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