFR) Difference yields the diversification component
Sample Calc.
Portfolio Average Standard Annual Rate Beta Deviation of Return
Reliance Growth Fund - (G) Nifty 50
36.757
0.935
9.429
24.563
1.000
8.668
Components
? ? ? ? ?
? ? ?
Overall performance = 32.172% Risk component = 18.676% [0.935*(24.563-4.5842)]. Selectivity component = 13.497%. Ratio of fund’s risk to the market risk = 1.088 [9.429/8.668]. New Risk Component = 21.73% Diversification Component = 3.058% Net Selectivity Component = 10.439%
Graphically
Fund Name
Overall Perfor mance Birla Sun Life Advantage Fund (D) Birla Sun Life Equity Fund (G) Birla Sun Life Tax Relief '96 (D) … 10.745 20.431
Block 1
Net Select Diversi- Selec Ra ivity fication tivity nk 9.663 0.348 0.262 9.315 21 18.93 14 9 27.71 8 …
Risk 1.082
1.229 19.201
29.211
…
1.169 28.043
… …
0.325
…
5
…
R^2 Vs Cost of Diversification
R^2 Vs Cost of diversification - Block 1
1.400 1.200
Cost of diversification
1.000 0.800 0.600 0.400 0.200 0.000 0.000
0.200
0.400
0.600
0.800
1.000
R^2
Contd.
?
?
?
R^2 value for the Reliance Growth Fund - (G) (Rank = 1) is 0.738 Cost of diversification = 3.058%. R^2 value for Birla Sun Life Advantage Fund = (Rank = 20) 0.918 Cost of diversification is 0.905%. Reason : Poor Net Selectivity (-2.14 vs 10.439)
Rank Correlations
Block 1
Treynor Sharpe Jensen IR Treynor Sharpe Jensen IR Net Selectivity 0.917 0.918 0.804 0.929 0.912 0.952 0.964 0.883 0.965 0.923 Net Selectivity
Rank Correlations Block 2
Treynor Sharpe Jensen IR Treynor Sharpe Jensen IR Net Selectivity 0.976 0.986 0.973 0.980 0.952 0.984 0.995 0.963 0.958 0.98 3 Net Selectivity
Reliability Testing
?
?
? ? ?
Cronbach’s Alpha – reliability coefficient Range = 0 to 1 Block 1, Value = 0.982 Block 2, Value = 0.995. Well above cut off values
Fund Name
Block 1 Rank based on returns 22 6 2 9 20 5 18 16 Final
Block 2
Rank based on returns 3 16 27 11 21 10 8 6 Final
DSP BR Equity Fund Franklin India Bluechip Fund - (G) Franklin India Prima Fund Franklin India Prima Plus HDFC Capital Builder HDFC Equity Fund HDFC Tax Saver Fund HDFC Top 200 Fund
Rank 22
5 4 10 18 2 20 17
Rank 3
15 27 9 18 13 10 7
…
…
…
…
…
Conclusion
?
?
? ? ?
Very high correlation Distinct at individual level Final rank can be analyzed at the components level. Makes a significant difference to clients Helps wealth managers in better and informed decision making.
References
?
?
?
?
Investment Analysis and Portfolio Management Sixth Edition by Frank K. Reilly & Keith C. Brown. NAV India – Internal Database of Sundaram BNP Paribas Fama Eugene. F (1972), “Components of Investment Performance”, Journal of Finance. www.amfiindia.com
doc_159303689.ppt