Unit 5 portfolio Management
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Prof. Saptarshi Mukherjee teaches at ISBR Business School in Bangalore. The document discusses performance measurement and attribution for investment portfolios. It provides three examples to illustrate performance attribution: (1) excess return attribution between a managed portfolio and benchmark, (2) asset allocation contribution, and (3) security selection contribution. A summary shows the total excess return was attributed to asset allocation and security selection. Various performance evaluation measures are also outlined such as Sharpe's measure and Treynor's measure. The document concludes by demonstrating the construction of an optimal active portfolio implied by the Treynor-Black model.
![Performance Evaluation Measures
Sharpe’s measure
(rP rf ) / P
Treynor’s measure
(rP rf ) / P
Jensen’s measure
P rP [rf
Appraisal ratio
( P / ( eP )
Copyright ©1998 Ian H. Giddy
P ( rM
rf )]
Portfolio Management 9](https://image.slidesharecdn.com/unit5portflolioevaluationparta-131212053950-phpapp02/85/Unit-5-portfolio-Management-9-320.jpg)
![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)
= 0.9519
s(eA) = [w21s21+w22s22+w23s23]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)
= 0.1506
w = w0 /[1+(1-bA) w0 ]
= 0.1495
Copyright ©1998 Ian H. Giddy
Portfolio Management 11](https://image.slidesharecdn.com/unit5portflolioevaluationparta-131212053950-phpapp02/85/Unit-5-portfolio-Management-11-320.jpg)
Unit 5 portfolio Management
- 1. Prof. Saptarshi Mukherjee B.Com ( Hons.), MBA(Finance), IA, CFA. ISBR Business School, Bangalore 1
- 2. Why Measure Performance? 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? 2
- 3. How well did the portfolio do? How do we adjust for risk, to compare different managers? Why? ◦ ◦ ◦ ◦ Risk Timing Asset allocation Security selection 3
- 4. 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 4
- 5. Performance Attribution: 1. Excess Return Excess Return: Managed Portfolio vs Benchmark Component Equity Bonds Cash Benchmark Return of Index Performance Weight during Period 60% 5.81% 3.49% 30% 1.45% 0.44% 10% 0.48% 0.05% Bogey (Benchmark Portfolio) Return Return of Managed Portfolio Excess return of managed portfolio Copyright ©1998 Ian H. Giddy 3.97% 5.34% 1.37% Portfolio Management 5
- 6. Performance Attribution: 2. Asset Allocation Contribution of Asset Allocation to Performance (1) (4) (3)x(4) Component Managed Benchmark Return minus Portfolio Portfolio Excess Total Benchmark Contribution to Component Weights Weights Weight Return 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 Copyright ©1998 Ian H. Giddy (2) (3) 0.310% Portfolio Management 6
- 7. Performance Attribution: 3. Security Selection Contribution of Security Selection to Performance (1) (2) (3) (4) (3)x(4) Managed Component Excess Managed Portfolio Contribution to Portfolio Index Component Performance Performance Performance Weight 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 Copyright ©1998 Ian H. Giddy 1.060% Portfolio Management 7
- 8. Performance Attribution: 4. Summary Portfolio Attribution Summary 1 Asset Allocation 2 Selection 1 Equity excess return 2 Bonds excess return 3 Cash excess return Total excess return on portfolio Copyright ©1998 Ian H. Giddy Contribution 0.310% 1.029% 0.031% 0.000% 1.060% 1.370% Portfolio Management 8
- 9. Performance Evaluation Measures Sharpe’s measure (rP rf ) / P Treynor’s measure (rP rf ) / P Jensen’s measure P rP [rf Appraisal ratio ( P / ( eP ) Copyright ©1998 Ian H. Giddy P ( rM rf )] Portfolio Management 9
- 10. Illustration of TB Model Stock a alpha b beta Residual Risk s(e) 1 7% 1.6 45% 2 -5 1.0 32 3 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 2 -0.05/0.322 = -0.4883 3 0.03/0.262= 0.4438 Total (T) 0.3012 Copyright ©1998 Ian H. Giddy (1)/T = 1.1477 (2)/T = -1.6212 (3)/T = 1.4735 Portfolio Management 10
- 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) = 0.9519 s(eA) = [w21s21+w22s22+w23s23]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) = 0.1506 w = w0 /[1+(1-bA) w0 ] = 0.1495 Copyright ©1998 Ian H. Giddy Portfolio Management 11
- 12. Composition of the optimal portfolio: Stock Final Position w (wk) 1 0.1495(1.1477)=0.1716 2 0.1495(-1.6212)=-0.2424 3 0.1495(1.4735)=0.2202 Active portfolio 0.1495 Passive portfolio 0.8505 1.0 Copyright ©1998 Ian H. Giddy Portfolio Management 12