Unit 5 portfolio Management

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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%


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%


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%


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%


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


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


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


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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Unit 5 portfolio Management

Economy & Finance

Transcript of Unit 5 portfolio Management