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Portfolio Evaluation Prof. Saptarshi Mukherjee
B.Com ( Hons.), MBA(Finance), IA, CFA.ISBR Business School, Bangalore
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Performance evaluation: “the science of attribution”
Example: Why did this taxi take so long?The traffic; the driver; my lousy
instructions?How much should I tip this
taxi driver?Would I use this taxi
company again?
Why Measure Performance?
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Portfolio Performance Evaluation How well did the portfolio do? How do we adjust for risk, to compare
different managers? Why?
◦ Risk◦ Timing◦ Asset allocation◦ Security selection
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Performance Evaluation Issues
Theoretically correct measures are difficult to construct
Different statistics or measures are appropriate for different types of investment decisions or portfolios
Many industry and academic measures are different
The nature of active management leads to measurement problems
Copyright ©1998 Ian H. Giddy Portfolio Management 5
Performance Attribution:1. Excess Return
Excess Return: Managed Portfolio vs Benchmark
ComponentBenchmark Weight
Return of Index during Period Performance
Equity 60% 5.81% 3.49%Bonds 30% 1.45% 0.44%Cash 10% 0.48% 0.05%
Bogey (Benchmark Portfolio) Return 3.97%Return of Managed Portfolio 5.34%Excess return of managed portfolio 1.37%
Copyright ©1998 Ian H. Giddy Portfolio Management 6
Performance Attribution:2. Asset Allocation
Contribution of Asset Allocation to Performance
(1) (2) (3) (4) (3)x(4)
Component
Managed Portfolio Weights
Benchmark Portfolio Weights
Excess Weight
Component Return minus Total Benchmark Return
Contribution to Performance
Equity 70% 60% 10% 1.84% 0.184%Bonds 7% 30% -23% -2.52% 0.579%Cash 23% 10% 13% -3.49% -0.454%
Contribution of Asset Allocation 0.310%
Copyright ©1998 Ian H. Giddy Portfolio Management 7
Performance Attribution:3. Security Selection
Contribution of Security Selection to Performance
(1) (2) (3) (4) (3)x(4)
Component
Managed Portfolio Performance
Component Index Performance
Excess Performance
Managed Portfolio Weight
Contribution to Performance
Equity 7.28% 5.81% 1.47% 70.00% 1.029%Bonds 1.89% 1.45% 0.44% 7.00% 0.031%Cash 0.48% 0.48% 0.00% 23.00% 0.000%
Contribution of Security Selection 1.060%
Copyright ©1998 Ian H. Giddy Portfolio Management 8
Performance Attribution:4. Summary
Portfolio Attribution Summary
Contribution1 Asset Allocation 0.310%2 Selection
1 Equity excess return 1.029%2 Bonds excess return 0.031%3 Cash excess return 0.000% 1.060%
Total excess return on portfolio 1.370%
Copyright ©1998 Ian H. Giddy Portfolio Management 9
Performance Evaluation Measures
Sharpe’s measure
Treynor’s measure
Jensen’s measure
Appraisal ratio
( ) /r rP f P
( ) /r rP f P
P r r r rP f P M f [ ( )]
( / ( ) P Pe
Copyright ©1998 Ian H. Giddy Portfolio Management 10
Illustration of TB Model Stock a alpha b beta Residual Risk s(e)
1 7% 1.6 45%2 -5 1.0 323 3 0.5 26
rm-rf =0.08; smarket =0.2 Let us construct the optimal active portfolio
implied by the TB model as:Stock a/s2(e) Weight (wk)1 0.07/0.452 = 0.3457 (1)/T = 1.14772 -0.05/0.322 = -0.4883 (2)/T = -1.62123 0.03/0.262 = 0.4438 (3)/T = 1.4735Total (T) 0.3012
Copyright ©1998 Ian H. Giddy Portfolio Management 11
Composition of active portfolio:
aA = w1a1+w2a2+w3a3
=1.1477(7%)-1.6212(-5%)+1.4735(3%) =20.56%bA = w1b1+w2b2+w3b3
= 1.1477(1.6)-1.6212(1)+1.4735(0.5) = 0.9519s(eA) = [w2
1s21+w2
2s22+w2
3s23]0.5
= [1.14772(0.452)+1.62122(0.322) +1.47352(0.262)]0.5
= 0.8262
Composition of the optimal portfolio:W0 = (alpha A/ sd2) / ( Rm- Rf/sd m2)w0 = (0.2056/0.82622) / (0.08/0.22)
= 0.1506w = w0 /[1+(1-bA) w0 ] = 0.1495
Copyright ©1998 Ian H. Giddy Portfolio Management 12
Composition of the optimal portfolio:
Stock Final Positionw (wk)
1 0.1495(1.1477)=0.17162 0.1495(-1.6212)=-0.24243 0.1495(1.4735)=0.2202Active portfolio 0.1495Passive portfolio 0.8505
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